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LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered when solving an optimization problem. Standard floating-point algorithms are highly efficient but remain susceptible to the accumulation of round-off errors, which can lead solvers to return feasibility and optimality claims that are actually invalid. This paper introduces a novel direct solution approach for solving sequences of closely related SLEs encountered in nonlinear programming efficiently and without round-off errors. Specifically, it introduces rank-one update algorithms for the round-off error–free factorization framework, a tool set built on integer-preserving arithmetic that has led to the development and implementation of extremely reliable subroutines for solving SLEs occurring in linear programming. The formal guarantees of the presented algorithms are established through the derivation of theoretical insights. Their advantages are supported with computational experiments, which demonstrate upward of 75× improvements over exact factorization runtimes on fully dense matrices with more than one million entries. A significant advantage of the featured integer-preserving framework is that the length of any matrix coefficient produced by its algorithms is bounded polynomially in the size of the inputs without having to resort to greatest common divisor operations, which are required by and thereby hinder an efficient implementation of exact rational arithmetic approaches. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0331) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0331). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

When designing a patrol route, it is often necessary to pay more attention to locations with high crime rates. In this paper, we study a patrol routing problem for a fleet of patrol cars patrolling a region with a high-crime neighborhood (HCN) consisting of multiple hot spots. Considering the disorder and chaos in the HCN, at least one patrol car is required in the HCN at any given time during the patrol. We call this routing problem the hot spot coverage patrol problem (HSCPP). In the HSCPP, the importance of a patrol location is quantified by a prize, and the prize is collected if a patrol car visits the location. Our objective is to maximize the sum of prizes collected by the patrol cars, obeying all operational requirements. We propose mathematical formulations and develop several solution approaches for the HSCPP. The global approach consists of finding the routing solution for all patrol cars with a single integer programming (IP) formulation. The partition approach involves first partitioning the region geographically and solving the routing problem in each subregion with two IP formulations. Next, we strengthen the partition approach by developing a column generation (CG) approach in which the initial columns of the CG approach are the solutions generated from the partition approach. We conduct a detailed computational case study using instances based on real crime data from Montgomery County, Maryland. To further understand the computational tractability of our solution approaches, we also perform a sensitivity analysis using synthetic instances under various scenarios. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search & Approximation Algorithms. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0192) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0192). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

In the context of community detection, correlation clustering (CC) provides a measure of balance for social networks as well as a tool to explore their structures. However, CC does not encompass features such as the mediation between the clusters, which could be all the more relevant with the recent rise of ideological polarization. In this work, we study correlation clustering under mediation (CCM), a new variant of CC in which a set of mediators is determined. This new signed graph clustering problem is proved to be NP-hard and formulated as an integer programming formulation. An extensive investigation of the mediation set structure leads to the development of two efficient exact enumeration algorithms for CCM. The first one exhaustively enumerates the maximal sets of mediators in order to provide several relevant solutions. The second algorithm implements a pruning mechanism, which drastically reduces the size of the exploration tree in order to return a single optimal solution. Computational experiments are presented on two sets of instances: signed networks representing voting activity in the European Parliament and random signed graphs. History: Accepted by Van Hentenryck, Area Editor for Pascal. Funding: This work was supported by Fondation Mathématique Jacques Hadamard [Grant P-2019-0031]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0129) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0129). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

Although most methods for solving mixed-integer optimization problems compute a single optimal solution, a diverse set of near-optimal solutions can often lead to improved outcomes. We present a new method for finding a set of diverse solutions by emphasizing diversity within the search for near-optimal solutions. Specifically, within a branch-and-bound framework, we investigated parameterized node selection rules that explicitly consider diversity. Our results indicate that our approach significantly increases the diversity of the final solution set. When compared with two existing methods, our method runs with similar runtime as regular node selection methods and gives a diversity improvement between 12% and 190%. In contrast, popular node selection rules, such as best-first search, in some instances performed worse than state-of-the-art methods by more than 35% and gave an improvement of no more than 130%. Furthermore, we find that our method is most effective when diversity in node selection is continuously emphasized after reaching a minimal depth in the tree and when the solution set has grown sufficiently large. Our method can be easily incorporated into integer programming solvers and has the potential to significantly increase the diversity of solution sets. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the Army Research Office [Grant W911NF-21-1-0079]. The views expressed in this study do not represent those of the U.S. Government, the U.S. Department of Defense, or the U.S. Army. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0164) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0164). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

Recently, parallel computing environments have become significantly popular. In order to obtain the benefit of using parallel computing environments, we have to deploy our programs for these effectively. This paper focuses on a parallelization of SCIP (Solving Constraint Integer Programs), which is a mixed-integer linear programming solver and constraint integer programming framework available in source code. There is a parallel extension of SCIP named ParaSCIP, which parallelizes SCIP on massively parallel distributed memory computing environments. This paper describes FiberSCIP, which is yet another parallel extension of SCIP to utilize multi-threaded parallel computation on shared memory computing environments, and has the following contributions: First, we present the basic concept of having two parallel extensions, and the relationship between them and the parallelization framework provided by UG (Ubiquity Generator), including an implementation of deterministic parallelization. Second, we discuss the difficulties in achieving a good performance that utilizes all resources on an actual computing environment, and the difficulties of performance evaluation of the parallel solvers. Third, we present a way to evaluate the performance of new algorithms and parameter settings of the parallel extensions. Finally, we demonstrate the current performance of FiberSCIP for solving mixed-integer linear programs (MIPs) and mixed-integer nonlinear programs (MINLPs) in parallel. The online appendix is available at . [ABSTRACT FROM AUTHOR]

The integral column generation algorithm (ICG) was recently introduced to solve set partitioning problems involving a very large number of variables. This primal algorithm generates a sequence of integer solutions with decreasing costs, leading to an optimal or near-optimal solution. ICG combines the well-known column generation algorithm and a primal algorithm called the integral simplex using decomposition algorithm (ISUD). In this paper, we develop a generalized version of ICG, denoted I2CG, that can solve efficiently large-scale set partitioning problems with side constraints. This new algorithm can handle the side constraints in the reduced problem of ISUD, in its complementary problem, or in both components. Computational experiments on instances of the airline crew pairing problem (CPP) and the multidepot vehicle routing problem with time windows show that the latter strategy is the most efficient one and I2CG significantly outperforms basic variants of two popular column generation heuristics, namely, a restricted master heuristic and a diving heuristic. For the largest tested CPP instance with 1,761 constraints, I2CG can produce in less than one hour of computational time more than 500 integer solutions leading to an optimal or near-optimal solution. Summary of Contribution: In this paper, we develop a new integral column generation algorithm that can solve efficiently large-scale set partitioning problems with side constraints. The latter alter the quasi-integrality property needed for primal integral algorithms. The paper adds a methodological contribution remedying this issue. This remedy should, in our opinion, boost the use of primal exact methods, especially in the column generation context. The paper also has a computational contribution. Effectively, computational experiments on instances of the airline crew pairing problem and the multidepot vehicle routing problem with time windows are extensively discussed. We compare the proposed algorithm to basic variants of two popular column generation heuristics. [ABSTRACT FROM AUTHOR]

We introduce a prescriptive machine learning approach to speed up the process of solving mixed-integer convex optimization (MICO) problems. We solve multiple optimization instances and train a machine learning model in advance, which we use to solve new instances. Previous works have shown that the predictions of classification algorithms enable us to solve optimization problems much faster than commercial solvers. What distinguishes this paper from the previous work is that we use a prescriptive algorithm, Optimal Policy Trees (OPT), instead of classification algorithms. Whereas classification algorithms aim to predict the correct label and consider all other labels equally undesirable, a prescriptive approach takes into account all the available decision options and their counterfactuals. We first introduce an algorithm that is purely based on OPT and also its extension. We compare their performance with Optimal Classification Trees (OCT) on various MICO problems. Test problems include transportation optimization, portfolio optimization, facility location, and hybrid vehicle control. We also experiment on real-world instances taken from the Mixed Integer Programming Library. OPT-based methods have a significant edge on finding feasible solutions, whereas OCT-based methods have a slight edge on the degree of suboptimality. The proposed extension of the pure OPT algorithm improves on the suboptimality of the solutions the algorithm produces. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: The research was funded in part by a grant from OCP to MIT. [ABSTRACT FROM AUTHOR]

This paper introduces the hub location problem under interhub link failures, a hub location problem in which activated interhub links may fail with a given probability. Two different optimization models are studied, which construct hub backbone networks protected under interhub link disruptions by imposing that, for each commodity, an additional routing path exists besides its original routing path. Both models consider the minimization of the fixed costs of the activated hubs and interhub links plus the expected value of the routing costs of the original and alternative paths. The first model builds explicitly the alternative routing paths, whereas the second model guarantees that, for each commodity, at least one alternative path exists using a large set of connectivity constraints although the alternative paths are not built explicitly. The results of extensive computational testing allow us to analyze the performance of the two proposed models and to evaluate the extra cost required to design a robust backbone network under interhub link failures. The obtained results support the validity of the proposal. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Application. Funding: The authors of this research acknowledge financial support by the Spanish Ministerio de Ciencia y Tecnología, Agencia Estatal de Investigación and Fondos Europeos de Desarrollo Regional (FEDER) via projects PID2020-114594GB-C21 and MTM2019-105824GB-I00. The authors also acknowledge partial support from projects FEDER-US-1256951, Junta de Andalucía P18-FR-422, P18-FR-2369, B-FQM-322-UGR20 (COXMOS), and NetmeetData: Ayudas Fundación BBVA a equipos de investigación científica 2019. The first author was partially supported by the IMAG-Maria de Maeztu grant [CEX2020-001105-M/AEI/10.13039/501100011033] and UE-NextGenerationEU (ayudas de movilidad para la recualificación del profesorado universitario). Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2023.1296. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general algorithmic framework for rotating workforce scheduling. We develop a graph representation that allows to model a schedule as a Eulerian cycle of stints, which we then use to derive a problem formulation that is compact toward the number of employees. We develop a general branch-and-cut framework that solves rotating workforce scheduling in its basic variant, as well as several additional problem variants that are relevant in practice. These variants comprise, among others, objectives for the maximization of free weekends and the minimization of employees. Our computational studies show that the developed framework constitutes a new state of the art for rotating workforce scheduling. For the first time, we solve all 6,000 instances of the status quo benchmark for rotating workforce scheduling to optimality with an average computational time of 0.07 seconds and a maximum computational time of 2.53 seconds. These results reduce average computational times by more than 99% compared with existing methods. Our algorithmic framework shows consistent computational performance, which is robust across all studied problem variants. Summary of Contribution: This paper proposes a novel exact algorithmic framework for the well-known rotating workforce scheduling problem (RWSP). Although the RWSP has been extensively studied in different problem variants and for different exact and heuristic solution approaches, the presented algorithmic framework constitutes a new state-of-the-art for the RWSP that solves all known benchmark sets to optimality and improves on the current state-of-the-art by orders of magnitude with respect to computational times, especially for large-scale instances. The paper is both of methodological value for researchers and of high interest for practitioners. For researchers, the presented framework is amenable for various problem variants and provides a common ground for further studies and research. For practitioners and software developers, low computational times of a few seconds allows the framework to be to embedded into personnel scheduling software. [ABSTRACT FROM AUTHOR]

Motivated by applications arising on social networks, we study a generalization of the celebrated dominating set problem called the Positive Influence Dominating Set (PIDS). Given a graph G with a set V of nodes and a set E of edges, each node i in V has a weight bi, and a threshold requirement gi. We seek a minimum weight subset T of V, so that every node i not in T is adjacent to at least gi members of T. When gi is one for all nodes, we obtain the weighted dominating set problem. First, we propose a strong and compact extended formulation for the PIDS problem. We then project the extended formulation onto the space of the natural node-selection variables to obtain an equivalent formulation with an exponential number of valid inequalities. Restricting our attention to trees, we show that the extended formulation is the strongest possible formulation, and its projection (onto the space of the node variables) gives a complete description of the PIDS polytope on trees. We derive the necessary and sufficient facet-dening conditions for the valid inequalities in the projection and discuss their polynomial time separation. We embed this (exponential size) formulation in a branch-and-cut framework and conduct computational experiments using real-world graph instances, with up to approximately 2.5 million nodes and 8 million edges. On a test-bed of 100 real-world graph instances, our approach finds solutions that are on average 0.2% from optimality and solves 51 out of the 100 instances to optimality. Summary of Contribution: In influence maximization problems, a decision maker wants to target individuals strategically to cause a cascade at a minimum cost over a social network. These problems have attracted significant attention as their applications can be found in many different domains including epidemiology, healthcare, marketing, and politics. However, computationally solving large-scale influence maximization problems to near optimality remains a substantial challenge for the computing community, which thus represent significant opportunities for the development of operations-research based models, algorithms, and analysis in this interface. This paper studies the positive influence dominating set (PIDS) problem, an influence maximization problem on social networks that generalizes the celebrated dominating set problem. It focuses on developing exact methods for solving large instances to near optimality. In other words, the approach results in strong bounds, which then provide meaningful comparative benchmarks for heuristic approaches. The paper first shows that straightforward generalizations of well-known formulations for the dominating set problem do not yield strong (i.e., computationally viable) formulations for the PIDS problem. It then strengthens these formulations by proposing a compact extended formulation and derives its projection onto the space on the natural node-selection variables, resulting in two equivalent (stronger) formulations for the PIDS problem. The projected formulation on the natural node-variables contains a new class of valid inequalities that are shown to be facet-defining for the PIDS problem. These theoretical results are complemented by in-depth computational experiments using a branch-and-cut framework, on a testbed of 100 real-world graph instances, with up to approximately 2.5 million nodes and 8 million edges. They demonstrate the effectiveness of the proposed formulation in solving large scale problems finding solutions that are on average 0.2% from optimality and solving 51 of the 100 instances to optimality. [ABSTRACT FROM AUTHOR]

This paper addresses a single machine total weighted tardiness (TWT) batch-scheduling problem in which jobs have release dates, nonidentical sizes, and are compatible between each other. We propose two integer linear programming models: the first one is a time-indexed formulation (TIF), and the second is an innovative time-size-indexed formulation (TSIF). Although TIF clearly outperforms the existing formulation for the problem, TSIF is capable of producing much stronger bounds in practice. The latter also enables us to develop an efficient column-generation (CG) algorithm. The pricing subproblem corresponds to a resource-constrained shortest path problem that is solved using a bucket graph–based labeling algorithm. The solutions of such a subproblem may contain cycles (reprocessing of jobs), and thus, a memory mechanism called dynamic arc-based ng-sets is employed in the labeling with a view toward avoiding some of them. Moreover, we also implement a preprocessing scheme based on Lagrangian relaxation to perform variable fixing. Extensive computational experiments were carried out in 810 benchmark instances. The proposed CG algorithm is capable of solving instances with up to 100 jobs to optimality. In addition, we believe that this is the first exact approach for a TWT batch-scheduling variant capable of systematically solving instances with up to 50 jobs. High-quality results are also reported for three special cases of the problem—more precisely, when (i) the penalty weights are unitary, (ii) there are no release dates, and (iii) all due dates are set to zero and, hence, the objective becomes equivalent to minimizing the weighted completion time. Summary of Contribution: This paper provides the first exact algorithm for a standard variant of a batch-scheduling total weighted tardiness problem that can solve instances with up to 100 jobs to optimality, a considerable leap with respect to previous works. In particular, we propose a time-indexed formulation that has the advantage of being relatively simple to implement, and yet we show that it is not theoretically dominated by the other innovative formulation proposed in the paper referred to as the time-size-indexed formulation (TSIF). Moreover, we present a Lagrangian approach to quickly fix variables and an iterative column-generation (CG) procedure over a Dantzig–Wolfe decomposition of TSIF that combines an efficient pricing algorithm with a dynamic scheme to adjust the subproblem constraints. The proposed CG approach is capable of producing very strong bounds for the problem as well as for some of its special cases. [ABSTRACT FROM AUTHOR]

In critical node problems, the task is to identify a small subset of so-called critical nodes whose deletion maximally degrades a network's "connectivity" (however that is measured). Problems of this type have been widely studied, for example, for limiting the spread of infectious diseases. However, existing approaches for solving them have typically been limited to networks having fewer than 1,000 nodes. In this paper, we consider a variant of this problem in which the task is to delete b nodes so as to minimize the number of node pairs that remain connected by a path of length at most k. With the techniques developed in this paper, instances with up to 17,000 nodes can be solved exactly. We introduce two integer programming formulations for this problem (thin and path-like) and compare them with an existing recursive formulation. Although the thin formulation generally has an exponential number of constraints, it admits an efficient separation routine. Also helpful is a new, more general preprocessing procedure that, on average, fixes three times as many variables than before. Summary of Contribution: In this paper, we consider a distance-based variant of the critical node problem in which the task is to delete b nodes so as to minimize the number of node pairs that remain connected by a path of length at most k. This problem is motivated by applications in social networks, telecommunications, and transportation networks. In our paper, we aim to solve large-scale instances of this problem. Standard out-of-the-box approaches are unable to solve such instances, requiring new integer programming models, methodological contributions, and other computational insights. For example, we propose an algorithm for finding a maximum independent set of simplicial nodes that runs in time O(nm) that we use in a preprocessing procedure; we also prove that the separation problem associated with one of our integer programming models is NP-hard. We apply our branch-and-cut implementation to real-life networks from a variety of domains and observe speedups over previous approaches. [ABSTRACT FROM AUTHOR]

We study the uncapacitated lot-sizing problem with uncertain demand and costs. The problem is modeled as a multistage stochastic mixed-integer linear program in which the evolution of the uncertain parameters is represented by a scenario tree. To solve this problem, we propose a new extension of the stochastic dual dynamic integer programming algorithm (SDDiP). This extension aims at being more computationally efficient in the management of the expected cost-to-go functions involved in the model, in particular by reducing their number and by exploiting the current knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. The algorithm is based on a partial decomposition of the problem into a set of stochastic subproblems, each one involving a subset of nodes forming a subtree of the initial scenario tree. We then introduce a cutting plane–generation procedure that iteratively strengthens the linear relaxation of these subproblems and enables the generation of an additional strengthened Benders' cut, which improves the convergence of the method. We carry out extensive computational experiments on randomly generated large-size instances. Our numerical results show that the proposed algorithm significantly outperforms the SDDiP algorithm at providing good-quality solutions within the computation time limit. Summary of Contribution: This paper investigates a combinatorial optimization problem called the uncapacitated lot-sizing problem. This problem has been widely studied in the operations research literature as it appears as a core subproblem in many industrial production planning problems. We consider a stochastic extension in which the input parameters are subject to uncertainty and model the resulting stochastic optimization problem as a multistage stochastic integer program. To solve this stochastic problem, we propose a novel extension of the recently published stochastic dual dynamic integer programming (SDDiP) algorithm. The proposed extension relies on two main ideas: the use of a partial decomposition of the scenario tree and the exploitation of existing knowledge on the polyhedral structure of the stochastic uncapacitated lot-sizing problem. We provide the results of extensive computational experiments carried out on large-size randomly generated instances. These results show that the proposed extended algorithm significantly outperforms the SDDiP at providing good-quality solutions for the stochastic uncapacitated lot-sizing problem. Although the paper focuses on a basic lot-sizing problem, the proposed algorithmic framework may be useful to solve more complex practical production planning problems. [ABSTRACT FROM AUTHOR]

In the context of the maximum stable set problem, rank inequalities impose that the cardinality of any set of vertices contained in a stable set be, at most, as large as the stability number of the subgraph induced by such a set. Rank inequalities are very general, as they subsume many classical inequalities such as clique, hole, antihole, web, and antiweb inequalities. In spite of their generality, the exact separation of rank inequalities has never been addressed without the introduction of topological restrictions on the induced subgraph and the tightness of their closure has never been investigated systematically. In this work, we propose a methodology for optimizing over the closure of all rank inequalities with a right-hand side no larger than a small constant without imposing any restrictions on the topology of the induced subgraph. Our method relies on the exact separation of a relaxation of rank inequalities, which we call relaxed k-rank inequalities, whose closure is as tight. We investigate the corresponding separation problem, a bilevel programming problem asking for a subgraph of maximum weight with a bound on its stability number, whose study could be of independent interest. We first prove that the problem is Σ 2 P -hard and provide some insights on its polyhedral structure. We then propose two exact methods for its solution: a branch-and-cut algorithm (which relies on a family of faced-defining inequalities which we introduce in this paper) and a purely combinatorial branch-and-bound algorithm. Our computational results show that the closure of rank inequalities with a right-hand side no larger than a small constant can yield a bound that is stronger, in some cases, than Lovász's Theta function, and substantially stronger than bounds obtained with standard inequalities that are valid for the stable set problem, including odd-cycle inequalities and wheel inequalities. Summary of Contribution: This paper proposes two original methods for solving a challenging cut-separation problem (of bilevel type) for a large class of inequalities valid for one of the key operations research problems, namely, the max stable set problem. An extensive set of experimental results validates the proposed methods. All the source code and data sets are available online on GitHub. [ABSTRACT FROM AUTHOR]

We introduce the problem of selecting patient-donor pairs in a kidney exchange program to undergo a crossmatch test, and we model this selection problem as a two-stage stochastic integer programming problem. The optimal solutions of this new formulation yield a larger expected number of realized transplants than previous approaches based on internal recourse or subset recourse. We settle the computational complexity of the selection problem by showing that it remains NP-hard even for maximum cycle length equal to two. Furthermore, we investigate to what extent different algorithmic approaches, including one based on Benders decomposition, are able to solve instances of the model. We empirically investigate the computational efficiency of this approach by solving randomly generated instances and study the corresponding running times as a function of maximum cycle length, and of the presence of nondirected donors. Summary of Contribution: This paper deals with an important and very complex issue linked to the optimization of transplant matchings in kidney exchange programs, namely, the inherent uncertainty in the assessment of compatibility between donors and recipients of transplants. Although this issue has previously received some attention in the optimization literature, most attempts to date have focused on applying recourse to solutions selected within restricted spaces. The present paper explicitly formulates the maximization of the expected number of transplants as a two-stage stochastic integer programming problem. The formulation turns out to be computationally difficulty, both from a theoretical and from a numerical perspective. Different algorithmic approaches are proposed and tested experimentally for its solution. The quality of the kidney exchanges produced by these algorithms compares favorably with that of earlier models. [ABSTRACT FROM AUTHOR]

Targeted marketing strategies are of significant interest in the smartapp economy. Typically, one seeks to identify individuals to strategically target in a social network so that the network is influenced at a minimal cost. In many practical settings, the effects of direct influence predominate, leading to the positive influence dominating set with partial payments (PIDS-PP) problem that we discuss in this paper. The PIDS-PP problem is NP-complete because it generalizes the dominating set problem. We discuss several mixed integer programming formulations for the PIDS-PP problem. First, we describe two compact formulations on the payment space. We then develop a stronger compact extended formulation. We show that when the underlying graph is a tree, this compact extended formulation provides integral solutions for the node selection variables. In conjunction, we describe a polynomial-time dynamic programming algorithm for the PIDS-PP problem on trees. We project the compact extended formulation onto the payment space, providing an equivalently strong formulation that has exponentially many constraints. We present a polynomial time algorithm to solve the associated separation problem. Our computational experience on a test bed of 100 real-world graph instances (with up to approximately 465,000 nodes and 835,000 edges) demonstrates the efficacy of our strongest payment space formulation. It finds solutions that are on average 0.4% from optimality and solves 80 of the 100 instances to optimality. Summary of Contribution: The study of influence propagation is important in a number of applications including marketing, epidemiology, and healthcare. Typically, in these problems, one seeks to identify individuals to strategically target in a social network so that the entire network is influenced at a minimal cost. With the ease of tracking consumers in the smartapp economy, the scope and nature of these problems have become larger. Consequently, there is considerable interest across multiple research communities in computationally solving large-scale influence maximization problems, which thus represent significant opportunities for the development of operations research–based methods and analysis in this interface. This paper introduces the positive influence dominating set with partial payments (PIDS-PP) problem, an influence maximization problem where the effects of direct influence predominate, and it is possible to make partial payments to nodes that are not targeted. The paper focuses on model development to solve large-scale PIDS-PP problems. To this end, starting from an initial base optimization model, it uses several operations research model strengthening techniques to develop two equivalent models that have strong computational performance (and can be theoretically shown to be the best model for trees). Computational experiments on a test bed of 100 real-world graph instances (with up to approximately 465,000 nodes and 835,000 edges) attest to the efficacy of the best model, which finds solutions that are on average 0.4% from optimality and solves 80 of the 100 instances to optimality. [ABSTRACT FROM AUTHOR]

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest-path problem in an auxiliary network. We design techniques for exploiting network models in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows. [ABSTRACT FROM AUTHOR]

Quantum annealing (QA) can be used to quickly obtain near-optimal solutions for quadratic unconstrained binary optimization (QUBO) problems. In QA hardware, each decision variable of a QUBO should be mapped to one or more adjacent qubits in such a way that pairs of variables defining a quadratic term in the objective function are mapped to some pair of adjacent qubits. However, qubits have limited connectivity in existing QA hardware. This has spurred work on preprocessing algorithms for embedding the graph representing problem variables with quadratic terms into the hardware graph representing qubits adjacencies, such as the Chimera graph in hardware produced by D-Wave Systems. In this paper, we use integer linear programming to search for an embedding of the problem graph into certain classes of minors of the Chimera graph, which we call template embeddings. One of these classes corresponds to complete bipartite graphs, for which we show the limitation of the existing approach based on minimum odd cycle transversals (OCTs). One of the formulations presented is exact and thus can be used to certify the absence of a minor embedding using that template. On an extensive test set consisting of random graphs from five different classes of varying size and sparsity, we can embed more graphs than a state-of-the-art OCT-based approach, our approach scales better with the hardware size, and the runtime is generally orders of magnitude smaller. Summary of Contribution: Our work combines classical and quantum computing for operations research by showing that integer linear programming can be successfully used as a preprocessing step for adiabatic quantum optimization. We use it to determine how a quadratic unconstrained binary optimization problem can be solved by a quantum annealer in which the qubits are coupled as in a Chimera graph, such as in the quantum annealers currently produced by D-Wave Systems. The paper also provides a timely introduction to adiabatic quantum computing and related work on minor embeddings. [ABSTRACT FROM AUTHOR]

This paper considers a class of two-stage stochastic mixed-integer optimization problems where, for a given first-stage solution, we can determine the optimal values of recourse variables sequentially. This class of problems arises in a wide variety of applications. In the case of multivariate discrete distributions for uncertain parameters, a standard stochastic programming formulation of these problems involves an exponential number of scenarios, therefore an exponential number of variables and constraints. We propose a new mixed-integer programming modeling approach where the number of variables and constraints is independent of the number of scenarios and scales at most pseudopolynomially with the problem size. The proposed modeling approach relies on state variables that track the system's state as the uncertainty realizes sequentially. We demonstrate the advantages of the proposed approach in two applications arising in project scheduling and operating room allocation. Summary of Contribution: This paper proposes a new modeling approach for a class of two-stage stochastic optimization problems that is computationally more efficient than the traditional scenario-based stochastic integer programming models. The proposed modeling approach relies on state variables that track the system's state as the uncertainty realizes sequentially. We demonstrated the efficiency of the proposed approach by computational results on two applications in project scheduling and operating room allocation. [ABSTRACT FROM AUTHOR]

We consider a two-player interdiction problem staged over a graph where the attacker's objective is to minimize the cost of removing edges from the graph so that the defender's objective, that is, the weight of a minimum spanning tree in the residual graph, is increased up to a predefined level r. Standard approaches for graph interdiction frame this type of problems as bilevel formulations, which are commonly solved by replacing the inner problem by its dual to produce a single-level reformulation. In this paper, we study an alternative integer program derived directly from the attacker's solution space and show that this formulation yields a stronger linear relaxation than the bilevel counterpart. Furthermore, we analyze the convex hull of the feasible solutions of the problem and identify several families of facet-defining inequalities that can be used to strengthen this integer program. We then proceed by introducing a different formulation defined by a set of so-called supervalid inequalities that may exclude feasible solutions, albeit solutions whose objective value is not better than that of an edge cut of minimum cost. We discuss several computational aspects required for an efficient implementation of the proposed approaches. Finally, we perform an extensive set of computational experiments to test the quality of these formulations, analyzing and comparing the benefits of each model, as well as identifying further enhancements. Summary of Contribution: Network interdiction has received significant attention over the last couple of decades, with a notable peak of interest in recent years. This paper provides an interesting balance between the theoretical and computational aspects of solving a challenging network interdiction problem via integer programming. We present several technical developments, including a detailed study of the problem's solution space, multiple formulations, and a polyhedral analysis of the convex hull of feasible solutions. We then analyze the results of an extensive set of computational experiments that were used to validate the effectiveness of the different methods we developed in this paper. [ABSTRACT FROM AUTHOR]

The exact solution of the NP-hard (nondeterministic polynomial-time hard) maximum cut problem is important in many applications across, for example, physics, chemistry, neuroscience, and circuit layout—which is also due to its equivalence to the unconstrained binary quadratic optimization problem. Leading solution methods are based on linear or semidefinite programming and require the separation of the so-called odd-cycle inequalities. In their groundbreaking research, F. Barahona and A. R. Mahjoub have given an informal description of a polynomial-time algorithm for this problem. As pointed out recently, however, additional effort is necessary to guarantee that the inequalities obtained correspond to facets of the cut polytope. In this paper, we shed more light on a so enhanced separation procedure and investigate experimentally how it performs in comparison with an ideal setting where one could even employ the sparsest, most violated, or geometrically most promising facet-defining odd-cycle inequalities. Summary of Contribution: This paper aims at a better capability to solve binary quadratic optimization or maximum cut problems and their various applications using integer programming techniques. To this end, the paper describes enhancements to a well-known algorithm for the central separation problem arising in this context; it is demonstrated experimentally that these enhancements are worthwhile from a computational point of view. The linear relaxations of the aforementioned problems are typically solved using fewer iterations and cutting planes than with a nonenhanced approach. It is also shown that the enhanced procedure is only slightly inferior to an ideal, enumerative, and, in practice, intractable global cutting-plane selection. [ABSTRACT FROM AUTHOR]

Constraint programming (CP) has been recently in the spotlight after new CP-based procedures have been incorporated into state-of-the-art solvers, most notably the CP Optimizer from IBM. Classical CP solvers were only capable of guaranteeing the optimality of a solution, but they could not provide bounds for the integer feasible solutions found if interrupted prematurely due to, say, time limits. New versions, however, provide bounds and optimality guarantees, effectively making CP a viable alternative to more traditional mixed-integer programming (MIP) models and solvers. We capitalize on these developments and conduct a computational evaluation of MIP and CP models on 12 select scheduling problems.1 We carefully chose these 12 problems to represent a wide variety of scheduling problems that occur in different service and manufacturing settings. We also consider basic and well-studied simplified problems. These scheduling settings range from pure sequencing (e.g., flow shop and open shop) or joint assignment-sequencing (e.g., distributed flow shop and hybrid flow shop) to pure assignment (i.e., parallel machine) scheduling problems. We present MIP and CP models for each variant of these problems and evaluate their performance over 17 relevant and standard benchmarks that we identified in the literature. The computational campaign encompasses almost 6,623 experiments and evaluates the MIP and CP models along five dimensions of problem characteristics, objective function, decision variables, input parameters, and quality of bounds. We establish the areas in which each one of these models performs well and recognize their conceivable reasons. The obtained results indicate that CP sets new limits concerning the maximum problem size that can be solved using off-the-shelf exact techniques. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.1287) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0326) at (http://dx.doi.org/10.5281/zenodo.7541223). [ABSTRACT FROM AUTHOR]

We address a dynamic covering location problem of an unmanned aerial vehicle base station (UAV-BS), in which the location sequence of a single UAV-BS in a wireless communication network is determined to satisfy data demand arising from ground users. This problem is especially relevant in the context of smart grid and disaster relief. The vertical movement ability of the UAV-BS and nonconvex covering functions in wireless communication restrict utilizing classical planar covering location approaches. Therefore, we develop new formulations to this emerging problem for a finite time horizon to maximize the total coverage. In particular, we develop a mixed-integer nonlinear programming formulation that is nonconvex in nature and propose a Lagrangean decomposition algorithm (LDA) to solve this formulation. Because of the high complexity of the problem, the LDA is still unable to find good local solutions to large-scale problems. Therefore, we develop a continuum approximation (CA) model and show that CA would be a promising approach in terms of both computational time and solution accuracy. Our numerical study also shows that the CA model can be a remedy to build efficient initial solutions for exact solution algorithms. Summary of Contribution: This paper addresses a facet of mixed integer nonlinear programming formulations. Dynamic facility location problems (DFLPs) arise in a wide range of applications. However, classical DFLPs typically focus on the two-dimensional spaces. Emerging technologies in wireless communication and some other promising application areas, such as smart grids, have brought new location problems that cannot be solved with classical approaches. For practical reasons, many research attempts to solve this new problem, especially by researchers whose primary research area is not OR, have seemed far from analyzing the characteristics of the formulations. Rather, solution-oriented greedy heuristics have been proposed. This paper has two main objectives: (i) to close the gap between practical and theoretical sides of this new problem with the help of current knowledge that OR possesses to solve facility location problems and (ii) to support the findings with an exhaustive computational study to show how these findings can be applied to practice. [ABSTRACT FROM AUTHOR]

Scope and Mission In the paper, we present an original work related to the modeling and optimization approaches for kidney exchange programs (KEPs). Nowadays, KEPs represent an alternative way for patients suffering from renal failure to find a compatible (living) donor. The problem of determining an assignment of patients to (compatible) donors that maximizes the number of transplants in a KEP can be seen as a vertex-disjoint cycle-packing problem. Thus, KEPs have been extensively studied in the literature of integer programming. In practice, the assignment determined for a KEP might not be implemented due to withdrawals from the program (e.g., a more accurate compatible test shows a new incompatibility or a health condition makes it unable for a patient to participate in a KEP). In our paper, we model the problem of determining a robust solution to the KEP, that is, a solution that minimizes the material and emotional costs of changing an assignment. In this way, we propose and design solution approaches for three recourse policies that anticipate withdrawals. Through computational experiments, we compare the three recourse policies and validate the practical interest of robust solutions. Kidney exchange programs aim at matching end-stage renal disease patients who have a willing but incompatible kidney donor with another donor. The programs comprise a pool of such incompatible patient-donor pairs and, whenever a donor from one pair is compatible with the patient of another pair, and vice versa, the pairs may be matched and exchange kidneys. This is typically a two-step process in which, first, a set of pairs is matched based on preliminary compatibility tests and, second, the matched pairs are notified and more accurate compatibility tests are performed to verify that actual transplantation can take place. These additional tests may reveal incompatibilities not previously detected. When that happens, the planned exchange will not proceed. Furthermore, pairs may drop out before the transplant, and thus the planned exchange is canceled. In this paper, we study the case in which a new set of pairs may be matched if incompatibilities are discovered or a pair withdraws from the program. The new set should be as close as possible to the initial set in order to minimize the material and emotional costs of the changes. Various recourse policies that determine the admissible second-stage actions are investigated. For each recourse policy, we propose a novel adjustable robust integer programming model. We also propose solution approaches to solve this model exactly. The approaches are validated through thorough computational experiments. Summary of Contribution: In the paper, we present an original work related to the modeling and optimization approaches for Kidney Exchange Programs (KEPs). Currently, KEPs represent an alternative way for patients suffering from renal failure to find a compatible (living) donor. The problem of determining an assignment of patients to (compatible) donors that maximizes the number of transplants in a KEP can be seen as a vertex-disjoint cycle packing problem. Thus, KEPs have been extensively studied in the literature of integer programming. In practice, the assignment determined to a KEP might not be implemented due to withdraws from the program (e.g., a more accurate compatible test shows a new incompatibility or a patient health condition unable him/her to participate on the KEP). In our paper, we model the problem of determining a robust solution to the KEP, i.e., a solution that minimizes the material and emotional costs of changing an assignment. In this way, we propose and design solution approaches for three recourse policies that anticipate withdraws. Through computational experiments we compare the three recourse policies and validate the practical interest of robust solutions. [ABSTRACT FROM AUTHOR]

The generalization of mixed integer program (MIP) techniques to deal with nonlinear, potentially nonconvex, constraints has been a fruitful direction of research for computational mixed integer nonlinear programs (MINLPs) in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers toward the case of nonlinear optimization: the analysis of infeasible subproblems for learning additional valid constraints. To this end, we derive two different strategies, geared toward two different solution approaches. These are using local dual proofs of infeasibility for LP-based branch-and-bound and the creation of nonlinear dual proofs for NLP-based branch-and-bound, respectively. We discuss implementation details of both approaches and present an extensive computational study, showing that both techniques can significantly enhance performance when solving MINLPs to global optimality. Summary of Contribution: This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed integer nonlinear programs (MINLPs). It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be transferred to nonlinear optimization. Further, it develops theory for how nonlinear dual infeasibility proofs can be derived from a nonlinear relaxation. This paper features a thoroughly computational study regarding the impact of conflict analysis techniques on the overall performance of a state-of-the-art MINLP solver when solving MINLPs to global optimality. [ABSTRACT FROM AUTHOR]

Two essential ingredients of modern mixed-integer programming solvers are diving heuristics, which simulate a partial depth-first search in a branch-and-bound tree, and conflict analysis, which learns valid constraints from infeasible subproblems. So far, these techniques have mostly been studied independently: primal heuristics for finding high-quality feasible solutions early during the solving process and conflict analysis for fathoming nodes of the search tree and improving the dual bound. In this paper, we pose the question of whether and how the orthogonal goals of proving infeasibility and generating improving solutions can be pursued in a combined manner such that a state-of-the-art solver can benefit. To do so, we integrate both concepts in two different ways. First, we develop a diving heuristic that simultaneously targets the generation of valid conflict constraints from the Farkas dual and the generation of improving solutions. We show that, in the primal, this is equivalent to the optimistic strategy of diving toward the best bound with respect to the objective function. Second, we use information derived from conflict analysis to enhance the search of a diving heuristic akin to classic coefficient diving. In a detailed computational study, both methods are evaluated on the basis of an implementation in the source-open-solver SCIP. The experimental results underline the potential of combining both diving heuristics and conflict analysis. Summary of Contribution. This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed-integer linear programs. It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be combined successfully with diving heuristics that aim at finding primal solutions. For two newly designed diving heuristics, this paper features a thoroughly computational study regarding their impact on the overall performance of a state-of-the-art MIP solver. [ABSTRACT FROM AUTHOR]

Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets. The objective is to minimize the sum of the distances of the chosen set of edges for the worst positions of the vertices in their uncertainty sets. We first prove that these problems are N P -hard even when the feasible sets consist either of all spanning trees or of all s – t paths. Given this hardness, we propose an exact solution algorithm combining integer programming formulations with a cutting plane algorithm, identifying the cases where the separation problem can be solved efficiently. We also propose a conservative approximation and show its equivalence to the affine decision rule approximation in the context of Euclidean distances. We compare our algorithms to three deterministic reformulations on instances inspired by the scientific literature for the Steiner tree problem and a facility location problem. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2023.1276. [ABSTRACT FROM AUTHOR]

After a blackout event, power system restoration is an essential activity for grid resilience; operators restart generators, re-establish transmission paths, and restore loads. With a goal of restoring electric service in the shortest time, the core decisions in restoration planning are to partition the grid into subnetworks, each of which has an initial power source for black-start (called sectionalization problem), and then restart all generators in each network (called generator startup sequencing (GSS) problem) as soon as possible. Due to their complexity, the sectionalization and GSS problems are usually solved separately, often resulting in a suboptimal solution. Our paper develops models and computational methods to solve the two problems simultaneously. We first study the computational complexity of the GSS problem and develop an efficient integer linear programming formulation. We then integrate the GSS problem with the sectionalization problem and develop an integer linear programming formulation for the parallel power system restoration (PPSR) problem to find exact optimal solutions. To solve larger systems, we then develop bounding approaches that find good upper and lower bounds efficiently. Finally, to address computational challenges for very large power grids, we develop a randomized approach to find a high-quality feasible solution quickly. Our computational experiments demonstrate that the proposed approaches are able to find good solutions for PPSR in up to 2,000-bus systems. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This research was supported by the Visiting Faculty Program of Argonne National Laboratory and the U.S. Department of Energy Advanced Grid Modeling Program [Grant DE-OE0000875]. [ABSTRACT FROM AUTHOR]

We study the unmanned aerial vehicle (UAV) route planning problem for information collection missions performed in terrains with stochastic attributes. Uncertainty is associated with the availability of information, the effectiveness of the search and collection sensors the UAV carries, and the flight time required to travel between target regions in the mission terrain. Additionally, uncertainties in flight duration vary the detection threat exposed in missions performed in nonfriendly terrains. We develop a mixed integer programming model to maximize the expected information collection while limiting the risks of not completing the mission on time and of being detected and restricting the variance imposed on flight duration. The model allows multiple path alternatives between target pairs and revisits to the same target regions. Computational experiments are performed on randomly generated instances to investigate the impact of problem parameters and mission restrictions. We also develop a case study with a military and a civilian application, each of which with different specifications. In addition, we validate that the actual performance of the optimal solution of the model is close to the result reported by the solver via a simulation study. We conclude that the developed model is robust and can be used for practical-sized missions, and the failure rate of its optimal routes in actual missions is negligibly small. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplementary Information [https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1245] or is available from the IJOC GitHub software repository (https://github.com/INFORMSJoC) at [http://dx.doi.org/10.5281/zenodo.7055494. [ABSTRACT FROM AUTHOR]

This paper is devoted to a study of computational speed-ups that may be possible in cut generation associated with decomposition-based branch-and-cut methods (e.g., D2-BAC) for stochastic mixed-integer programs (SMIPs). We discuss some bottlenecks in the cut generation process and suggest several enhancements to speed up this process. Our computational results show that significant improvements (approximately 50% reduction in computation times) may be possible by streamlining the computations associated with the cut generation process. This paper establishes new benchmarks for serial processing of two-stage SMIPs. [ABSTRACT FROM AUTHOR]

In this paper, we present a method to determine if a lift-and-project cut for a mixed-integer linear program is irregular, in which case the cut is not equivalent to any intersection cut from the bases of the linear relaxation. This is an important question due to the intense research activity for the past decade on cuts from multiple rows of simplex tableau as well as on lift-and-project cuts from nonsplit disjunctions. Although it has been known for a while that lift-and-project cuts from split disjunctions are always equivalent to intersection cuts and consequently to such multirow cuts, it has been recently shown that there is a necessary and sufficient condition in the case of arbitrary disjunctions: a lift-and-project cut is regular if, and only if, it corresponds to a regular basic solution of the Cut Generating Linear Program (CGLP). This paper has four contributions. First, we state a result that simplifies the verification of regularity for basic CGLP solutions. Second, we provide a mixed-integer formulation that checks whether there is a regular CGLP solution for a given cut that is regular in a broader sense, which also encompasses irregular cuts that are implied by the regular cut closure. Third, we describe a numerical procedure based on such formulation that identifies irregular lift-and-project cuts. Finally, we use this method to evaluate how often lift-and-project cuts from simple t-branch split disjunctions are irregular, and thus not equivalent to multirow cuts, on 74 instances of the Mixed Integer Programming Library (MIPLIB) benchmarks. [ABSTRACT FROM AUTHOR]

Modern integrated circuit design involves the layout of circuits consisting of millions of switching elements or transistors. Due to the sheer complexity of the problem, optimizing the connectivity between transistors is very difficult. The circuit interconnection is the single most important factor in performance criteria such as signal delay, power dissipation, circuit size, and cost. These factors dictate that interconnections, i.e., wires, be made as short as possible. The wire-minimization problem is generally formulated as a sequence of discrete optimization subproblems that are known to be NP-hard. Hence, they can only be solved approximately using meta-heuristics. These methods are computationally expensive and the quality of the solution depends to a great extent on an appropriate choice of starting configuration and modeling techniques. In this paper, new modeling techniques are used to solve the routing problem formulated as an integer programming problem. The main contribution of this paper is a proposed global routing heuristic that combines the wire length, channel congestion, and number of pins in routes to find the best wiring layout of a circuit. By adding information such as channel congestion and the number of pins in each route as well as the wire length, the quality of the solution is improved. In addition, the solutions of the large relaxed linear programming problems are skewed towards a zero-one solution, resulting in faster convergence. The developed LP models in this paper are useful when solving the global routing problem for two reasons; first, the new interior-point algorithms to solve the LP problem are polynomial in time. Second, ‘near optimal wiring’ is obtained in polynomial time without performing randomized rounding. [ABSTRACT FROM AUTHOR]

In this paper, we study a new problem that we refer to as the multiple knapsack with color constraints (MKCP). Motivated by a real application from the steel industry, the MKCP can be formulated by generalizing the multiple knapsack problem. A real-life instance (called mkc) of this problem class is available through MIPLIB (Bixby 2004) and a larger instance (mkc7) is downloadable from the COIN site (IBM 2004). The focus of this paper is to present improved computational results for the two mentioned instances of this problem using a column-generation approach. We solve mkc to optimality and use Dantzig-Wolfe decomposition for upper bounding the other instance. Solving mkc to optimality took less time than it takes to solve the LP relaxation of the original formulation. The larger instance is solved to near optimality (within 0.5% of optimality) in a fraction of the time required to solve the original relaxed LP. [ABSTRACT FROM AUTHOR]

In this paper we study the closest-string problem (CSP), which can be defined as follows: Given a finite set T = {s¹, s²,&hellip,sn} of strings, each string with length m, find a center string t of length m minimizing d, such that for every string sI ϵ T, dH(t, si) ≥ d. By dH(t, si we mean the Hamming distance between t and si . This is an NP-hard problem, with applications in molecular biology and coding theory. Even though there are good approximation algorithms for this problem, and exact algorithms for instances with d constant, there are no studies trying to solve it exactly for the general case. In this paper we propose three integer-programming (IP) formulations and a heuristic, which is used to provide upper bounds on the value of an optimal solution. We report computational results of a branch-and-bound algorithm based on one of the IP formulations, and of the heuristic, executed over randomly generated instances. These results show that it is possible to solve CSP instances of moderate size to optimality. [ABSTRACT FROM AUTHOR]

Linear complementarity problems (LCPs) are an important modeling tool for many practically relevant situations and also have many important applications in mathematics itself. Although the continuous version of the problem is extremely well-studied, much less is known about mixed-integer LCPs (MILCPs) in which some variables have to be integer-valued in a solution. In particular, almost no tailored algorithms are known besides reformulations of the problem that allow us to apply general purpose mixed integer linear programming solvers. In this paper, we present, theoretically analyze, enhance, and test a novel branch-and-bound method for MILCPs. The main property of this method is that we do not "branch" on constraints as usual but by adding suitably chosen penalty terms to the objective function. By doing so, we can either provably compute an MILCP solution if one exists or compute an approximate solution that minimizes an infeasibility measure combining integrality and complementarity conditions. We enhance the method by MILCP-tailored valid inequalities, node selection strategies, branching rules, and warm-starting techniques. The resulting algorithm is shown to clearly outperform two benchmark approaches from the literature. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: M. De Santis acknowledges support within the project RM120172A2970290, which has received funding from Sapienza, University of Rome. M. Schmidt thanks the Deutsche Forschungsgemeinschaft (DFG) for its support within project A05 and B08 in the "SFB TRR 154 Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks." L. Winkel is supported by the DFG within the Research Training Group 2126: "Algorithmic Optimization." Supplemental Material: The online supplementary material is available at https://doi.org/10.1287/ijoc.2022.1216. [ABSTRACT FROM AUTHOR]

We consider binary integer programming problems with the min-max regret objective function under interval objective coefficients. We propose a heuristic framework, the iterated dual substitution (iDS) algorithm, which iteratively invokes a dual substitution heuristic and excludes from the search space any solution already checked in previous iterations. In iDS, we use a best scenario–based lemma to improve performance. We apply iDS to four typical combinatorial optimization problems: the knapsack problem, the multidimensional knapsack problem, the generalized assignment problem, and the set covering problem. For the multidimensional knapsack problem, we compare the iDS approach with two algorithms widely used for problems with the min-max regret criterion: a fixed-scenario approach, and a branch-and-cut approach. The results of computational experiments on a broad set of benchmark instances show that the proposed iDS approach performs best on most tested instances. For the knapsack problem, the generalized assignment problem, and the set covering problem, we compare iDS with state-of-the-art results. The iDS algorithm successfully updates best-known records for a number of benchmark instances. Summary of Contribution: This paper proposes a heuristic framework for binary integer programming (BIP) problems with the min-max regret objective function under interval objective coefficients. We selected four representative NP-hard combinatorial optimization problems: the knapsack problem, the multidimensional knapsack problem, the set covering problem, and the generalized assignment problem. We show the effectiveness and efficiency of the approach by comparing with state-of-the-art results. [ABSTRACT FROM AUTHOR]

In a telecommunication network, routing and wavelength assignment (RWA) is the problem of finding lightpaths for incoming connection requests. When facing a dynamic traffic, greedy assignment of lightpaths to incoming requests based on predefined deterministic policies leads to a fragmented network that cannot make use of its full capacity because of stranded bandwidth. At this point, service providers try to recover the capacity via a defragmentation process. We study this setting from two perspectives: (i) while granting the connection requests via the RWA problem and (ii) during the defragmentation process by lightpath rerouting. For both problems, we present the first two-stage stochastic integer programming model incorporating incoming request uncertainty to maximize the expected grade of service. We develop a decomposition-based solution approach, which uses various relaxations of the problem and a newly developed problem-specific cut family. Simulation of two-stage policies for a variety of instances in a rolling-horizon framework of 52 stages shows that our stochastic models provide high-quality solutions when compared with traditionally used deterministic ones. Specifically, the proposed provisioning policies yield improvements of up to 19% in overall grade of service and 20% in spectrum saving, while the stochastic lightpath rerouting policies grant up to 36% more requests, using up to just 4% more bandwidth spectrum. Summary of Contribution: For handling the intrinsic uncertainty of demand in the telecommunications industry, this paper proposes novel stochastic models and solution methodology for two fundamental problems in telecommunications at operational level: (i) routing and wavelength assignment (RWA) and (ii) lightpath rerouting problem. Despite the vast literature on the RWA problem, stochastic optimization has not been considered as a viable solution for resource allocation in optical networks. We propose two-stage stochastic programming models for both problems and design efficient decomposition-based solution methods that use various relaxations of the models and a new family of cutting planes. Our extensive and rigorous numerical experiments show the significant merit of incorporating uncertainty into decision making, as well as the effectiveness of the decomposition framework and our newly designed family of cuts in enhancing the solvability of both models. This work opens new avenues to explore where the powerful stochastic programming literature can be leveraged to make operational decisions in telecommunications problems, a field that currently relies mostly on deterministic and heuristic solution methods. [ABSTRACT FROM AUTHOR]

Mixed-integer second-order cone programs (MISOCPs) form a novel class of mixed-integer convex programs, which can be solved very efficiently as a result of the recent advances in optimization solvers. This paper shows how various performance metrics of M/G/1 queues can be modeled by different MISOCPs. To motivate the reformulation method, it is first applied to a challenging stochastic location problem with congestion, which is broadly used to design socially optimal service systems. Three different MISOCPs are developed and compared on different sets of benchmark test problems. The new formulations efficiently solve very large-size test problems that cannot be solved by the two existing methods developed based on linear programming within reasonable time. The superiority of the conic reformulation method is next shown over a state-space decomposition method recently used to solve an assignment problem in queueing systems. Finally, the general applicability of the method is shown for similar optimization problems that use queue-theoretic performance measures to address customer satisfaction and service quality. [ABSTRACT FROM AUTHOR]

We introduce and motivate several variants of the bin packing problem where bins are assigned to time slots, and minimum and maximum lags are required between some pairs of items. We suggest two integer programming formulations for the general problem: a compact one and a stronger formulation with an exponential number of variables and constraints. We propose a branch-cut-and-price approach that exploits the latter formulation. For this purpose, we devise separation algorithms based on a mathematical characterization of feasible assignments for two important special cases of the problem: when the number of possible bins available at each period is infinite and when this number is limited to one and time lags are nonnegative. Computational experiments are reported for instances inspired from a real-case application of chemical treatment planning in vineyards, as well as for literature instances for special cases of the problem. The experimental results show the efficiency of our branch-cut-and-price approach, as it outperforms the compact formulation on newly proposed instances and is able to obtain improved lower and upper bounds for literature instances. Summary of Contribution: The paper considers a new variant of the bin packing problem, which is one of the most important problems in operations research. A motivation for introducing this variant is given, as well as a real-life application. We present a novel and original exact branch-cut-and-price algorithm for the problem. We implement this algorithm, and we present the results of extensive computational experiments. The results show a very good performance of our algorithm. We give several research directions that can be followed by subsequent researchers to extend our contribution to more complex and generic problems. [ABSTRACT FROM AUTHOR]

This paper presents the capacitated and economic districting problem (CEDP), which searches for the best edge partition defining connected, capacitated, and balanced districts in an undirected connected graph, weighing the economic value of each district. This problem provides a comprehensive description of the decision making on service networks districting, where the order by which the districts are serviced plays a role in the profit. This is observed in the arrangement of districts for meter reading, as the day in which each district is read impacts the revenue. Two integer linear programming formulations are proposed for CEDP, accompanied by a proof of N P -hardness. To tackle large instances, a greedy randomized adaptive search procedure (GRASP) metaheuristic, embedded with reactive parameter tuning, statistical filtering of solutions subjected to intensification, and a set of solution repairing procedures, is proposed. The GRASP is hybridized to each model to evaluate the outcomes of combining their individual merits. Computational experiments were performed on a new benchmark composed of 144 instances of different sizes, edge densities, network topologies, balance tolerances, and district capacities. The results show the effectiveness of the exact methodologies in solving the models and providing optimal solutions for the set of small instances. The GRASP was capable of tackling large networks, achieving feasible solutions to almost all instances. The results also show that the hybridized methodologies outperformed their standalone counterparts with respect to the attained primal and dual bounds. [ABSTRACT FROM AUTHOR]

In the last decade, decision diagrams (DDs) have been the basis for a large array of novel approaches for modeling and solving optimization problems. Many techniques now use DDs as a key tool to achieve state-of-the-art performance within other optimization paradigms, such as integer programming and constraint programming. This paper provides a survey of the use of DDs in discrete optimization, particularly focusing on recent developments. We classify these works into two groups based on the type of diagram (i.e., exact or approximate) and present a thorough description of their use. We discuss the main advantages of DDs, point out major challenges, and provide directions for future work. [ABSTRACT FROM AUTHOR]

Closeness centrality is a class of distance-based measures in the network analysis literature to quantify reachability of a given vertex (or a group of vertices) by other network agents. In this paper, we consider a new class of critical edge detection problems, in which given a group of vertices that represent an important subset of network elements of interest (e.g., servers that provide an essential service to the network), the decision maker is interested in identifying a subset of critical edges whose removal maximally degrades the closeness centrality of those vertices. We develop a general optimization framework, in which the closeness centrality measure can be based on any nonincreasing function of distances between vertices, which, in turn, can be interpreted as communication efficiency between them. Our approach includes three well-known closeness centrality measures as special cases: harmonic centrality, decay centrality, and k -step reach centrality. Furthermore, for quantifying the centrality of a group of vertices we consider three different approaches for measuring the reachability of the group from any vertex in the network: minimum distance to a vertex in the group, maximum distance to a vertex in the group, and the average centrality of vertices in the group. We study the theoretical computational complexity of the proposed models and describe the corresponding mixed integer programming formulations. For solving medium- and large-scale instances of the problem, we first develop an exact algorithm that exploits the fact that real-life networks often have rather small diameters. Then we propose two conceptually different heuristic algorithms. Finally, we conduct computational experiments with real-world and synthetic network instances under various settings, which reveal interesting insights and demonstrate the advantages and limitations of the proposed models and algorithms. The online appendices are available at https://doi.org/10.1287/ijoc.2018.0829. [ABSTRACT FROM AUTHOR]

In this paper, I view and present the multiobjective discrete optimisation problem as a particular case of disjunctive programming where one seeks to identify efficient solutions from within a disjunction formed by a set of systems. The proposed approach lends itself to a simple yet effective iterative algorithm that is able to yield the set of all nondominated points, both supported and nonsupported, for a multiobjective discrete optimisation problem. Each iteration of the algorithm is a series of feasibility checks and requires only one formulation to be solved to optimality that has the same number of integer variables as that of the single objective formulation of the problem. The application of the algorithm shows that it is particularly effective when solving constrained multiobjective discrete optimisation problem instances. [ABSTRACT FROM AUTHOR]

Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Specifically, a general characterization of optimality conditions is established and leveraged to design new cutting plane solution algorithms. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date. [ABSTRACT FROM AUTHOR]

In the bin-packing problem with minimum color fragmentation (BPPMCF), we are given a fixed number of bins and a collection of items, each associated with a size and a color, and the goal is to avoid color fragmentation by packing items with the same color within as few bins as possible. This problem emerges in areas as diverse as surgical scheduling and group event seating. We present several optimization models for the BPPMCF, including baseline integer programming formulations, alternative integer programming formulations based on two recursive decomposition strategies that utilize decision diagrams, and a branch-and-price algorithm. Using the results from an extensive computational evaluation on synthetic instances, we train a decision tree model that predicts which algorithm should be chosen to solve a given instance of the problem based on a collection of derived features. Our insights are validated through experiments on the aforementioned applications on real-world data. Summary of Contribution: In this paper, we investigate a colored variant of the bin-packing problem. We present and evaluate several exact mixed-integer programming formulations to solve the problem, including models that explore recursive decomposition strategies based on decision diagrams and a set partitioning model that we solve using branch and price. Our results show that the computational performance of the algorithms depends on features of the input data, such as the average number of items per bin. Our algorithms and featured applications suggest that the problem is of practical relevance and that instances of reasonable size can be solved efficiently. [ABSTRACT FROM AUTHOR]

We consider a variant of the vehicle routing problem (VRP) where each customer has a unit demand and the goal is to minimize the total cost of routing a fleet of capacitated vehicles from one or multiple depots to visit all customers. We propose two parallel algorithms to efficiently solve the column-generation-based linear-programming relaxation for this VRP. Specifically, we focus on algorithms for the "pricing problem," which corresponds to the resource-constrained elementary shortest path problem. The first algorithm extends the pulse algorithm for which we derive a new bounding scheme on the maximum load of any route. The second algorithm is based on random coloring from parameterized complexity which can be also combined with other techniques in the literature for improving VRPs, including cutting planes and column enumeration. We conduct numerical studies using VRP benchmarks (with 50–957 nodes) and instances of a medical home care delivery problem using census data in Wayne County, Michigan. Using parallel computing, both pulse and random coloring can significantly improve column generation for solving the linear programming relaxations and we can obtain heuristic integer solutions with small optimality gaps. Combining random coloring with column enumeration, we can obtain improved integer solutions having less than 2% optimality gaps for most VRP benchmark instances and less than 1% optimality gaps for the medical home care delivery instances, both under a 30-minute computational time limit. The use of cutting planes (e.g., robust cuts) can further reduce optimality gaps on some hard instances, without much increase in the run time. Summary of Contribution: The vehicle routing problem (VRP) is a fundamental combinatorial problem, and its variants have been studied extensively in the literature of operations research and computer science. In this paper, we consider general-purpose algorithms for solving VRPs, including the column-generation approach for the linear programming relaxations of the integer programs of VRPs and the column-enumeration approach for seeking improved integer solutions. We revise the pulse algorithm and also propose a random-coloring algorithm that can be used for solving the elementary shortest path problem that formulates the pricing problem in the column-generation approach. We show that the parallel implementation of both algorithms can significantly improve the performance of column generation and the random coloring algorithm can improve the solution time and quality of the VRP integer solutions produced by the column-enumeration approach. We focus on algorithmic design for VRPs and conduct extensive computational tests to demonstrate the performance of various approaches. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of estimating the size of branch-and-bound (B&B) trees for solving mixed-integer programs. We first prove that the size of the B&B tree cannot be approximated within a factor of 2 for general binary programs, unless P = N P. Second, we review measures of progress of the B&B search, such as the well-known gap and the often-overlooked tree weight, and propose a new measure, which we call leaf frequency. We study two simple ways to transform these progress measures into B&B tree-size estimates, either as a direct projection or via double-exponential smoothing, a standard time-series forecasting technique. We then combine different progress measures and their trends into nontrivial estimates using machine learning techniques, which yield more precise estimates than any individual measure. The best method that we have identified uses all individual measures as features of a random forest model. In a large computational study, we train and validate all methods on the publicly available MIPLIB and Coral general purpose benchmark sets. On average, the best method estimates B&B tree sizes within a factor of 3 on the set of unseen test instances, even during the early stage of the search, and improves in accuracy as the search progresses. It also achieves a factor of 2 over the entire search on each of the six additional sets of homogeneous instances that we tested. All techniques are available in version 7 of the branch-and-cut framework SCIP. Summary of Contribution: This manuscript develops a method for online estimation of the size of branch-and-bound trees, thereby combining methods of mixed-integer programming and machine learning. We show that high-quality estimations can be obtained using the presented techniques. The methods are also useful in everyday use of branch-and-bound algorithms to obtain approximate search-completion information. The manuscript is accompanied by an extensive online supplement comprising the code used for our simulations and an implementation of all discussed methods in the academic solver SCIP, together with the tools and instructions to train estimators for custom instance sets. [ABSTRACT FROM AUTHOR]

We introduce MathOptInterface, an abstract data structure for representing mathematical optimization problems based on combining predefined functions and sets. MathOptInterface is significantly more general than existing data structures in the literature, encompassing, for example, a spectrum of problems classes from integer programming with indicator constraints to bilinear semidefinite programming. We also outline an automated rewriting system between equivalent formulations of a constraint. MathOptInterface has been implemented in practice, forming the foundation of a recent rewrite of JuMP, an open-source algebraic modeling language in the Julia language. The regularity of the MathOptInterface representation leads naturally to a general file format for mathematical optimization we call MathOptFormat. In addition, the automated rewriting system provides modeling power to users while making it easy to connect new solvers to JuMP. Summary of Contribution: This paper describes a new abstract data structure for representing mathematical optimization models with a corresponding file format and automatic transformation system. The advances are useful for algebraic modeling languages, allowing practitioners to model problems more naturally and more generally than before. [ABSTRACT FROM AUTHOR]

We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, checking node fathoming, presolve, and duality gap measurement. Our branch-and-bound is predominantly a decision space search method because the branching is performed on the decision variables, akin to single objective problems, although we also sometimes split gaps and branch in the objective space. The various algorithms are implemented using a data structure for storing Pareto sets. Computational experiments are carried out on literature instances and on a new set of instances that we generate using a benchmark library (MIPLIB2017) for single objective problems. We also perform comparisons against the triangle splitting method from literature, which is an objective space search algorithm. Summary of Contribution: Biobjective mixed-integer optimization problems have two linear objectives and a mixed-integer feasible region. Such problems have many applications in operations research, because many real-world optimization problems naturally comprise two conflicting objectives to optimize or can be approximated in such a manner and are even harder than single objective mixed-integer programs. Solving them exactly requires the computation of all the nondominated solutions in the objective space, whereas some applications may also require finding at least one solution in the decision space corresponding to each nondominated solution. This paper provides an exact algorithm for solving these problems using the branch-and-bound method, which works predominantly in the decision space. Of the many ingredients of this algorithm, some parts are direct extensions of the single-objective version, but the main parts are newly designed algorithms to handle the distinct challenges of optimizing over two objectives. The goal of this study is to improve solution quality and speed and show that decision-space algorithms perform comparably to, and sometimes better than, algorithms that work mainly in the objective-space. [ABSTRACT FROM AUTHOR]

This paper presents a new local search approach, called randomized decomposition (RD), for solving nonlinear, nonconvex mathematical programs. Starting from a feasible solution, RD partitions the problem's decision variables into a randomly ordered list of randomly generated subsets. RD then optimizes over the variables in each subset, keeping all other variables fixed. Unlike most other decomposition methods, no knowledge of the problem structure is required. RD has been combined with a metaheuristic RDPerturb, for escaping local optima, to create a generic framework for solving mathematical programs, especially hard combinatorial nonconvex problems. The framework has been implemented as an optimization platform we call RDSolver and successfully applied to over 400 instances of the quadratic assignment problem (QAP). The results obtained by RDSolver are competitive with the solutions obtained by heuristics specially tailored for those problems, even though RDSolver is a general purpose mathematical programming solver. In addition to a strong performance on previously solved problems, RDSolver has found two new best known solutions and provided solutions to 68 large QAP problems for which no solutions have been previously reported. [ABSTRACT FROM AUTHOR]