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19th IEEE Canadian Conference on Electrical and Computer Engineering

作者： Younes, Abdurmaser Basir, Otman Calamai, Paul Univ Waterloo Syst Design Engn Waterloo ON N2L 3G1 Canada

ISBN: (纸本)9781424400379

Them is a growing interest in the use of evolutionary algorithms in time-varying environments where the information is revealed progressively with time to the decision maker. However, most existing research basically targets continuous optimization, while little work is directed to discrete optimization even though many real-world problems are both discrete and time-varying. This paper seeks to enhance the ability of genetic algorithms to track the optima shifting due to environmental changes: First, parameters of the genetic operators react to changes in the environment and to changes in the population diversity in order to persevere after obsolete convergence and overcome premature convergence. Second, multi-populations are introduced to cooperatively maintain the search diversity. Third, the algorithm is hybridized with local search heuristics for better tuning. The final algorithm is tested on dynamic combinatorial benchmark problems from the literature. Collectively, results from the conducted experiments favor the strategies proposed in this paper.

关键词： genetic algorithms local search adaptation dynamic environments combinatorial problems Island Genetic algorithms dynamic tmvelling Salesman problem

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Third grade students' multimodal mathematical reasoning when collaboratively solving combinatorial problems in small groups

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MATHEMATICAL THINKING AND LEARNING 2024年第3期26卷 258-277页

作者： Wathne, Unni Carlsen, Martin Univ Agder Dept Math Sci Kristiansand Norway

The aim of this study is to investigate Norwegian primary school students' multimodal mathematical reasoning when solving combinatorial problems. The data collection took place in four small groups of altogether thirteen 8-9 years old third-graders. Our study shows a variety of approaches used to solve the given combinatorial problems, such as count-all and grouping. These approaches were characterized by the students' use of inscriptions that displayed all combinations and inscriptions that did not display all combinations. Moreover, the students used gestures such as pointing and sliding. The students' multimodal reasoning was characterized by the ways their utterances, inscriptions, and gestures emerged and supplemented each other. The students' pointing gestures mediated the intended mathematical meaning solely when combined with inscriptions displaying all possible combinations. Sliding gestures, on the other hand, did mediate the intended mathematical meaning when their inscriptions were not displaying all possible combinations. In this latter case, the shortcomings of their inscriptions were complemented and compensated by the sliding gestures. The students' multimodal mathematical reasoning made explicit their combinatorial thinking, mediated the intended mathematical meaning, and facilitated their solving of the given combinatorial problems.

关键词： combinatorial problems gestures inscriptions multimodal reasoning

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Learning a Prior for Monte Carlo Search by Replaying Solutions to combinatorial problems 18th

Learning a Prior for Monte Carlo Search by Replaying Solutio...

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18th International Conference on Parallel Problem Solving from Nature (PPSN)

作者： Cazenave, Tristan Univ Paris 09 CNRS LAMSADE PSL Paris France

ISBN: (纸本)9783031700545;9783031700552

Monte Carlo Search gives excellent results in multiple difficult combinatorial problems. Using a prior to perform non uniform playouts during the search improves a lot the results compared to uniform playouts. Handmade heuristics tailored to the combinatorial problem are often used as priors. We propose a method to automatically compute a prior. It uses statistics on solved problems. It is a simple and general method that incurs no computational cost at playout time and that brings large performance gains. The method is applied to three difficult combinatorial problems: Latin Square Completion, Kakuro, and Inverse RNA Folding.

关键词： Monte Carlo Tree Search combinatorial problems Learning Search Heuristics Latin Square Completion Kakuro Inverse RNA Folding

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Population Size Management in a Cuckoo Search Algorithm Solving combinatorial problems 1st

Population Size Management in a Cuckoo Search Algorithm Solv...

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1st International Conference on Informatics and Intelligent Applications (ICIIA)

作者： Chavez, Marcelo Crawford, Broderick Soto, Ricardo Palma, Wenceslao Becerra-Rozas, Marcelo Cisternas-Caneo, Felipe Astorga, Gino Misra, Sanjay Pontificia Univ Catolica Valparaiso Valparaiso Chile Univ Valparaiso Valparaiso Chile Ostfold Univ Coll Halden Norway

ISBN: (纸本)9783030956301;9783030956295

As is well known in the scientific community, optimization problems are becoming increasingly common, complex, and difficult to solve. The use of metaheuristics to solve these problems is gaining momentum thanks to their great adaptability. Because of this, there is a need to generate robust metaheuristics with a good balance of exploration and exploitation for different optimization problems. Our proposal seeks to improve the exploration and exploitation balance by incorporating a dynamic variation of the population. For this purpose, we implement the Cuckoo Search metaheuristic in its two versions, with and without dynamic population, to solve 3 classical optimization problems. Preliminary results are very good in terms of performance but indicate that it is not enough to vary the population dynamically, but it is necessary to add additional perturbation operators to force changes in the metaheuristic behavior.

关键词： Exploration and exploitation Cuckoo search algorithm Dynamic population Metaheuristics combinatorial problems

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Calculational solutions to combinatorial problems 10

Calculational solutions to combinatorial problems

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10th Colombian Computing Conference, 10CCC 2015

作者： Bohorquez, V. Jaime A. Escuela Colombiana of Ingeniería AK 45 # Bogotá205-59 Colombia

ISBN: (纸本)9781467394642

Many numerical identities are proved applying clever but informal combinatorial arguments. A way of proving these identities by a formal representation that closely follows these arguments is presented. Operationals, the main formal tool we use for this purpose, are basically, an abstract and axiomatic generalization of the Sigma (Σ) notation used to express and manipulate summations and counts. Operationals are endowed with algebraic properties that allow performing various natural operations that have a combinatorial significance. In this paper, we give a formal version of the typical combinatorial proof of the Inclusion-Exclusion theorem and some more examples showing how to formally interpret, in a practical way, combinatorial arguments used in the literature. © 2015 IEEE.

关键词： combinatorial mathematics mathematics computing symbol manipulation axiomatic generalization calculational solutions combinatorial arguments combinatorial problems counts manipulation formal representation formal tool inclusion-exclusion theorem numerical identities sigma notation summation manipulation Context Electronic mail Finite element analysis Indexes Instruments Mathematical model Silicon

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Reinforcement and Supervised Learning for combinatorial problems in Electronics Design Automation

Reinforcement and Supervised Learning for Combinatorial Prob...

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作者： Liao, Haiguang Carnegie Mellon University

学位级别：Ph.D., Doctor of Philosophy

Electronic Design Automation (EDA) software automates the IC design process and increases the design efficiency and capabilities. With the scaling of semiconductor technologies, the importance of EDA has rapidly increased. At the heart of most EDA design problems are combinatorial optimization problems, which are usually solved with heuristics, or analytical method in classical methods. Owing to the increasing difficulties of the EDA problems and demand for EDA tools designing increasingly complicated electronic systems, classical EDA algorithms are struggling to keep up with the ever more challenging EDA design tasks. Thus, better and more efficient EDA solutions are urgently needed to address the challenge. In recent years, there have been some major development in the field of machine learning, especially in (deep) reinforcement learning. Recent success of reinforcement learning has been demonstrated in fields including robotics, games as well as combinatorial optimization problems. This motivates us to explore the possibility of applying machine learning specifically reinforcement learning to come up with better EDA algorithms. In this research, we propose new algorithms to solve combinatorial problems in EDA based on reinforcement learning and supervised learning. To achieve this, we identified two research objectives. The first one is to developing reinforcement learning algorithms for solving EDA routing problems that performs better and more efficient than the current EDA routing solutions. Under this research objective, we propose three technical goals: (1) DQN Global Routing that solves global routing with Deep Q-learning; (2) Attention Routing that solves detailed routing with attention-based reinforcement learning; (3) Spectral DQN Routing that solves generic EDA routing and obstacle avoiding routing with combination of DQN and spectral method. Our proposed RL-based routing solutions provide better and more efficient alternatives compared with existing r

关键词： Supervised learning combinatorial problems Design automation Electronic design automation DQN routing

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Application of the cohort-intelligence optimization method to three selected combinatorial optimization problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2016年第2期250卷 427-447页

作者： Kulkarni, Anand J. Baki, M. F. Chaouch, Ben A. Univ Windsor Odette Sch Business 401 Sunset Ave Windsor ON N9B 3P4 Canada

The real world problems in the supply-chain domain are generally constrained and combinatorial in nature. Several nature-/bio-/socio-inspired metaheuristic methods have been proposed so far solving such problems. An emerging metaheuristic methodology referred to as Cohort Intelligence (CI) in the socio-inspired optimization domain is applied in order to solve three selected combinatorial optimization problems. The problems considered include a new variant of the assignment problem which has applications in healthcare and inventory management, a sea-cargo mix problem and a cross-border shipper selection problem. In each case, we use two benchmarks for evaluating the effectiveness of the CI method in identifying optimal solutions. To assess the quality of solutions obtained by using CI, we do comparative testing of its performance against solutions generated by using CPLEX. Furthermore, we also compare the performance of the CI method to that of specialized multi-random-start local search optimization methods that can be used to find solutions to these problems. The results are robust with a reasonable computational time and accuracy. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： Cohort intelligence combinatorial problems Assignment problem Cross-border shipper selection problem Sea-Cargo mix problem

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On the computational complexity of combinatorial flexibility problems

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2010年第15期87卷 3330-3343页

作者： Leoni, V. A. Nasini, G. L. Consejo Nacl Invest Cient & Tecn Buenos Aires DF Argentina Univ Nacl Rosario FCEIA RA-2000 Rosario Santa Fe Argentina

The concept of flexibility - originated in the context of heat exchanger networks design - is associated with a substructure which allows the same optimal value on the substructure (for example an optimal flow) as in the whole structure, for all the costs in a given range of costs. In this work, we extend the concept of flexibility to general combinatorial optimization problems, and prove several computational complexity results in this new framework. Under some monotonicity conditions, we prove that a combinatorial optimization problem can be polynomially reduced to its associated flexibility problem. However, the minimum cut, maximum weighted matching and shortest path problems have NP-complete associated flexibility problems. In order to obtain polynomial flexibility problems, we have to restrict ourselves to combinatorial optimization problems on matroids.

关键词： combinatorial problems test sets flexibility problems computational complexity matroids

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A Systematic Review of Hyper-Heuristics on combinatorial Optimization problems

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IEEE ACCESS 2020年 8卷 128068-128095页

作者： Sanchez, Melissa Cruz-Duarte, Jorge M. Carlos Ortiz-Bayliss, Jose Ceballos, Hector Terashima-Marin, Hugo Amaya, Ivan Tecnol Monterrey Sch Engn & Sci Monterrey 64849 Mexico

Hyper-heuristics aim at interchanging different solvers while solving a problem. The idea is to determine the best approach for solving a problem at its current state. This way, every time we make a move it gets us closer to a solution. The problem changes;so does its state. As a consequence, for the next move, a different solver may be invoked. Hyper-heuristics have been around for almost 20 years. However, combinatorial optimization problems date from way back. Thus, it is paramount to determine whether the efforts revolving around hyper-heuristic research have been targeted at the problems of the highest interest for the combinatorial optimization community. In this work, we tackle such an endeavor. We begin by determining the most relevant combinatorial optimization problems, and then we analyze them in the context of hyper-heuristics. The idea is to verify whether they remain as relevant when considering exclusively works related to hyper-heuristics. We find that some of the most relevant problem domains have also been popular for hyper-heuristics research. Alas, others have not and few efforts have been directed towards solving them. We identify the following problem domains, which may help in furthering the impact of hyper-heuristics: Shortest Path, Set Cover, Longest Path, and Minimum Spanning Tree. We believe that focusing research on ways for solving them may lead to an increase in the relevance and impact that hyper-heuristics have on combinatorial optimization problems.

关键词： Optimization Systematics Space exploration Vehicle routing Licenses Benchmark testing Biological system modeling combinatorial problems hyper-heuristics job-shop scheduling longest path NP-hard problems optimization set cover shortest path systematic review vehicle routing

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A note on robustness tolerances for combinatorial optimization problems

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INFORMATION PROCESSING LETTERS 2010年第16期110卷 725-729页

作者： Libura, Marek Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland

We consider so-called generic combinatorial optimization problem, where the set of feasible solutions is some family of nonempty subsets of a finite ground set with specified positive initial weights of elements, and the objective function represents the total weight of elements of the feasible solution. We assume that the set of feasible solutions is fixed, but the weights of elements may be perturbed or are given with errors. All possible realizations of weights form the set of scenarios. A feasible solution, which for a given set of scenarios guarantees the minimum value of the worst-case relative regret among all the feasible solutions, is called a robust solution. The maximum percentage perturbation of a single weight, which does not destroy the robustness of a given solution, is called the robustness tolerance of this weight with respect to the solution considered. In this paper we give formulae for computing the robustness tolerances with respect to an optimal solution obtained for some initial weights and we show that this can be done in polynomial time whenever the optimization problem is polynomially solvable itself. (C) 2010 Elsevier B.V. All rights reserved.

关键词： combinatorial problems Robust solutions Robustness tolerances

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