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检索条件"任意字段=16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013"

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Recycling Inequalities for Robust combinatorial optimization with Budget Uncertainty 1

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24th International conference on integer programming and combinatorial optimization (ipco)

作者： Buesing, Christina Gersing, Timo Koster, Arie M. C. A. Rhein Westfal TH Aachen Combinatorial Optimizat Aachen Germany Rhein Westfal TH Aachen Discrete Optimizat Aachen Germany

ISBN: (数字)9783031327261

ISBN: (纸本)9783031327254;9783031327261

Robust combinatorial optimization with budget uncertainty is one of the most popular approaches for integrating uncertainty in optimization problems. the existence of a compact reformulation for (mixed-integer) linear programs and positive complexity results give the impression that these problems are relatively easy to solve. However, the practical performance of the reformulation is actually quite poor when solving robust integer problems due to its weak linear relaxation. To overcome the problems arising from the weak formulation, we propose a procedure to derive new classes of valid inequalities for robust binary optimization problems. For this, we recycle valid inequalities of the underlying deterministic problem such that the additional variables from the robust formulation are incorporated. the valid inequalities to be recycled may either be readily available model constraints or actual cutting planes, where we can benefit from decades of research on valid inequalities for classical optimization problems. We first demonstrate the strength of the inequalities theoretically, by proving that recycling yields a facet-defining inequality in surprisingly many cases, even if the original valid inequality was not facet-defining. Afterwards, we show in a computational study that using recycled inequalities leads to a significant improvement of the computation time when solving robust optimization problems.

关键词： Robust optimization combinatorial optimization integer programming Polyhedral Combinatorics

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Constant-Competitiveness for Random Assignment Matroid Secretary Without Knowing the Matroid 24th

Constant-Competitiveness for Random Assignment Matroid Secre...

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24th International conference on integer programming and combinatorial optimization (ipco)

作者： Santiago, Richard Sergeev, Ivan Zenklusen, Rico Swiss Fed Inst Technol Dept Mathemat Zurich Switzerland

ISBN: (纸本)9783031327254;9783031327261

the Matroid Secretary Conjecture is a notorious open problem in online optimization. It claims the existence of an O(1)-competitive algorithm for the Matroid Secretary Problem (MSP). Here, the elements of a weighted matroid appear one-by-one, revealing their weight at appearance, and the task is to select elements online with the goal to get an independent set of largest possible weight. O(1)-competitive MSP algorithms have so far only been obtained for restricted matroid classes and for MSP variations, including Random-Assignment MSP (RA-MSP), where an adversary fixes a number of weights equal to the ground set size of the matroid, which then get assigned randomly to the elements of the ground set. Unfortunately, these approaches heavily rely on knowing the full matroid upfront. this is an arguably undesirable requirement, and there are good reasons to believe that an approach towards resolving the MSP Conjecture should not rely on it. thus, both Soto [SIAM Journal on Computing 2013] and Oveis Gharan & Vondrak [Algorithmica 2013] raised as an open question whether RA-MSP admits an O(1)-competitive algorithm even without knowing the matroid upfront. In this work, we answer this question affirmatively. Our result makes RA-MSP the first well-known MSP variant with an O(1)-competitive algorithm that does not need to know the underlying matroid upfront and without any restriction on the underlying matroid. Our approach is based on first approximately learning the rank-density curve of the matroid, which we then exploit algorithmically.

关键词： combinatorial mathematics

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16th Annual International conference on combinatorial optimization and Applications, COCOA 2023

16th Annual International Conference on Combinatorial Optimi...

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16th Annual International conference on combinatorial optimization and Applications, COCOA 2023

ISBN: (纸本)9783031496103

the proceedings contain 73 papers. the special focus in this conference is on combinatorial optimization and Applications. the topics include: Improved Scheduling with a Shared Resource;an Energy-Efficient Scheduling Method for Real-Time Multi-workflow in Container Cloud;weakly Nondominated Solutions of Set-Valued optimization Problems with Variable Ordering Structures in Linear Spaces;the MaxIS-Shapley Value in Perfect Graphs;asteroidal Sets and Dominating Paths;a Novel Approximation Algorithm for Max-Covering Circle Problem;GAMA: Genetic Algorithm for k-Coverage and Connectivity with Minimum Sensor Activation in Wireless Sensor Networks;simple Heuristics for the Rooted Max Tree Coverage Problem;efficient Algorithms for k-Submodular Function Maximization with p-System and d-Knapsack Constraint;algorithms on a Path Covering Problem with Applications in Transportation;data Summarization Beyond Monotonicity: Non-monotone Two-Stage Submodular Maximization;greedy+Max: An Efficient Approximation Algorithm for k-Submodular Knapsack Maximization;improved Lower Bound for Estimating the Number of Defective Items;popularity on the Roommate Diversity Problem;on Half Guarding Polygons;dynamic programming for the Fixed Route Hybrid Electric Aircraft Charging Problem;algorithms for the Ridesharing with Profit Constraint Problem;multi-Candidate Carpooling Routing Problem and Its Approximation Algorithms;maximizing Utilitarian and Egalitarian Welfare of Fractional Hedonic Games on Tree-Like Graphs;the Line-Constrained Maximum Coverage Facility Location Problem;faster Algorithms for Evacuation Problems in Networks with a Single Sink of Small Degree and Bounded Capacitated Edges;on Connectedness of Solutions to integer Linear Systems;an Exact Algorithm for the Line-Constrained Bottleneck k-Steiner Tree Problem;the Longest Subsequence-Repeated Subsequence Problem;an Approximation Algorithm for Covering Vertices by 4+ -Paths;V-Words, Lyndon Words and Substring circ-UMFFs;the Two-Center

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16th Annual International conference on combinatorial optimization and Applications, COCOA 2023

16th Annual International Conference on Combinatorial Optimi...

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16th Annual International conference on combinatorial optimization and Applications, COCOA 2023

ISBN: (纸本)9783031496134

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Review of Quantum(-Inspired) optimization Methods for System Reliability Problems 16

Review of Quantum(-Inspired) Optimization Methods for System...

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16th International conference on Probabilistic Safety Assessment and Management, PSAM 2022

作者： Araújo, Lavínia Maria Mendes Lins, Isis Didier Figueroa, Diego Andres Aichele Maior, Caio Bezerra Souto das Chagas Moura, Márcio Droguett, Enrique López Universidade Federal de Pernambuco Recife Brazil Technology Center Universidade Federal de Pernambuco Caruaru Brazil University of California Los Angeles United States

Many industrial systems demand equipment with high levels of reliability. Companies and academia have been developing, over the years, mathematical methods and advancing engineering techniques to assist in the maintenance of active and reliable systems. there are different optimization problems in this context, highlighting (1) the redundancy allocation problem (RAP), (2) the reliability allocation problem, and (3) the reliability-redundancy allocation problem (RRAP). Many solving methods have already been applied to these problems, e.g., dynamic, linear, integer, and nonlinear programming, as well as classical metaheuristics based on evolutionary algorithms, such as the Genetic Algorithm (GA). Either way, these methods are modeled according to the specificities of the systems. However, these approaches can be very computationally expensive depending on the problem instances. Meanwhile, quantum computing has gained ground for combinatorial optimization problems. It is expected that problems with a high level of complexity can be solved more efficiently using these new methods than classical ones. optimization methods have attempted to improve their efficiency by adding quantum concepts, as is the case of Quantum-inspired Evolutionary Algorithms (QEA). the QEA has a better diversity and convergence rate than other EAs because it uses qubit representation instead of numerical, binary, or symbolic representations. In this context, this paper aims to develop a systematic review of the literature through keyword filtering, article reading, and bibliometric analysis on applying purely quantum and quantum-inspired methods in system reliability optimization problems, specifically in RAP, the reliability allocation problem, and the RRAP. Our goal is to identify quantum-based techniques' advantages, limitations, and potential in such a context and suggest a research plan based on the observed literature gaps. We observed few studies in the context, especially in classical qua

关键词： Nonlinear programming

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A Bundle Approach for SDPs with Exact Subgraph Constraints 1

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20th International conference on integer programming and combinatorial optimization (ipco)

作者： Gaar, Elisabeth Rendl, Franz Alpen Adria Univ Klagenfurt Inst Math Univ Str 65-67 A-9020 Klagenfurt Austria

ISBN: (数字)9783030179533

ISBN: (纸本)9783030179533;9783030179526

the 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational challenge because of the potentially large number of violated subgraph constraints. We introduce a computational framework for these relaxations designed to cope with these difficulties. We suggest a partial Lagrangian dual, and exploit the fact that its evaluation decomposes into two independent subproblems. this opens the way to use the bundle method from non-smooth optimization to minimize the dual function. Computational experiments on the Max-Cut, stable set and coloring problem show the efficiency of this approach.

关键词： Semidefinite programming Relaxation hierarchy Max-Cut Stable set Coloring

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Intersection Cuts for Polynomial optimization 1

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20th International conference on integer programming and combinatorial optimization (ipco)

作者： Bienstock, Daniel Chen, Chen Munoz, Gonzalo Columbia Univ IEOR New York NY USA Ohio State Univ ISE Columbus OH 43210 USA Polytech Montreal Montreal PQ Canada

ISBN: (数字)9783030179533

ISBN: (纸本)9783030179533;9783030179526

We consider dynamically generating linear constraints (cutting planes) to tighten relaxations for polynomial optimization problems. Many optimization problems have feasible set of the form S boolean AND P, where S is a closed set and P is a polyhedron. integer programs are in this class and one can construct intersection cuts using convex "forbidden" regions, or S-free sets. Here, we observe that polynomial optimization problems can also be represented as a problem with linear objective function over such a feasible set, where S is the set of real, symmetric matrices representable as outer-products of the form xx(T). Accordingly, we study outer-product-free sets and develop a thorough characterization of several (inclusion-wise) maximal intersection cut families. In addition, we present a cutting plane approach that guarantees polynomial-time separation of an extreme point in P \ S using our outer-product-free sets. Computational experiments demonstrate the promise of our approach from the point of view of strength and speed.

关键词： integer programming

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Online Submodular Maximization: Beating 1/2 Made Simple 1

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20th International conference on integer programming and combinatorial optimization (ipco)

作者： Buchbinder, Niv Feldman, Moran Filmus, Yuval Garg, Mohit Tel Aviv Univ Tel Aviv Israel Open Univ Israel Raanana Israel Technion Haifa Israel

ISBN: (数字)9783030179533

ISBN: (纸本)9783030179533;9783030179526

the problem of Submodular Welfare Maximization (SWM) captures an important subclass of combinatorial auctions and has been studied extensively from both computational and economic perspectives. In particular, it has been studied in a natural online setting in which items arrive one-by-one and should be allocated irrevocably upon arrival. In this setting, it is well known that the greedy algorithm achieves a competitive ratio of 1/2, and recently Kapralov et al. [22] showed that this ratio is optimal for the problem. Surprisingly, despite this impossibility result, Korula et al. [25] were able to show that the same algorithm is 0.5052-competitive when the items arrive in a uniformly random order, but unfortunately, their proof is very long and involved. In this work, we present an (arguably) much simpler analysis that provides a slightly better guarantee of 0.5096-competitiveness for the greedy algorithm in the random-arrival model. Moreover, this analysis applies also to a generalization of online SWM in which the sets defining a (simple) partition matroid arrive online in a uniformly random order, and we would like to maximize a monotone submodular function subject to this matroid. Furthermore, for this more general problem, we prove an upper bound of 0.576 on the competitive ratio of the greedy algorithm, ruling out the possibility that the competitiveness of this natural algorithm matches the optimal offline approximation ratio of 1 - 1/e.

关键词： Submodular optimization Online auctions Greedy algorithms

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A Computational Comparison of optimization Methods for the Golomb Ruler Problem 16th

A Computational Comparison of Optimization Methods for the G...

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16th International conference on the Integration of Constraint programming, Artificial Intelligence, and Operations Research (CPAIOR)

作者： Kocuk, Burak van Hoeve, Willem-Jan Sabanci Univ TR-34956 Istanbul Turkey Carnegie Mellon Univ Pittsburgh PA 15213 USA

ISBN: (纸本)9783030192129;9783030192112

the Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is minimized. the Golomb ruler problem has applications in information theory, astronomy and communications, and it can be seen as a challenge for combinatorial optimization algorithms. Although constructing high quality rulers is well-studied, proving optimality is a far more challenging task. In this paper, we provide a computational comparison of different optimization paradigms, each using a different model (linear integer, constraint programming and quadratic integer) to certify that a given Golomb ruler is optimal. We propose several enhancements to improve the computational performance of each method by exploring bound tightening, valid inequalities, cutting planes and branching strategies. We conclude that a certain quadratic integer programming model solved through a Benders decomposition and strengthened by two types of valid inequalities performs the best in terms of solution time for small-sized Golomb ruler problem instances. On the other hand, a constraint programming model improved by range reduction and a particular branching strategy could have more potential to solve larger size instances due to its promising parallelization features.

关键词： Golomb ruler integer programming Constraint programming

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Compact Representation of Time-Index Job Shop Problems Using a Bit-Vector Formulation

Compact Representation of Time-Index Job Shop Problems Using...

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IEEE International conference on Automation Science and Engineering (CASE)

作者： Sabino Francesco Roselli Kristofer Bengtsson Knut Åkesson Department Electrical Engineering Chalmers University of Technology Göeborg Sweden

ISBN: (数字)9781728169040

ISBN: (纸本)9781728169057

the Job Shop Scheduling Problem (JSP) is a combinatorial optimization problem where jobs visit single-capacity machines while minimizing a cost function, typically the makespan. the problem can be extended to fit typical industrial scenarios such as flexible assembly shop floors or for coordinating fleets of automated vehicles. General purpose optimizers can handle extended versions of the problem that typically arise in industrial problems. Mixed integer Linear programming (MILP) solvers and recently optimizing Satisfiability Modulo theory (SMT) solvers can be used as general solvers for JSP problems. there exist different formulations of JSP problems, among them the time-index (TI) model. the TI offers the advantage of providing strong lower bounds, though its drawback is the model *** this paper we present a new formulation of the TI model suitable for optimizing SMT-solvers that support bit-vector theories. the new formulation is significantly more compact than the standard TI formulation and is thus reducing one of the major issues with the TI *** benchmark two different optimizing SMT solvers supporting bit-vector theories, comparing the standard formulation of the TI to the new formulation on a set of benchmark instances. the computational analysis shows that the new formulation outperforms the standard one, being up to twice faster and regardless of the solver employed; moreover the model generated with the new formulation is considerably smaller than with the standard formulation.

关键词： Mathematical model Standards Upper bound Computational modeling Benchmark testing optimization Analytical models

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