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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]

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]

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]

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]

The introduction of edge-finding techniques was a significant development in constraint-based scheduling. Today, edge finders are still the state of the art in the disjunctive case and a technique of interest in cumulative scheduling. This paper reconsiders edge-finding algorithms for cumulative scheduling and shows that Nuijten's edge finder, and its derivatives, are incomplete because they use an invalid dominance rule. We then present a correct cumulative edge finder running in time O(n²k), where n is the number of tasks and k the number of different capacity requirements of the tasks. The new algorithm is organized in two phases and first uses dynamic programming to precompute the innermost maximization in the edge-finder specification. The paper also proposes the first extended edge-finding algorithms that run in time O(n²k), improving the running time of available algorithms. Finally, the paper discusses how to speed up the algorithm in practice and how the first phase can be used to improve algorithms based on energetic reasoning. [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]

In this paper, we present two versions of an algorithm for the computation of all nondominated extreme points in the outcome set of a multiobjective integer programme. We define adjacency of these points based on weight space decomposition. Thus, our algorithms generalise the well-known dichotomic scheme to compute the set of nondominated extreme points in the outcome set of a biobjective programme. Both algorithms are illustrated with and numerically tested on instances of the assignment and knapsack problems with three objectives. [ABSTRACT FROM AUTHOR]

With improved tools for collecting genetic data from natural and experimental populations, new opportunities arise to study fundamental biological processes, including behavior, mating systems, adaptive trait evolution, and dispersal patterns. Full use of the newly available genetic data often depends upon reconstructing genealogical relationships of individual organisms, such as sibling reconstruction. This paper presents a new optimization framework for sibling reconstruction from single generation microsatellite genetic data. Our framework is based on assumptions of parsimony and combinatorial concepts of Mendel's inheritance rules. Here, we develop a novel optimization model for sibling reconstruction as a large-scale mixed-integer program (MIP), shown to be a generalization of the set covering problem. We propose a new heuristic approach to efficiently solve this large-scale optimization problem. We test our approach on real biological data as presented in other studies as well as simulated data, and compare our results with other state-of-the-art sibling reconstruction methods. The empirical results show that our approaches are very efficient and outperform other methods while providing the most accurate solutions for two benchmark data sets. The results suggest that our framework can be used as an analytical and computational tool for biologists to better study ecological and evolutionary processes involving knowledge of familial relationships in a wide variety of biological systems. [ABSTRACT FROM AUTHOR]

In many branch-and-price algorithms, the column generation pricing problem consists of computing feasible paths in a network. In this paper, we show how, in this context, path-reduced costs can be used to remove some arcs from the underlying network without compromising optimality, and we introduce a bidirectional search technique to compute these reduced costs. This arc elimination method can lead to a substantial speedup of the pricing process and the overall branch-and-price algorithm. Special attention is given to variants of shortestpath problems with resource constraints. Computational results obtained for the vehicle routing problem with time windows show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Despite the fact that no polynomial-time algorithm is known for solving mixed-integer programming (MIP) problems, there has been remarkable success in recent years in solving a wide range of difficult MIPs. In this paper, we take a look at some of the hardest problems in the MIPLIB 2003 test set and show how Xpress-MP can be used to solve some of the problems that were previously thought to be intractable. [ABSTRACT FROM AUTHOR]

This paper solves FC_2TDC, the two-staged fixed-orientation two-dimensional cutting stock problem. FC_2TDC is a variant of the constrained two-dimensional cutting problem where each piece is produced, in the final cutting pattern, by at most two cuts, and each piece has a fixed orientation. It is solved by an algorithm that combines a strip-generation procedure with beam search (BS). BS, which is a truncated branch-andbound, investigates a subset of elite nodes and permanently fathoms the others. It chooses the elite nodes based on an evaluation operator. The importance of the evaluation operator on the performance of BS is highlighted by comparing a local beam search (LBS) that uses a priority cost-evaluation operator to a global beam search (GBS) that adopts a global cost-evaluation operator. Computational results, based on several medium and large instances, further show that LBS provides good solutions, whereas GBS gives (near) optimal solutions within reasonable computational time. [ABSTRACT FROM AUTHOR]

Embedding cuts into a branch-and-cut framework is a delicate task, especially when a large set of cuts is available. In this paper we describe a separation heuristic for {0, ⅛}-cuts, a special case of Chvátal-Gomory cuts, that tends to produce many violated inequalities within relatively short time. We report computational results on a large testbed of integer linear programming (ILP) instances of combinatorial problems including satisfiability, max-satisfiability, and linear ordering problems, showing that a careful cut-selection strategy produces a considerable speedup with respect to the cases in which either the separation heuristic is not used at all, or all of the cuts it produces are added to the LP relaxation. [ABSTRACT FROM AUTHOR]

This paper considers the multimode resource-constrained project-scheduling problem (MRCPSP) with a minimum-makespan objective. An exact branch and cut algorithm is presented based on the integer linear programming (ILP) formulation of the problem. In the preprocessing stage, lower bounds on the distance between each pair of precedence-constrained activities are derived. These bounds are used to reduce the number of variables in the model and to generate cuts that tighten the linear programming relaxation. The solution process is accelerated by an adaptive branching scheme in conjunction with a bound-tightening scheme that is called iteratively after branching. To find good feasible solutions in the early stages of the computations, a high-level neighborhood search strategy known as local branching is included. Here, a neighborhood of a feasible solution is defined by the linear inequalities in the ILP model and is searched first. As implemented, the full algorithm is exact rather than heuristic in nature. Numerical results are reported for 20- and 30-activity benchmark problems. These are the largest instances available and are generally viewed to be notoriously difficult. Up until now, there were no confirmed optimal solutions for any of the 552 30-activity instances. We were able to find several better solutions and to show that at least 506 are optimal. [ABSTRACT FROM AUTHOR]

This paper intends to show that the time needed to solve mixed-integer-programming problems by branch and bound can be roughly predicted early in the solution process. We construct a procedure that can be implemented as part of an MIP solver. It is based on analyzing the partial tree resulting from running the algorithm for a short period of time and predicting the shape of the whole tree. The procedure is tested on instances from the literature. This work was inspired by the practical applicability of such a result. [ABSTRACT FROM AUTHOR]

This paper presents a new network-flow formulation for the problem of predicting 3D protein structures using threading. Several integer-programming models based on this formulation are proposed and compared. These models allow for an efficient decomposition and for the application of a parallel branch-and-cut algorithm, significantly reducing the running time. The efficiency of our approach has been confirmed by extensive computational experiments. [ABSTRACT FROM AUTHOR]

In this paper we address the pure parsimony haplotyping problem: Find a minimum number of haplotypes that explains a given set of genotypes. We prove that the problem is APX-hard and present a 2k-1-approximation algorithm for the case in which each genotype has at most k ambiguous positions. We further give a new integer-programming formulation that has (for the first time) a polynomial number variables and constraints. Finally, we give approximation algorithms, not based on linear programming, whose running times are almost linear in the input size. [ABSTRACT FROM AUTHOR]

In this paper, a tabu-search algorithm enhanced by scatter search is presented. The algorithm solves the DNA sequencing problem with negative and positive errors, yielding outcomes of high quality We compare the new method with two other metaheuristic approaches: a previous tabu-search method and a hybrid genetic algorithm, and also with an old branch-and-bound approach. [ABSTRACT FROM AUTHOR]

Stochastic integer programs (SIPs) represent a very difficult class of optimization problems arising from the presence of both uncertainty and discreteness in planning and decision problems. Although applications of SIPs are abundant, nothing is available by way of computational software. On the other hand, commercial software packages for solving deterministic integer programs have been around for quite a few years, and more recently, a package for solving stochastic linear programs has been released. In this paper, we describe how these software tools can be integrated and exploited for the effective solution of general-purpose SIPs. We demonstrate these ideas on four problem classes from the literature and show significant computational advantages. [ABSTRACT FROM AUTHOR]

The partially observed Markov decision process (POMDP) is a generalization of a Markov decision process that allows for noise-corrupted and costly observations of the underlying system state. The value function of the finite horizon POMDP is known to be piecewise affine and convex in the probability mass vector over the state space. Such a function can be represented by a finite set of affine functions. In this paper, we develop and evaluate an exact algorithm, GAMIP, which combines a genetic algorithm and a mixed integer program to construct the minimal set of affine functions that describes the value function. Numerical results indicate that GAMIP takes up to 60% less time to construct the minimal set than does the most efficient linear programming-based exact solution method in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the Reversal Median Problem (RMP), which arises in computational biology as a basic model for the reconstruction of evolutionary trees. Given q genomes, RMP calls for another genome such that the sum of the reversal distances between this genome and the given ones is minimized. So far, the problem has been considered too complex to derive mathematical models useful for its analysis and solution. We provide a powerful graph-theoretic relaxation of RMP, essentially calling for a perfect matching in a graph that forms the maximum number of cycles jointly with q given perfect matchings. By using this relaxation, we can show the complexity of RMP as well as design effective algorithms for its exact and heuristic solution. We report the solution of a few hundred instances associated with real-world genomes. [ABSTRACT FROM AUTHOR]

Algorithms and computer-based tools for analyzing infeasible linear and nonlinear programs have been developed in recent years, but few such tools exist for infeasible mixed-integer or integer linear programs. One approach that has proven especially useful for infeasible linear programs is the isolation of an Irreducible Infeasible Set of constraints (IIS), a subset of the constraints defining the overall linear program that is itself infeasible, but for which any proper subset is feasible. Isolating an IIS from the larger model speeds the diagnosis and repair of the model by focussing the analytic effort. This paper describes and tests algorithms for finding small infeasible sets in infeasible mixed-integer and integer linear programs; where possible these small sets are IISs. [ABSTRACT FROM AUTHOR]