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We study the quadratic cycle cover problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and use facial reduction to make these strictly feasible. We investigate a nontrivial relationship between the transformation matrix used in the reduction and the structure of the graph, which is exploited in an efficient algorithm that constructs this matrix for any instance of the problem. To solve our relaxations, we propose an algorithm that incorporates an augmented Lagrangian method into a cutting-plane framework by utilizing Dykstra's projection algorithm. Our algorithm is suitable for solving SDP relaxations with a large number of cutting-planes. Computational results show that our SDP bounds and efficient cutting-plane algorithm outperform other QCCP bounding approaches from the literature. Finally, we provide several SDP-based upper bounding techniques, among which is a sequential Q-learning method that exploits a solution of our SDP relaxation within a reinforcement learning environment. Summary of Contribution: The quadratic cycle cover problem (QCCP) is the problem of finding a set of node-disjoint cycles covering all the nodes in a graph such that the total interaction cost between successive arcs is minimized. The QCCP has applications in many fields, among which are robotics, transportation, energy distribution networks, and automatic inspection. Besides this, the problem has a high theoretical relevance because of its close connection to the quadratic traveling salesman problem (QTSP). The QTSP has several applications, for example, in bioinformatics, and is considered to be among the most difficult combinatorial optimization problems nowadays. After removing the subtour elimination constraints, the QTSP boils down to the QCCP. Hence, an in-depth study of the QCCP also contributes to the construction of strong bounds for the QTSP. In this paper, we study the application of semidefinite programming (SDP) to obtain strong bounds for the QCCP. Our strongest SDP relaxation is very hard to solve by any SDP solver because of the large number of involved cutting-planes. Because of that, we propose a new approach in which an augmented Lagrangian method is incorporated into a cutting-plane framework by utilizing Dykstra's projection algorithm. We emphasize an efficient implementation of the method and perform an extensive computational study. This study shows that our method is able to handle a large number of cuts and that the resulting bounds are currently the best QCCP bounds in the literature. We also introduce several upper bounding techniques, among which is a distributed reinforcement learning algorithm that exploits our SDP relaxations. [ABSTRACT FROM AUTHOR]

A recent study on the classical capacitated vehicle routing problem (CVRP) introduced an adaptive version of the widely used iterated local search paradigm, hybridized with a path-relinking (PR) strategy. The solution method, called adaptive iterated local search (AILS)-PR, outperformed existing meta-heuristics for the CVRP on benchmark instances. However, tests on large-scale instances suggest that PR is too slow, making AILS-PR less advantageous in this case. To overcome this challenge, this paper presents an AILS combined with mechanisms to handle large CVRP instances, called AILS-II. The computational cost of this implementation is reduced, whereas the algorithm also searches the solution space more efficiently. AILS-II is very competitive on smaller instances, outperforming the other methods from the literature with respect to the average gap to the best-known solutions. Moreover, AILS-II consistently outperforms the state of the art on larger instances with up to 30,000 vertices. History: Accepted by Ted Ralphs, Area Editor for Software Tools. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Software Tools for Vehicle Routing. Funding: This work was supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo [Grants 2013/07375-0, 2019/22067-6, and 2022/05803-3] and the Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grants 309385/2021-0 and 403735/2021-1]. 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.2023.0106) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2023.0106). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

Model calibration is challenging for large-scale system models with a great number of variables. Existing approaches to partitioning system models and prioritizing data acquisition rely on heuristics rather than formal treatments. The sensor placement problem in physical dynamic systems points to a promising avenue for formalizing data acquisition priorities, which addresses the following question for system models: With the model at hand and pre-existing data availability on a subset of model variables, what are the (next) k model variables that would bring the largest utility to model calibration, once their data are acquired? In this study, we formalize this problem as a combinatorial optimization and adapt two solutions, the information-entropy approach and the miss-probability approach, from physical dynamic systems to system models in management sciences. Next, based on the idea of the data availability partition, we develop a third solution. The new approach can be understood from the entropy perspective and is embedded in the theoretical framework for the evaluation of side information. Our solution applies to system models of all topologies: analytical results of the optimal placement are derived for binary/multinary trees; for general (directed) tree structures, an algorithm to determine the optimal placement is devised, whose complexity is upper-bounded by O(nlog2(n)) for an n-variable system; for arbitrary model topologies with the presence of loops, sequential-optimal and simulated-annealing schemes are formulated. Three approaches are compared on a validating example; our solution outperforms the two alternatives. Application on a multicompartment system demonstrates the toolkit's practical use. 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.2022.0128) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0128). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

The time-dependent traveling salesman problem with time windows (TDTSPTW) is a variant of the well-known traveling salesman problem with time windows, in which travel times are not assumed to be constant. The TDTSPTW accounts for the effects of congestion at the planning level, being particularly suited for distribution problems in large cities. In this paper we develop a labeling-based algorithm for the TDTSPTW that incorporates partial dominance and generalizes several state-of-the-art components from the time-independent related literature. We propose a framework general enough to be applied to the TDTSPTW and its variant without time windows, with the objective of minimizing the duration or the makespan. As part of the framework, we introduce a new state-space relaxation specifically designed for the time-dependent context. Extensive computational experiments show the effectiveness of the overall approach and the impact of the new relaxation, outperforming several recent algorithms proposed for these variants on more than 9,000 benchmark instances. In addition, we frame the minimum tour duration problem within the time-dependent literature and include it as a benchmark for our algorithm, obtaining improved computation times and 31 new optimal solutions. Summary of Contribution: In this paper, we study the time-dependent traveling salesman problem with time windows (TDTSPTW), a difficult single-vehicle routing problem that incorporates more realistic travel time functions than its classic time-independent counterpart. As a result, the TDTSPTW is harder to solve, as it requires more complex models and algorithms. Using state-of-the-art optimization techniques, we propose an efficient solution approach for the TDTSPTW and some related variants that outperforms the previous approaches in the literature. Our paper emphasizes the importance of algorithmic design and efficient implementations to tackle relevant practical combinatorial optimization problems—in particular, for time-dependent problems. Moreover, the resulting algorithm fosters a new research direction regarding exact algorithms for time-dependent problems using dynamic programming and relaxation techniques. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research has been funded by Fondo para la Investigación Científica y Tecnológica (FONCyT) [Grants PICT-2016-2677 and PICT-2018-2961] from the Ministry of Science, Argentina, and by the Google Latin America Research Award (LARA) 2019. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.1236. [ABSTRACT FROM AUTHOR]

In designing ideal multiple recursive random number (RN) generators (MRGs), the best set of multipliers, in terms of the lattice structure of the RNs produced, is sought. As the order of the MRG increases, the number of possible sets of multipliers to be examined grows exponentially This paper proposes a genetic algorithm for designing good MRGs. The set of multipliers associated with the MRG is encoded as a binary string. Via the operations of reproduction, crossover, and mutation, new sets of multipliers are generated. The spectral values of the MRGs are calculated to guide the search process. As an illustration, the proposed algorithm is employed to find good sets of multipliers for MRGs of orders three and four. The results are better than those derived from other studies. To conclude, this paper not only finds better MRGs of orders three and four, but also develops an algorithm for designing MRGs of higher orders. [ABSTRACT FROM AUTHOR]

In this paper, we consider a variant of adaptive robust combinatorial optimization problems where the decision maker can prepare K solutions and choose the best among them upon knowledge of the true data realizations. We suppose that the uncertainty may affect the objective and the constraints through functions that are not necessarily linear. We propose a new exact algorithm for solving these problems when the feasible set of the nominal optimization problem does not contain too many good solutions. Our algorithm enumerates these good solutions, generates dynamically a set of scenarios from the uncertainty set, and assigns the solutions to the generated scenarios using a vertex p-center formulation, solved by a binary search algorithm. Our numerical results on adaptive shortest path and knapsack with conflicts problems show that our algorithm compares favorably with the methods proposed in the literature. We additionally propose a heuristic extension of our method to handle problems where it is prohibitive to enumerate all good solutions. This heuristic is shown to provide good solutions within a reasonable solution time limit on the adaptive knapsack with conflicts problem. Finally, we illustrate how our approach handles nonlinear functions on an all-or-nothing subset problem taken from the literature. Summary of Contribution: Our paper describes a new exact algorithm for solving adaptive robust combinatorial optimization problems when the feasible set of the nominal optimization problems does not contain too many good solutions. Its development relies on a progressive relaxation of the problem augmented with a row-and-column generation technique. Its efficient execution requires a reformulation of this progressive relaxation, coupled with dominance rules and a binary search algorithm. The proposed algorithm is amenable to exploiting the special structures of the problems considered as illustrated with various applications throughout the paper. A practical view is provided by the proposition of a heuristic variant. Our computational experiments show that our proposed exact solution method outperforms the existing methodologies and therefore pushes the computational envelope for the class of problems considered. [ABSTRACT FROM AUTHOR]

We propose and evaluate branch-and-price approaches for vehicle routing problems with picking, loading, and soft time windows. This general type of vehicle routing problem is of particular relevance in the same-day delivery context, in which fast routing algorithms are required because of the commitment to real-time delivery in the presence of high customer order frequencies. To boost the performance of the branch-and-price algorithms, we introduce the new method of tree-compatible labeling with nondominance trees. This method represents cost functions by a fixed number of breakpoints and uses a specialized tree-based data structure to store Pareto-optimal labels. We prove the theoretical soundness of the new method and evaluate its performance numerically with respect to pricing, column generation, and branch-and-price. Our numerical results show that the method yields substantial performance gains. In particular, we show that, with the new method, branch-and-price is able to reliably generate within a few minutes close to optimal solutions for problem instances with 50 customers. By additional experiments with classic vehicle routing problems with hard time windows, we show that the performance gains of our method result from its ability to handle cost functions in the pricing step. Our approach is the first branch-and-price approach for vehicle routing with picking, loading, and soft time windows. As such, it represents an exact routing algorithm that is able to reliably satisfy the runtime requirements of real-time delivery services. Summary of Contribution: In this paper, we propose the first branch-and-price approaches for a general class of vehicle routing problems with picking, loading, and soft time windows. This problem class is of particular importance for real-time delivery services, for which customers expect to be served within only a few hours after their order has been placed. We provide a problem formulation that takes into account that short runtimes of routing algorithms are required, that the upper bounds of the customers' time windows may be violated at a certain cost, and that a significant part of the delivery time window is consumed by picking orders from a warehouse and loading orders into vehicles. Solving the problem with branch-and-price requires the use of cost functions as elements of the labels in the pricing step. We propose a method that approximates these cost functions and leverages the computational performance of nondominance tree data structures for solving the pricing problem. We prove the theoretical soundness of this new method for exact branch-and-price, and we show numerically that the method leads to a significant performance increase of branch-and-price. The paper lies at the intersection of computing and operations research, in particular because our algorithms are designed to leverage the computational performance of advanced data structures for solving a combinatorial optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we tackle the resolution of chance-constrained problems reformulated via sample average approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program (MIP) cursed with Big-Ms. We introduce an exact resolution method for the MIP that combines the addition of a set of valid inequalities to tighten the linear relaxation bound with coefficient strengthening and constraint screening algorithms to improve its Big-Ms and considerably reduce its size. The proposed valid inequalities are based on the notion of k-envelopes and can be computed off-line using polynomial-time algorithms and added to the MIP program all at once. Furthermore, they are equally useful to boost the strengthening of the Big-Ms and the screening rate of superfluous constraints. We apply our procedures to a probabilistically constrained version of the DC optimal power flow problem with uncertain demand. The chance constraint requires that the probability of violating any of the power system's constraints be lower than some positive threshold. In a series of numerical experiments that involve five power systems of different size, we show the efficiency of the proposed methodology and compare it with some of the best performing convex inner approximations currently available in the literature. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported in part by the European Research Council under the EU Horizon 2020 research and innovation program [Grant 755705], in part by the Spanish Ministry of Science and Innovation [Grant AEI/10.13039/501100011033] through project PID2020-115460GB-I00, and in part by the Junta de Andalucía and the European Regional Development Fund through the research project P20_00153. Á. Porras is also financially supported by the Spanish Ministry of Science, Innovation and Universities through the University Teacher Training Program with fellowship number FPU19/03053. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.0302. [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]

This paper makes a contribution to the branch and cut approach to the capacitated vehicle-routing problem (CVRP). In the CVRP, the demands of a set of customers have to be met at minimum total travel cost using vehicles of identical capacity based at a single depot. The potential of maximally violated mod-p cutting-planes (Caprara et al. 2000) for the CVRP is investigated via a computational study. The foundation of the assessment is formed by classes of problem-specific constraints taken from the literature. In several separation algorithms for the CVRP, it is advantageous to shrink inclusionwise maximal minimum-weight cuts in support graphs as preprocessing. It is mentioned how a partition of the set of customers into such mincuts can be computed in a fast and elegant way using the mincut algorithm of Hao and Orlin (1994). Interestingly, maximally violated mod-p cuts, which are general-purpose cuts of Chvátal-Gomory type, stand comparison with problem-specific cuts for the CVRP and they are clearly useful on top of such cuts. The first-time proven optimal solution of the CVRP instance B-n68-k9 is reported. The computation used a branching strategy with far lookahead and relied on maximally violated mod-p cuts. This paper on maximally violated cuts belongs to a set of papers originating from Applegate et al. (1995) where a separation of maximally violated combs for the traveling-salesman problem (TSP) is suggested. [ABSTRACT FROM AUTHOR]

Recent studies employ collections of binary decision diagrams (BDDs) to solve combinatorial optimization problems. This paper focuses on the problem of optimally aligning two BDDs, that is, transforming them to enforce a common order of variables while keeping the total size of the diagrams as small as possible. We address this problem, which is known to be NP-hard, by introducing and studying a simplified problem instead of working with the more complex original diagrams. We discuss some basic properties of the simplified problem, design a corresponding heuristic for the original problem, and show empirically that this approach yields good quality alignments while significantly reducing the complexity of intermediate diagram transformations. We highlight the practicality of this approach in the context of a variation of the uncapacitated facility location problem. History: Accepted by Andrea Lodi, Area Editor for Design and Analysis of Algorithms–Discrete. Funding: This work was supported by the Office of Naval Research [Grant N00014-17-1-2421]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/ijoc.2023.1293. [ABSTRACT FROM AUTHOR]

This paper presents an exact algorithm for the team formation problem, in which the aim is, given a project and its required skills, to construct a capable team that can communicate and collaborate effectively. This combinatorial optimization problem is modeled as a quadratic set covering problem. The study provides a novel branch-and-bound algorithm where a reformulation of the problem is relaxed so that it decomposes into a series of linear set covering problems, and the relaxed constraints are imposed through branching. The algorithm is able to solve instances that are intractable for commercial solvers. The study illustrates an efficient usage of algorithmic methods and modeling techniques for an operations research problem. It contributes to the field of computational optimization by proposing a new application and a new algorithm to solve a quadratic version of a classical combinatorial optimization problem. The team formation problem (TFP) aims to construct a capable team that can communicate and collaborate effectively. The cost of communication is quantified using the proximity of the potential members in a social network. We study a TFP with two measures for communication effectiveness; namely, we minimize the sum of communication costs, and we impose an upper bound on the largest communication cost. This problem can be formulated as a constrained quadratic set covering problem. Our experiments show that a general-purpose solver is capable of solving small and medium-sized instances to optimality. We propose a branch-and-bound algorithm to solve larger sizes: we reformulate the problem and relax it in such a way that it decomposes into a series of linear set covering problems, and we impose the relaxed constraints through branching. Our computational experiments show that the algorithm is capable of solving large-size instances, which are intractable for the solver. Summary of Contribution: This paper presents an exact algorithm for the Team Formation Problem (TFP), in which the aim is, given a project and its required skills, to construct a capable team that can communicate and collaborate effectively. This combinatorial optimization problem is modeled as a quadratic set covering problem. The study provides a novel branch-and-bound algorithm where a reformulation of the problem is relaxed so that it decomposes into a series of linear set covering problems and the relaxed constraints are imposed through branching. The algorithm is able to solve instances that are intractable for commercial solvers. The study illustrates an efficient usage of algorithmic methods and modelling techniques for an operations research problem. It contributes to the field of computational optimization by proposing a new application as well as a new algorithm to solve a quadratic version of a classical combinatorial optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the one-machine scheduling problem with release and delivery times with the minimum makespan objective. Both heuristics and branch-and-bound algorithms have been formulated for the problem. One such branch-and-bound algorithm solves the problem and a variation that requires a delay between the completion of one job and the start of another (delayed precedence constraints). This paper analyzes key components of this branch-and-bound algorithm and proposes an improved heuristic to be used in conjunction with a different search strategy. Computational experiments demonstrate that the modifications lead to substantial improvements in running time and number of iterations on the one-machine problem instances both with and without delayed precedence constraints. [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]

In this paper, a new branch-and-price-and-cut algorithm is proposed to solve the one-dimensional bin-packing problem (1D-BPP). The 1D-BPP is one of the most fundamental problems in combinatorial optimization and has been extensively studied for decades. Recently, a set of new 500 test instances were proposed for the 1D-BPP, and the best exact algorithm proposed in the literature can optimally solve 167 of these new instances, with a time limit of 1 hour imposed on each execution of the algorithm. The exact algorithm proposed in this paper is based on the classical set-partitioning model for the 1DBPPs and the subset row inequalities. We describe an ad hoc label-setting algorithm to solve the pricing problem, dominance, and fathoming rules to speed up its computation and a new primal heuristic. The exact algorithm can easily handle some practical constraints, such as the incompatibility between the items, and therefore, we also apply it to solve the one-dimensional bin-packing problem with conflicts (1D-BPPC). The proposed method is tested on a large family of 1D-BPP and 1D-BPPC classes of instances. For the 1D-BPP, the proposed method can optimally solve 237 instances of the new set of difficult instances; the largest instance involves 1,003 items and bins of capacity 80,000. For the 1D-BPPC, the experiments show that the method is highly competitive with state-of-the-art methods and that it successfully closed several open 1D-BPPC instances. [ABSTRACT FROM AUTHOR]

The quadratic assignment problem (QAP) consists of assigning n facilities to n locations to minimize the total weighted cost of interactions between facilities. The QAP arises in many diverse settings, is known to be NP-hard, and can be solved to optimality only for fairly small instances (typically, n ⩽ 30). Neighborhood search algorithms are the most popular heuristic algorithms for solving larger instances of the QAP. The most extensively applied neighborhood structure for the QAP is the 2-exchange neighborhood. This neighborhood is obtained by swapping the locations of two facilities; its size is therefore O(n2). Previous efforts to explore larger neighborhoods (such as 3-exchange or 4-exchange neighborhoods) were not very successful, as it took too long to evaluate the larger set of neighbors. In this paper, we propose very large-scale neighborhood (VLSN) search algorithms when the size of the neighborhood is very large, and we propose a novel search procedure to enumerate good neighbors heuristically. Our search procedure relies on the concept of an improvement graph that allows us to evaluate neighbors much faster than existing methods. In this paper, we present extensive computational results of our algorithms when applied to standard benchmark instances. [ABSTRACT FROM AUTHOR]

Makespan minimization in permutation flow-shop scheduling is a well-known hard combinatorial optimization problem. Among the 120 standard benchmark instances proposed by E. Taillard in 1993, 23 have remained unsolved for almost three decades. In this paper, we present our attempts to solve these instances to optimality using parallel Branch-and-Bound (BB) on the GPU-accelerated Jean Zay supercomputer. We report the exact solution of 11 previously unsolved problem instances and improved upper bounds for eight instances. The solution of these problems requires both algorithmic improvements and leveraging the computing power of peta-scale high-performance computing platforms. The challenge consists in efficiently performing parallel depth-first traversal of a highly irregular and fine-grained search tree on distributed systems composed of hundreds of massively parallel accelerator devices and multicore processors. We present and discuss the design and implementation of our permutation-based BB and experimentally evaluate its parallel performance on up to 384 V100 GPUs (2 million CUDA cores) and 3840 CPU cores. The optimality proof for the largest solved instance requires about 64 CPU-years of computation—using 256 GPUs and over 4 million parallel search agents, the traversal of the search tree is completed in 13 hours, exploring 339 × 10 12 nodes. [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]

Splitting methods in optimization arise when one can divide an optimization problem into two or more simpler subproblems. They have proven particularly successful for relaxations of problems involving discrete variables. We revisit and strengthen splitting methods for solving doubly nonnegative relaxations of the particularly difficult, NP-hard quadratic assignment problem. We use a modified restricted contractive splitting method approach. In particular, we show how to exploit redundant constraints in the subproblems. Our strengthened bounds exploit these new subproblems and new dual multiplier estimates to improve on the bounds and convergence results in the literature. Summary of Contribution: In our paper, we consider the quadratic assignment problem (QAP). It is one of the fundamental combinatorial optimization problems in the fields of optimization and operations research and includes many fundamental applications. We revisit and strengthen splitting methods for solving doubly nonnegative (DNN) relaxation of the QAP. We use a modified restricted contractive splitting method. We obtain strengthened bounds from improved lower and upper bounding techniques, and in fact, we solve many of these NP-hard problems to (provable) optimality, thus illustrating both the strength of the DNN relaxation and our new bounding techniques. [ABSTRACT FROM AUTHOR]

Binary programs with a quadratic objective function are NP-hard in general, even if the linear optimization problem over the same feasible set is tractable. In this paper, we address such problems by computing quadratic global underestimators of the objective function that are separable but not necessarily convex. Exploiting the binary constraint on the variables, a minimizer of the separable underestimator over the feasible set can be computed by solving an appropriate linear minimization problem over the same feasible set. Embedding the resulting lower bounds into a branch-and-bound framework, we obtain an exact algorithm for the original quadratic binary program. The main practical challenge is the fast computation of an appropriate underestimator, which in our approach reduces to solving a series of semidefinite programs.We exploit the special structure of the resulting problems to obtain a tailored coordinate-descent method for their solution. Our extensive experimental results on various quadratic combinatorial optimization problems show that our approach outperforms both CPLEX and the related QCR method as well as the SDP-based software BiqCrunch on instances of the quadratic shortest path problem and the quadratic assignment problem. [ABSTRACT FROM AUTHOR]

We investigate the discrete parallel machine scheduling and location problem, which consists of locating multiple machines to a set of candidate locations, assigning jobs from different locations to the located machines, and sequencing the assigned jobs. The objective is to minimize the maximum completion time of all jobs, that is, the makespan. Though the problem is of theoretical significance with a wide range of practical applications, it has not been well studied as reported in the literature. For this problem, we first propose three new mixed-integer linear programs that outperform state-of-the-art formulations. Then, we develop a new logic-based Benders decomposition algorithm for practical-sized instances, which splits the problem into a master problem that determines machine locations and job assignments to machines and a subproblem that sequences jobs on each machine. The master problem is solved by a branch-and-cut procedure that operates on a single search tree. Once an incumbent solution to the master problem is found, the subproblem is solved to generate cuts that are dynamically added to the master problem. A generic no-good cut is first proposed, which is later improved by some strengthening techniques. Two optimality cuts are also developed based on optimality conditions of the subproblem and improved by strengthening techniques. Numerical results on small-sized instances show that the proposed formulations outperform state-of-the-art ones. Computational results on 1,400 benchmark instances with up to 300 jobs, 50 machines, and 300 locations demonstrate the effectiveness and efficiency of the algorithm compared with current approaches. Summary of Contribution: This paper employs operations research methods and computing techniques to address an NP-hard combinatorial optimization problem: the parallel discrete machine scheduling and location problem. The problem is of practical significance but has not been well studied in the literature. For the problem, we formulate three novel mixed-integer linear programs that outperform state-of-the-art formulations and develop a new logic-based Benders decomposition algorithm. Extensive computational experiments on 1,400 benchmark instances with up to 300 jobs, 50 machines, and 300 locations are conducted to evaluate the performance of the proposed models and algorithms. [ABSTRACT FROM AUTHOR]

We study the design of large-scale group testing schemes under a heterogeneous population (i.e., subjects with potentially different risk) and with the availability of multiple tests. The objective is to classify the population as positive or negative for a given binary characteristic (e.g., the presence of an infectious disease) as efficiently and accurately as possible. Our approach examines components often neglected in the literature, such as the dependence of testing cost on the group size and the possibility of no testing, which are especially relevant within a heterogeneous setting. By developing key structural properties of the resulting optimization problem, we are able to reduce it to a network flow problem under a specific, yet not too restrictive, objective function. We then provide results that facilitate the construction of the resulting graph and finally provide a polynomial time algorithm. Our case study, on the screening of HIV in the United States, demonstrates the substantial benefits of the proposed approach over conventional screening methods. Summary of Contribution: This paper studies the problem of testing heterogeneous populations in groups in order to reduce costs and hence allow for the use of more efficient tests for high-risk groups. The resulting problem is a difficult combinatorial optimization problem that is NP-complete under a general objective. Using structural properties specific to our objective function, we show that the problem can be cast as a network flow problem and provide a polynomial time algorithm. [ABSTRACT FROM AUTHOR]

Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in R K such that the distance between pairs of vertex coordinates is equal to the corresponding edge weights in G. The so-called discretization assumptions reduce the search space of the realization to a finite discrete one, which can be explored via the branch-and-prune (BP) algorithm. Given a discretization vertex order in G, the BP algorithm constructs a binary tree where the nodes at a layer provide all possible coordinates of the vertex corresponding to that layer. The focus of this paper is on finding optimal BP trees for a class of discretizable DGPs. More specifically, we aim to find a discretization vertex order in G that yields a BP tree with the least number of branches. We propose an integer programming formulation and three constraint programming formulations that all significantly outperform the state-of-the-art cutting-plane algorithm for this problem. Moreover, motivated by the difficulty in solving instances with a large and low-density input graph, we develop two hybrid decomposition algorithms, strengthened by a set of valid inequalities, which further improve the solvability of the problem. Summary of Contribution: We present a new model to solve a combinatorial optimization problem on graphs, MIN DOUBLE, which comes from the highly active area of distance geometry and has applications in a wide variety of fields. We use integer programming (IP) and present the first constraint programming (CP) models and hybrid decomposition methods, implemented as a branch-and-cut procedure, for MIN DOUBLE. Through an extensive computational study, we show that our approaches advance the state of the art for MIN DOUBLE. We accomplish this by not only combining generic techniques from IP and CP but also exploring the structure of the problem in developing valid inequalities and variable fixing rules. Our methods significantly improve the solvability of MIN DOUBLE, which we believe can also provide insights for tackling other problem classes and applications. [ABSTRACT FROM AUTHOR]

We solve the type-2 assembly line balancing problem in the presence of sequence-dependent setup times, denoted SUALBP-2. The problem consists of a set of tasks of a product, requiring to be processed in different assembly stations. Each task has a definite processing and setup times. The magnitude of setup times for each task is dependent on the processing sequence within each station. Processing and setup times of tasks assigned to each station constitute the station time. The goal is to minimize the cycle time (the maximum station time) by optimally (i) assigning tasks to assembly stations and (ii) sequencing these tasks within each station. To solve this challenging optimization problem, we first improve upon an existing mixed-integer programming (MIP) model by our proposed lower and upper bounds. These enhancements reduce the MIP model's (solved CPLEX) average optimality gap from 41.61% to 20.77% on extra-large instances of the problem. To further overcome the intractability of the MIP model, we develop an exact logic-based Benders decomposition (LBBD) algorithm. The LBBD algorithm effectively incorporates a novel two-phase solution approach, the lower and upper bounds, various preprocessing techniques, relaxations, and valid inequalities. Using existing benchmarks in the literature, we demonstrate that our LBBD algorithm finds integer feasible solutions for 100% of all 788 instances (64% for the MIP), verifies optimality for 47% of instances (37% for the MIP), and achieves an average optimality gap of 5.04% (7.72% for the MIP obtained over 64% solved small instances). The LBBD algorithm also significantly reduces the computational time required to solve these benchmarks. Summary of Contribution: Assembly line balancing plays a crucial role in productivity enhancement in manufacturing and service companies. A balanced assembly line ensures higher throughput rate and fairer distribution of workload among assembly stations (workers). Assembly line balancing, in its simplest form, is one of the most challenging combinatorial optimization problems. Its complexity is further intensified when the sequence of executing tasks assigned to each station influences the magnitude of the setup performed between any two successive tasks. In view of such complexity, most assembly line balancing problems have been solved by randomized search techniques that do not provide any guarantee on the quality of solutions found. The mission of this paper is to understand whether there is any special structure within the existing mathematical models in the literature and, if so, exploit them toward developing computationally efficient exact techniques that can provide guarantee on the quality of solutions. Indeed, we demonstrate that such a special mathematical structure exists and we thus develop the first decomposition technique in form of a logic-based Benders decomposition (LBBD) to efficiently solve the type-2 sequence-dependent assembly line balancing problem. Specifically, we show that our LBBD significantly reduces cycle time and the time required for decision making. Our LBBD generalizes the scope of exact techniques for decision-making beyond the assembly line problems and is extendable to many other shop scheduling problems that arrange their stations (machines) serially and there are sequence-dependent setup times among their tasks. [ABSTRACT FROM AUTHOR]

This paper presents an data type (ADT) for producing higher-dimensional rectilinear packings using constructive methods, the Skyline ADT. Furthermore, a novel method and several approaches from the literature are presented in the form of concrete implementations of the presented ADT. Formal definitions of two three-dimensional packing problems are given, the concept of gaps is explained, and the polynomial growth worst-case behaviour of gaps is shown. The complexity of both the best-fit algorithm and implementations of the ADT are presented, and comparative runtime speeds are analysed over a range of data sets from the literature. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a column generation-based algorithm for the classical cutting stock problem. This algorithm is known to have convergence issues, which are addressed in this paper. Our methods are based on the fact that there are interesting characterizations of the structure of the dual problem, and that a large number of dual solutions are known. First, we describe methods based on the concept of dual cuts, proposed by Valério de Carvalho [Valério de Carvalho, J. M. 2005. Using extra dual cuts to accelerate column generation. INFORMS J. Comput. 17(2) 175-182]. We introduce a general framework for deriving cuts, and we describe a new type of dual cut that excludes solutions that are linear combinations of some other known solutions. We also explore new lower and upper bounds for the dual variables. Then we show how the prior knowledge of a good dual solution helps improve the results. It tightens the bounds around the dual values and makes the search converge faster if a solution is sought in its neighborhood first. A set of computational experiments on very hard instances is reported at the end of the paper; the results confirm the effectiveness of the methods proposed. [ABSTRACT FROM AUTHOR]

Problem-specific encodings can improve the performance of metaheuristics, such as genetic algorithms or simulated annealing. This paper studies the link-biased (LB) encoding, which is a tree representation, and applies metaheuristics using this encoding to the minimum communication spanning tree (MCST) problem. Given the communication requirements of the nodes, the MCST problem seeks a communication spanning tree with minimum total cost. Optimal solutions for MCST problems are similar to minimum spanning trees (MSTs), and the LB encoding exploits this property by encoding trees similar to MSTs with higher probability. The paper investigates how to systematically design problem-specific encodings for MCST problems and how to set the encoding-specific parameter that controls the bias of the LB encoding towards MSTs; it then presents performance results for various MCST problems. [ABSTRACT FROM AUTHOR]

In recent years, much attention has been devoted to the development of metaheuristics and local search algorithms for tackling stochastic combinatorial optimization problems. This paper focuses on local search algorithms; their effectiveness is greatly determined by the evaluation procedure that is used to select the best of several solutions in the presence of uncertainty. In this paper, we propose an effective evaluation procedure that makes use of empirical estimation techniques. We illustrate this approach and we assess its performance on the probabilistic traveling salesman problem. Experimental results on a large set of instances show that the proposed approach can lead to a very fast and highly effective local search algorithm. [ABSTRACT FROM AUTHOR]

This paper introduces simultaneous generalized hill-climbing (SGHC) algorithms as a framework for simultaneously addressing a set of related discrete optimization problems using heuristics. Many well-known heuristics can be embedded within the SGHC algorithm framework, including simulated annealing, pure local search, and threshold accepting (among others). SGHC algorithms probabilistically move between a set of related discrete optimization problems during their execution according to a problem probability mass function. When an SGHC algorithm moves between discrete optimization problems, information gained while optimizing the current problem is used to set the initial solution in the subsequent problem. The information used is determined by the practitioner for the particular set of problems under study. However, effective strategies are often apparent based on the problem description. SGHC algorithms are motivated by a discrete manufacturing process design optimization problem (that is used throughout the paper to illustrate the concepts needed to implement a SGHC algorithm). This paper discusses effective strategies for three examples of sets of related discrete optimization problems (a set of traveling salesman problems, a set of permutation flow shop problems, and a set of MAX 3-satisfiability problems). Computational results using the SGHC algorithm for randomly generated problems for two of these examples are presented. For comparison purposes, the associated generalized hill-climbing (GHC) algorithms are applied to the individual discrete optimization problems in the sets. These computational results suggest that near-optimal solutions can be reached more effectively and efficiently using SGHC algorithms. [ABSTRACT FROM AUTHOR]

Mathematical-modeling and constraint-programming languages have orthogonal strengths in stating combinatorial optimization problems. Modeling languages typically feature high-level set and algebraic notations, while constraint-programming languages provide a rich constraint language and the ability to specify search procedures. This paper shows that many of the functionalities typically found in modeling languages can be integrated elegantly in constraint-programming libraries without defining a specific language or preprocessor In particular, it presents the design of MODELER, a C++ modeling layer for constraint programming which demonstrates how to enhance the expressiveness of constraint-programming libraries and to bridge much of the gap between libraries and modeling languages. [ABSTRACT FROM AUTHOR]

This paper proposes and tests variants of GRASP (greedy randomized adaptive search procedure) with path relinking for the three-index assignment problem (AP3). GRASP is a multistart metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and of a local search. Path relinking is an intensification strategy that explores trajectories that connect high-quality solutions. Several variants of the heuristic are proposed and tested. Computational results show clearly that this GRASP for AP3 benefits from path relinking and that the variants considered in this paper compare well with previously proposed heuristics for this problem. GRASP with path relinking was able to improve the solution quality of heuristics proposed by Balas and Seltzman (1991), Burkard et al. (1996), and Crama and Spieksma (1992) on all instances proposed in those papers. We show that the random variable ‘time to target solution,’ for all proposed GRASP with path-relinking variants, fits a two-parameter exponential distribution. To illustrate the consequence of this, one of the variants of GRASP with path relinking is shown to benefit from parallelization. [ABSTRACT FROM AUTHOR]

Many combinatorial problems require that their solutions achieve a certain balance of given features. For this important aspect of modeling, the spread and deviation constraints have been proposed in Constraint Programming to express balance among a set of variables by constraining their mean and overall deviation from the mean. To our knowledge, the only practical filtering algorithms known for these constraints achieve bounds consistency. In this paper we improve that filtering by presenting an efficient domain consistency algorithm that applies to both constraints. We also extend it to count solutions so that it can be used in counting-based search, a generic and effective family of branching heuristics that free the user from having to write problem-specific search heuristics. We provide a time complexity analysis of our contributions and empirically evaluate them on benchmark problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a generic algorithm to compute exactly the set of nondominated points for multiobjective discrete optimization problems. Our algorithm extends the ε-constraint method, originally designed for the biobjective case only, to solve problems with two or more objectives. For this purpose, our algorithm splits the search space into zones that can be investigated separately by solving an integer program. We also propose refinements, which provide extra information on several zones, allowing us to detect, and discard, empty parts of the search space without checking them by solving the associated integer programs. This results in a limited number of calls to the integer solver. Moreover, we can provide a feasible starting solution before solving every program, which significantly reduces the time spent for each resolution. The resulting algorithm is fast and simple to implement. It is compared with previous state-of-the-art algorithms and is seen to outperform them significantly on the experimented problem instances. [ABSTRACT FROM AUTHOR]

We introduce a simple technique for disjunctive machine scheduling problems and show that this method can match or even outperform state-of-the-art algorithms on a number of problem types. Our approach combines a number of generic search techniques such as restarts, adaptive heuristics, and solution-guided branching on a simple model based on a decomposition of disjunctive constraints and on the reification of these disjuncts. This paper describes the method and its application to variants of the job shop scheduling problem (JSP). We show that our method can easily be adapted to handle additional side constraints and different objective functions, often outperforming the state-of-the-art and closing a number of open problems. Moreover, we perform in-depth analysis of the various factors that make this approach efficient. We show that, while most of the factors give moderate benefits, the variable and value ordering components are key. [ABSTRACT FROM AUTHOR]

Most real-world optimization problems are multi-objective by nature, with conflicting and incomparable objectives. Solving a multi-objective optimization problem requires a method that can generate all rational compromises between the objectives. This paper proposes two distinct bound set-based branch-and-cut algorithms for general bi-objective combinatorial optimization problems based on implicit and explicit lower-bound sets. The algorithm based on explicit lower-bound sets computes, for each branching node, a lower-bound set and compares it with an upper-bound set. The other fathoms branching nodes by generating a single point on the lower-bound set for each local nadir point. We outline several approaches for fathoming branching nodes, and we propose an updating scheme for the lower-bound sets that prevents us from solving the bi-objective linear programming relaxation of each branching node. To strengthen the lower-bound sets, we propose a bi-objective cutting-plane algorithm that adjusts the weights of the objective functions such that different parts of the feasible set are strengthened by cutting planes. In addition, we suggest an extension of the branching strategy "Pareto branching." We prove the effectiveness of the algorithms through extensive computational results. [ABSTRACT FROM AUTHOR]

A phylogeny is an unrooted binary tree that represents the evolutionary relationships of a set of n species. A Phylogenies find applications in several scientific areas ranging from medical research, to drug discovery, to epidemiology, to systematics, and to population dynamics. In such applications, the available information is usually restricted to the leaves of a phylogeny and is represented by molecular data extracted from the analyzed species, such as DNA, RNA, amino acid, or codon fragments. On the contrary, the information about the phylogeny itself is generally missing and is determined by solving an optimization problem, called the phylogeny estimation problem (PEP), whose versions depend on the criterion used to select a phylogeny from among plausible alternatives. In this paper, we investigate a recent version of the PEP, called the balanced minimum evolution problem (BMEP). We present a mixed-integer linear programming model to exactly solve instances of the BMEP and develop branching rules and families of valid inequalities to further strengthen the model. Our results give perspective on the mathematics of the BMEP and suggest new directions on the development of future efficient exact approaches to solutions of the problem. [ABSTRACT FROM AUTHOR]

When the leader's objective function of a nonlinear bilevel programming problem is nondifferentiable and the follower's problem of it is nonconvex, the existing algorithms cannot solve the problem. In this paper, a new effective evolutionary algorithm is proposed for this class of nonlinear bilevel programming problems. First, based on the leader's objective function, a new fitness function is proposed that can be easily used to evaluate the quality of different types of potential solutions. Then, based on Latin squares, an efficient crossover operator is constructed that has the ability of local search. Furthermore, a new mutation operator is designed by using some good search directions so that the offspring can approach a global optimal solution quickly. To solve the follower's problem efficiently, we apply some efficient deterministic optimization algorithms in the MATLAB Toolbox to search for its solutions. The asymptotically global convergence of the algorithm is proved. Numerical experiments on 25 test problems show that the proposed algorithm has a better performance than the compared algorithms on most of the test problems and is effective and efficient. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of technical transient gas network optimization, which can be considered a minimum cost flow problem with a nonlinear objective function and additional nonlinear constraints on the network arcs. Applying an implicit box scheme to the isothermal Euler equation, we derive a mixed-integer nonlinear program. This is solved by means of a combination of (i) a novel mixed-integer linear programming approach based on piecewise linearization and (ii) a classical sequential quadratic program applied for given combinatorial constraints. Numerical experiments show that better approximations to the optimal control problem can be obtained by using solutions of the sequential quadratic programming algorithm to improve the mixed-integer linear program. Moreover, iteratively applying these two techniques improves the results even further. [ABSTRACT FROM AUTHOR]

In many fields, we come across problems where we want to optimize several conflicting objectives simultaneously. To find a good solution for such multiobjective optimization problems, an approximation of the Pareto set is often generated. In this paper, we consider the approximation of higher-dimensional convex Pareto sets using sandwich algorithms. We extend higher-dimensional sandwich algorithms in three different ways. First, we introduce the new concept of adding dummy points to the inner approximation of a Pareto set. By using these dummy points, we can determine accurate inner and outer approximations more efficiently, i.e., using less time-consuming optimizations. Second, we introduce a new method for the calculation of an error measure that is easy to interpret. Third, we show how transforming certain objective functions can improve the results of sandwich algorithms and extend their applicability to certain nonconvex problems. To show the effect of these enhancements, we make a numerical comparison using four test cases, including a four-dimensional case from the field of intensity-modulated radiation therapy. The results of the different cases show that we can achieve an accurate approximation using significantly fewer optimizations by using the enhancements. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an exact method based on constraint programming ideas for a combinatorial optimization problem that arises from the treatment planning of intensity-modulated radiotherapy-the minimum cardinality problem (MCP). The MCP is to find a decomposition of a given integer matrix into a weighted sum of binary matrices with consecutive ones, such that the number of such binary matrices is minimised. We compare our method with two recent exact methods for the same problem and a recent exact method for a special case of the problem. Numerical results are presented that indicate that our method is computationally more efficient than the three existing methods. [ABSTRACT FROM AUTHOR]

This paper is a survey of the literature on applications of evolutionary algorithms for vehicle routing problems. It reports on genetic algorithms, evolution strategies, and particle swarm optimization when applied to the classical capacitated vehicle routing problem and many of its variants. The performance of evolutionary algorithms is also compared with the best alternative problem-solving approaches on benchmark instances. [ABSTRACT FROM AUTHOR]

This paper is concerned with the single-row facility layout problem (SRFLP). A globally optimal solution to the SRFLP is a linear placement of rectangular facilities with varying lengths that achieves the minimum total cost associated with the (known or projected) interactions between them. We demonstrate that the combination of a semidefinite programming relaxation with cutting planes is able to compute globally optimal layouts for large SRFLPs with up to 30 facilities. In particular, we report the globally optimal solutions for two sets of SRFLPs previously studied in the literature, some of which have remained unsolved since 1988. [ABSTRACT FROM AUTHOR]

This paper focuses on a multiobjective derivation of branch-and-bound procedures. Such a procedure aims to provide the set of Pareto-optimal solutions of a multiobjective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that a node in the search tree can be discarded if one can define a separating hypersurface in the objective space between the set of feasible solutions in the subtree and the set of points corresponding to potential Pareto-optimal solutions. Numerical experiments on the biobjective spanning tree problem are provided that show the efficiency of the approach in a biobjective setting. [ABSTRACT FROM AUTHOR]

This paper presents a new unified modeling and heuristic solution framework for vehicle-routing problems (VRPs) with complex side constraints. The work is focused on strong modeling capabilities as well as efficient solution procedures to be used in all kinds of metaheuristics. From the modeling point of view, the framework covers a variety of standard VRP types with classical constraints such as capacity, distance, route length, time window, pairing, and precedence constraints, but also nonstandard "rich" VRPs. From the methodological point of view, local search (LS) is the key solver engine to be used in heuristic solution procedures. First and foremost, the framework introduces two generic techniques for the efficient exploration of edge- and node-exchange neighborhoods. New preprocessing methods allow O(nk) neighborhoods to be searched in time complexity O(nk), i.e., without an additional effort for feasibility testing in the worst case. Moreover, for accelerating LS in the average case, Irnich et al. [Irnich, S., B. Funke, T. Grünert. 2006. Sequential search and its application to vehiclerouting problems. Comput. Oper. Res. 33 2405-2429] have introduced sequential search that is here adapted to cope with rich VRPs (complex side constraints). Computational tests on different types of VRPs indicate that the proposed techniques are highly efficient. Sequential search procedures outperform the currently most efficient search methods, which are based on lexicographic search, on large-scale instances and for nearly all types of neighborhoods by factors of between 10 and 1,000. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms adopt a natural-selection analogy, exploiting concepts such as population, combination, mutation, and selection to explore a diverse space of possible solutions to combinatorial optimization problems while, at the same time, retaining desirable properties from known solutions. This paper describes an evolutionary approach to improving solutions to mixed integer programming (MIP) models. We propose coarse-grained approaches to mutating and combining MIP solutions, both built within a large-neighborhood search framework. These techniques are then integrated within a MIP branch-and-bound framework. The resulting solution-polishing heuristic often finds significantly better feasible solutions to very difficult MIP models than do available alternatives. In contrast to most evolutionary algorithms, our polishing heuristic is domain-independent, requiring no structural information about the underlying combinatorial problem, above and beyond the information contained in the original MIP formulation. [ABSTRACT FROM AUTHOR]

In this paper we discuss a special pallet-loading problem, which we encountered at a manufacturing company. In graph-theoretical terms, the problem is equivalent to partitioning a permutation graph into bounded-size cliques. We formulate the problem as an integer program, and present two exact algorithms for solving it. The first algorithm is a branch-and-price algorithm based on the integer-programming formulation; the second one is an algorithm based on the concept of bounded clique width. The latter algorithm was motivated by the structure present in the real-world instances. Test results are given, both for real-world instances and randomly generated instances. As far as we are aware, this is the first implementation of an algorithm based on bounded clique width. [ABSTRACT FROM AUTHOR]

This paper presents a quantitative model for telecommunication network installation by companies in the broadband-access business, specialized to the fixed-wireless case. Under stochastic demand modeled using scenarios, we maximize the expected demand coverage subject to a budget constraint on hub installation, and technological constraints on demand coverage by installed hubs. There are multiple hub types, differing in costs and capacities. We present a practical greedy heuristic based on the budgeted maximum-coverage problem and analyze its worst-case performance. For special cases with a single hub type or a single demand scenario, we show that a guarantee of 1 - 1/e or 63.2% applies to our greedy heuristic. For the general case we develop a data-dependent performance guarantee. Through computational experiments, we show that the greedy heuristic's empirical performance is, on average, within 2% of the optimal expected demand coverage. [ABSTRACT FROM AUTHOR]

Finding a linear layout of a graph having minimum bandwidth is a combinatorial optimization problem that has been studied since the 1960s. Unlike other classical problems, the approach based on stating a suitable integer linear program and solving the associated linear-programming relaxation seems to be useless in this case. This makes it nontrivial to design algorithms capable of solving to optimality instances of reasonable size. In this paper, we illustrate a new simple lower bound on the optimal bandwidth and its extension within an enumerative algorithm, leading to integer linear-programming relaxations that can be solved efficiently and provide effective lower bounds if part of the layout is fixed. Keeping the integrality constraints in these relaxations is essential for this purpose. We show that the resulting method can solve to proven optimality 24 out of the 30 instances from the literature with less than 200 nodes, each in less than a minute on a personal computer. The new approach is also analyzed on randomly generated instances with up to 1,000 nodes. Moreover, we propose a method to compute the well-known density lower bound on the optimal bandwidth, which succeeds in finding this bound within minutes for most instances in the literature with up to 250 nodes. [ABSTRACT FROM AUTHOR]