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Shared parking can fully utilize idle parking resources and alleviate parking conflicts. However, existing operational strategies suffer from low utilization of parking resources and neglect of parker preferences. This paper focuses on how to solve the problem of matching many-to-one in the shared parking process considering the benefits of parkers and parking lots. Given this, a stable matching mechanism is proposed based on the improved deferred-acceptance algorithm. Meanwhile, we develop a parking space rental and allocation model for multiple parking lots. A series of factors were considered in the model, such as the profits of the parking lot, the potential loss due to refusal of parking requests and rented spaces, and the walking distance to the destination of parkers. Parking requests are assigned to specific parking lots considering the preferences of the parkers, and then the allocation of shared parking spaces is achieved through the proposed matching mechanism. In numerical examples, we compare the proposed allocation method with the other two allocation methods. The results indicate that compared with the other two allocation methods, the proposed matching mechanism could achieve optimal allocation of parking spaces and a stable match between shared parking and parkers, which verifies the superiority of our method. [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]

Large-scale natural disaster or malicious attacks could cause serious damages to the communication network in smart grids. If the damaged network cannot be recovered timely, greater threat will be brought to the secure and stable operation of smart grids. In this paper, a link importance-based network recovery method for large-scale failures in smart grids has been proposed. Firstly, the link importance for the network can be obtained according to the link importance for the service type and the importance of the service type for the network; secondly, a network recovery model, which is 0–1 integer programming, has been established to recover more important communication services with limited recovery resources; finally, we propose a heuristic algorithm to solve the problem and reduce the computational expenditure. The simulation experiments are carried out to evaluate the performance of the proposed algorithm. The simulation results illustrate that our network recovery method is applicable to the large-scale failures and the link which carries the high-priority service can be first recovered in this paper, thus which further ensures the safe and stable operation of smart grids. [ABSTRACT FROM AUTHOR]

Multi-objective programming problem often contains numerous efficient solutions, which confuses the decision-maker. To assist in selecting the most desirable solution, optimizing a function over the efficient set becomes crucial. In this paper, we present a novel method for optimizing a general quadratic function over the efficient set of a multi-objective integer linear programming problem. To solve this problem, a ranking approach and efficiency test is utilized. The proposed methodology obtains a globally optimal solution by systematically scanning ranked solutions of an integer quadratic programming problem until the efficiency condition is satisfied. For generating ranked solutions, we construct a related integer linear programming problem. Then, ranked solutions of the integer linear programming problem are used for enumerating ranked solutions of the integer quadratic programming problem. The convergence of our algorithm is established theoretically, and its steps are illustrated using a numerical example. Aparticular case of the proposed method for optimizing a linear function over the efficient set of a multi-objective integer linear programming problem is also discussed. Further, extensive computational results demonstrate the effectiveness of our method for solving problems with large number of constraints, variables, and objective functions. Moreover, comparative analysis shows that the developed algorithm came out to be computationally more efficient as compared to the existing state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

This document presents in detail the mathematical formulation of the second renewable energy auction in Colombia, used for the allocation of long-term energy contracts, which was carried out through a double-sided auction, defined in Resolutions 4-0590 and 4-0591 of 2019 from the UPME. The mixed integer linear programming model developed in this paper solves an optimization problem that seeks the combination of offers that maximizes the benefit of the consumer, subject to operational and economic constraints proposed by regulatory mechanisms. The effectiveness of the algorithm developed in Python was tested by validating it with real data, obtaining the same results published by UPME. [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 uncertainty factors operation scheduling in the lead to inability to obtain accurate time of operation and ends under emergency rescue situation. In order to solve the problem, this paper proposed a grey scheduling model and a hybrid grey cuckoo algorithm. The model used three parameters interval grey number and the four parameters interval grey number to describe the uncertain time of operation and the uncertain ends. Then, it defined the possibility measure and necessity measure, proposed the index of delay confidence, which was used to estimate the probability of operation tardiness. After that, this paper established a gray mixed integer programming model with minimize average credibility of operation tardiness, and presented a solution method of the mixed grey cuckoo search algorithm. A classic example of size 6 ( 3) X 3 verified the proposed algorithm. The results show that the proposed algorithm can solve the problem very well, and the performance is better than the basic cuckoo algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a new mixed integer programming formulation and branch and cut (BC) algorithm to solve the dial-a-ride problem (DARP). The DARP is a route-planning problem where several vehicles must serve a set of customers, each of which has a pickup and delivery location, and includes time window and ride time constraints. We develop "restricted fragments," which are select segments of routes that can represent any DARP route. We show how to enumerate these restricted fragments and prove results on domination between them. The formulation we propose is solved with a BC algorithm, which includes new valid inequalities specific to our restricted fragment formulation. The algorithm is benchmarked on existing and new instances, solving nine existing instances to optimality for the first time. In comparison with current state-of-the-art methods, run times are reduced between one and two orders of magnitude on large instances. [ABSTRACT FROM AUTHOR]

This paper explores the improvement of the network robustness against cascading failures by edge addition. Several edge-adding strategies are compared, including the random edge-adding strategy, the high betweenness centrality edge-adding strategy, the high Pagerank centrality strategy and the min–max edge-adding strategy. In the min–max edge-adding strategy, the problem for robustness improvement of complex networks is formulated as a nonlinear integer programming problem, and an algorithm is proposed to solve this problem. From the numerical experiments, we find that the min–max edge-adding strategy is more effective in improving the network robustness against cascading failures than the other strategies. Finally, this work can provide guidance for the design of complex networks to prevent potential cascading failures. [ABSTRACT FROM AUTHOR]

This paper investigates a very practical and commonly encountered problem in state estimation. It is related to the placement of measurements in order to make an otherwise unobservable system observable. Typically, this is a situation that is frequently encountered during the daily operation as one or more of the measurements become unavailable due to various unexpected reasons. Under such circumstances, the state estimator resorts to the use of pseudo-measurements in order to recover observability and solve the state estimation problem. Pseudo-measurements that will make the system observable can be selected by applying one of the well-developed network observability analysis techniques in a repetitive fashion adding one candidate measurement at a time until the system is no longer unobservable. As the system size increases, this approach may prove computationally expensive. A nonrepetitive solution has also been proposed. However, its computational requirements grow rapidly with increasing number of observable islands that may exist in large scale systems. This paper presents an alternative approach which will be shown to be suitable for large scale power systems providing a compromise between the two existing techniques. Examples are given to highlight the main benefits of the proposed method. [ABSTRACT FROM PUBLISHER]

The paper proposes a mathematical formalism for describing artificial sense-of-touch systems. Mathematical models for obtaining, processing, and interpreting tactile information are provided. Problems of encoding and reproducing tactile information are formulated and algorithms for solving these problems are proposed. The problem of interpreting tactile information is considered, and the corresponding simple mathematical model is studied. Within the framework of this simple model, an exact solution of the interpretation problem is obtained for the case of finite deformations, and the insufficiency of the linear method (Hooke’s law) for describing problems of interpreting tactile data is shown. The presentation of mathematical models for the theory of artificial sense-of-touch systems in this paper is the first such detailed presentation in the Russian literature. These models are of interest to mathematicians, mechanicians, physicians, and engineers who construct or use artificial sense-of-touch systems. [ABSTRACT FROM AUTHOR]

The maximum cardinality subset selection problem requires finding the largest possible subset from a set of objects, such that one or more conditions are satisfied. An important extension of this problem is to extract multiple subsets, where the addition of one more object to a larger subset would always be preferred to increases in the size of one or more smaller subsets. We refer to this as the multiple subset maximum cardinality selection problem ( MSMCSP). A recently published branch-and-bound algorithm solves the MSMCSP as a partitioning problem. Unfortunately, the computational requirement associated with the algorithm is often enormous, thus rendering the method infeasible from a practical standpoint. In this paper, we present an alternative approach that successively solves a series of binary integer linear programs to obtain a globally optimal solution to the MSMCSP. Computational comparisons of the methods using published similarity data for 45 food items reveal that the proposed sequential method is computationally far more efficient than the branch-and-bound approach. [ABSTRACT FROM AUTHOR]

In the clutter environments, persistently tracking multiple objects is still a very challenging problem. In this paper, an A * algorithm with dynamic weights is developed to solve this problem. Firstly, the problem of multiple object tracking is considered as an integer programming of flow network model. Based on this model, afterward, we relax the problem of integer programming problem to a standard linear programming and achieve the global optimal solution with the proposed algorithm, which has been proven in this work. Compared with other advanced methods employed in the modern complex environments, the proposed method is on the merit of lower calculation complexity and better tracking accuracy and robustness. Finally, the simulation result is demonstrated, which reveals that the proposed algorithm saves the time costs vastly. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Minimum Reaction Insertion (MRI) problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA)-based model, the solution of the FBA-based model tends to include more reactions than that of the Boolean model. However, solving MRI using the Boolean model is computationally more expensive than using the FBA-based model since the Boolean model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database, we have found that the developed method can appropriately solve MRI in the Boolean model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean model. Our developed software is available at “http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html.” [ABSTRACT FROM AUTHOR]

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of lower dimension. Combining this approach with knowledge of the geometry of feasible integer solutions yields an algorithm for solving highly symmetric integer linear programs which only takes time which is linear in the number of constraints and quadratic in the dimension. [ABSTRACT FROM AUTHOR]

Abstract: Quadratic knapsack problem has a central role in integer and nonlinear optimization, which has been intensively studied due to its immediate applications in many fields and theoretical reasons. Although quadratic knapsack problem can be solved using traditional nonlinear optimization methods, specialized algorithms are much faster and more reliable than the nonlinear programming solvers. In this paper, we study a mixed linear and quadratic knapsack with a convex separable objective function subject to a single linear constraint and box constraints. We investigate the structural properties of the studied problem, and develop a simple method for solving the continuous version of the problem based on bi-section search, and then we present heuristics for solving the integer version of the problem. Numerical experiments are conducted to show the effectiveness of the proposed solution methods by comparing our methods with some state of the art linear and quadratic convex solvers. [Copyright &y& Elsevier]

Abstract: There are many problems in computational geometry for which the best know algorithms take time (or more) in the worst case while only very low lower bounds are known. In this paper we describe a large class of problems for which we prove that they are all at least as difficult as the following base problem 3sum: Given a set S of n integers, are there three elements of S that sum up to 0. We call such problems 3sum-hard. The best known algorithm for the base problem takes time. The class of 3sum-hard problems includes problems like: Given a set of lines in the plane, are there three that meet in a point?; or: Given a set of triangles in the plane, does their union have a hole? Also certain visibility and motion planning problems are shown to be in the class. Although this does not prove a lower bound for these problems, there is no hope of obtaining solutions for them unless we can improve the solution for the base problem. [Copyright &y& Elsevier]

Abstract: In this paper we study the permutation flow shop scheduling problem with order acceptance and weighted tardiness (PFSS-OAWT) faced by firms that have a number of candidate orders to be selected and scheduled on a flow shop production line. The objective is to maximize the total net profit with weighted tardiness penalties. We formulate the PFSS-OAWT problem as an integer programming (IP) model. A heuristic algorithm named Simulated Annealing Based on Partial Optimization (SABPO) is developed for solving the IP model and obtaining near-optimal solutions. Computational studies are carried out on solving 160 problem instances with different scales (small, medium, large, and very large). The experimental results show that the SABPO algorithm exhibits good optimality for small-sized problems and robustness for medium/large-sized problems compared with benchmarks. [Copyright &y& Elsevier]

Presenting a more efficient mathematical model for the problem of integrating lot sizing, loading, and scheduling in capacitated flexible flow shops with sequence-dependent setups is the main novelty of this paper. In comparison to the former model, fewer variables and constraints of the current model makes it easier to be solved. Comparison between this model and the former one shows the superiority of this model. To validate the new model, an efficient lower bound has been provided. Mixed integer programming-based algorithms have been used to solve this model. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we integrate at the tactical level two decision problems arising in container terminals: the berth allocation problem, which consists of assigning and scheduling incoming ships to berthing positions, and the quay crane assignment problem, which assigns to incoming ships a certain quay crane profile (i.e. number of quay cranes per working shift). We present two formulations: a mixed integer quadratic program and a linearization which reduces to a mixed integer linear program. The objective function aims, on the one hand, to maximize the total value of chosen quay crane profiles and, on the other hand, to minimize the housekeeping costs generated by transshipment flows between ships. To solve the problem we developed a heuristic algorithm which combines tabu search methods and mathematical programming techniques. Computational results on instances based on real data are presented and compared to those obtained through a commercial solver. [Copyright &y& Elsevier]

In this paper, we consider the optimal design of finite-impulse response (FIR) filters with coefficients expressed as sums of signed powers-of-two (SPT) terms, where the normalized peak ripple (NPR) is taken as the performance measure. This problem is formulated as a mixed-integer programming problem. Based on a transformation between two different integer spaces and the computation of the optimal scaling factor for a given set of coefficients, this mixed integer programming problem is transformed into an equivalent integer programming problem. Then, an efficient algorithm based on a discrete filled function is developed for solving this equivalent problem. For illustration, some numerical examples are solved. [ABSTRACT FROM AUTHOR]

In this paper an integer linear program is formulated to identify the least cost two-level hierarchical network. This network must include a primary path from a predetermined starting node to a predetermined terminus node. In addition, each node not on the primary path must be connected to some node on that path via a secondary path. Transshipment facilities are required at the intersections of the primary and secondary paths. Consequently, the formulation directly considers the number and locations o[ transshipment facilities in determining the minimal cost network. A heuristic is presented which employs a K Shortest Path algorithm and a Minimum Spanning Tree algorithm. Heuristic results of two sample problems are presented and compared to the results obtained by solving the integer LP formulation. [ABSTRACT FROM AUTHOR]