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Автор: Grafiati

Опубліковано: 15 червня 2024

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1

Adjiashvili, David, Sebastian Stiller, and Rico Zenklusen. "Bulk-Robust combinatorial optimization." Mathematical Programming 149, no. 1-2 (February 13, 2014): 361–90. http://dx.doi.org/10.1007/s10107-014-0760-6.

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2

Kawase, Yasushi, and Hanna Sumita. "Randomized Strategies for Robust Combinatorial Optimization." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 7876–83. http://dx.doi.org/10.1609/aaai.v33i01.33017876.

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In this paper, we study the following robust optimization problem. Given an independence system and candidate objective functions, we choose an independent set, and then an adversary chooses one objective function, knowing our choice. The goal is to find a randomized strategy (i.e., a probability distribution over the independent sets) that maximizes the expected objective value in the worst case. This problem is fundamental in wide areas such as artificial intelligence, machine learning, game theory and optimization. To solve the problem, we propose two types of schemes for designing approximation algorithms. One scheme is for the case when objective functions are linear. It first finds an approximately optimal aggregated strategy and then retrieves a desired solution with little loss of the objective value. The approximation ratio depends on a relaxation of an independence system polytope. As applications, we provide approximation algorithms for a knapsack constraint or a matroid intersection by developing appropriate relaxations and retrievals. The other scheme is based on the multiplicative weights update (MWU) method. The direct application of the MWU method does not yield a strict multiplicative approximation algorithm but yield one with an additional additive error term. A key technique to overcome the issue is to introduce a new concept called (η,γ)-reductions for objective functions with parameters η and γ. We show that our scheme outputs a nearly α-approximate solution if there exists an α-approximation algorithm for a subproblem defined by (η,γ)-reductions. This improves approximation ratios in previous results. Using our result, we provide approximation algorithms when the objective functions are submodular or correspond to the cardinality robustness for the knapsack problem.

3

Buchheim, Christoph, and Jannis Kurtz. "Min–max–min robust combinatorial optimization." Mathematical Programming 163, no. 1-2 (July 14, 2016): 1–23. http://dx.doi.org/10.1007/s10107-016-1053-z.

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4

Poss, Michael. "Robust combinatorial optimization with knapsack uncertainty." Discrete Optimization 27 (February 2018): 88–102. http://dx.doi.org/10.1016/j.disopt.2017.09.004.

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5

Koster, Arie M. C. A., and Michael Poss. "Special issue on: robust combinatorial optimization." EURO Journal on Computational Optimization 6, no. 3 (September 2018): 207–9. http://dx.doi.org/10.1007/s13675-018-0102-1.

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6

Goerigk, Marc, and Stefan Lendl. "Robust Combinatorial Optimization with Locally Budgeted Uncertainty." Open Journal of Mathematical Optimization 2 (May 18, 2021): 1–18. http://dx.doi.org/10.5802/ojmo.5.

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7

Goerigk, Marc, and Stephen J. Maher. "Generating hard instances for robust combinatorial optimization." European Journal of Operational Research 280, no. 1 (January 2020): 34–45. http://dx.doi.org/10.1016/j.ejor.2019.07.036.

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8

Poss, Michael. "Robust combinatorial optimization with variable cost uncertainty." European Journal of Operational Research 237, no. 3 (September 2014): 836–45. http://dx.doi.org/10.1016/j.ejor.2014.02.060.

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9

Dokka, Trivikram, Marc Goerigk, and Rahul Roy. "Mixed uncertainty sets for robust combinatorial optimization." Optimization Letters 14, no. 6 (July 24, 2019): 1323–37. http://dx.doi.org/10.1007/s11590-019-01456-3.

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10

Kurtz, Jannis. "Robust combinatorial optimization under budgeted–ellipsoidal uncertainty." EURO Journal on Computational Optimization 6, no. 4 (May 8, 2018): 315–37. http://dx.doi.org/10.1007/s13675-018-0097-7.

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11

Poss, Michael. "Robust combinatorial optimization with variable budgeted uncertainty." 4OR 11, no. 1 (November 8, 2012): 75–92. http://dx.doi.org/10.1007/s10288-012-0217-9.

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12

Crema, Alejandro. "Min max min robust (relative) regret combinatorial optimization." Mathematical Methods of Operations Research 92, no. 2 (May 19, 2020): 249–83. http://dx.doi.org/10.1007/s00186-020-00712-y.

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13

Buchheim, Christoph, and Jannis Kurtz. "Robust combinatorial optimization under convex and discrete cost uncertainty." EURO Journal on Computational Optimization 6, no. 3 (September 2018): 211–38. http://dx.doi.org/10.1007/s13675-018-0103-0.

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14

Chassein, André, and Marc Goerigk. "On scenario aggregation to approximate robust combinatorial optimization problems." Optimization Letters 12, no. 7 (October 23, 2017): 1523–33. http://dx.doi.org/10.1007/s11590-017-1206-x.

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15

Goerigk, Marc, and Martin Hughes. "Representative scenario construction and preprocessing for robust combinatorial optimization problems." Optimization Letters 13, no. 6 (October 29, 2018): 1417–31. http://dx.doi.org/10.1007/s11590-018-1348-5.

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16

Raith, Andrea, Marie Schmidt, Anita Schöbel, and Lisa Thom. "Multi-objective minmax robust combinatorial optimization with cardinality-constrained uncertainty." European Journal of Operational Research 267, no. 2 (June 2018): 628–42. http://dx.doi.org/10.1016/j.ejor.2017.12.018.

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17

Chassein, André, and Marc Goerigk. "Compromise solutions for robust combinatorial optimization with variable-sized uncertainty." European Journal of Operational Research 269, no. 2 (September 2018): 544–55. http://dx.doi.org/10.1016/j.ejor.2018.01.056.

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18

Alesiani, Francesco. "Implicit Bilevel Optimization: Differentiating through Bilevel Optimization Programming." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 12 (June 26, 2023): 14683–91. http://dx.doi.org/10.1609/aaai.v37i12.26716.

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Bilevel Optimization Programming is used to model complex and conflicting interactions between agents, for example in Robust AI or Privacy preserving AI. Integrating bilevel mathematical programming within deep learning is thus an essential objective for the Machine Learning community. Previously proposed approaches only consider single-level programming. In this paper, we extend existing single-level optimization programming approaches and thus propose Differentiating through Bilevel Optimization Programming (BiGrad) for end-to-end learning of models that use Bilevel Programming as a layer. BiGrad has wide applicability and can be used in modern machine learning frameworks. BiGrad is applicable to both continuous and combinatorial Bilevel optimization problems. We describe a class of gradient estimators for the combinatorial case which reduces the requirements in terms of computation complexity; for the case of the continuous variable, the gradient computation takes advantage of the push-back approach (i.e. vector-jacobian product) for an efficient implementation. Experiments show that the BiGrad successfully extends existing single-level approaches to Bilevel Programming.

19

Montajabiha, Mahsa, Alireza Arshadi Khamseh, and Behrouz Afshar-Nadjafi. "A robust algorithm for project portfolio selection problem using real options valuation." International Journal of Managing Projects in Business 10, no. 2 (April 4, 2017): 386–403. http://dx.doi.org/10.1108/ijmpb-12-2015-0114.

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Purpose The principal concern of organization managers in the global rivalry of commerce environment is how to select the project portfolio among available projects. In this matter, organizations should consider the uncertainty intrinsic in the projects regarding an appropriate valuation technique within an optimization framework. In this research, the purpose of this paper is to formulate using a robust optimization algorithm to deal with the complexities and uncertainty inherent in the construction of the project portfolio. Design/methodology/approach First, a general mathematical formulation is presented, which in compound real options valuation is highlighted. This formulation gives managerial flexibility by correcting the deficiency of traditional discounted cash flow technique that excludes any form of flexibility. Then, considering a limitation on budget of the organization, an integer programming formulation to maximize the n-fold compound options for project portfolio selection is proposed. Finally, a robust optimization model is developed along with the robust combinatorial optimization algorithm, which is effective for solving problems under uncertainty. Findings Sensitivity analysis showed that projects in later phases of development, having survived several phases of pre-clinical and clinical tests, are worth more because they are more likely to pertain to business. However, the investment costs related to each project during development phases limit the number of projects that a company can bring to their final portfolio. Additionally, the analysis of conservatism level represented how project managers can quite easily determine their risk attitude and the corresponding portfolio composition. From a managerial point of view, the proposed framework is very useful because it requires only financial estimates. Hence, the proposed decision support tool can assist research and development (R&D) project managers in the pharmaceutical industry for making decisions. Originality/value The first is the application of the n-fold compound options on portfolio of R&D projects and the employment of compound options value of a project portfolio as an objective function. The second one is a mathematical formulation of these concepts and solving it by the robust combinatorial optimization algorithm. The literature is lacking in the application of the robust combinatorial optimization algorithm to R&D project portfolio selection based on the generalized n-fold compound option model of Cassimon et al. (2004). Every framework from calculation of the n-fold compound option to solving robust combinatorial algorithm is programmed in Matlab software, since it can be used as a business support tool.

20

Shahsavar, Moslem, Amir Abbas Najafi, and Seyed Taghi Akhavan Niaki. "Statistical Design of Genetic Algorithms for Combinatorial Optimization Problems." Mathematical Problems in Engineering 2011 (2011): 1–17. http://dx.doi.org/10.1155/2011/872415.

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Many genetic algorithms (GA) have been applied to solve different NP-complete combinatorial optimization problems so far. The striking point of using GA refers to selecting a combination of appropriate patterns in crossover, mutation, and and so forth and fine tuning of some parameters such as crossover probability, mutation probability, and and so forth. One way to design a robust GA is to select an optimal pattern and then to search for its parameter values using a tuning procedure. This paper addresses a methodology to both optimal pattern selection and the tuning phases by taking advantage of design of experiments and response surface methodology. To show the performances of the proposed procedure and demonstrate its applications, it is employed to design a robust GA to solve a project scheduling problem. Through the statistical comparison analyses between the performances of the proposed method and an existing GA, the effectiveness of the methodology is shown.

21

Zhang , Tianyi, and Yuan Ke. "\({\ell_0}\) Optimization with Robust Non-Oracular Quantum Search." Technologies 11, no. 5 (October 19, 2023): 148. http://dx.doi.org/10.3390/technologies11050148.

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In this article, we introduce an innovative hybrid quantum search algorithm, the Robust Non-oracle Quantum Search (RNQS), which is specifically designed to efficiently identify the minimum value within a large set of random numbers. Distinct from the Grover’s algorithm, the proposed RNQS algorithm circumvents the need for an oracle function that describes the true solution state, a feature often impractical for data science applications. Building on existing non-oracular quantum search algorithms, RNQS enhances robustness while substantially reducing running time. The superior properties of RNQS have been demonstrated through careful analysis and extensive empirical experiments. Our findings underscore the potential of the RNQS algorithm as an effective and efficient solution to combinatorial optimization problems in the realm of quantum computing.

22

Pessoa, Artur Alves, Michael Poss, Ruslan Sadykov, and François Vanderbeck. "Branch-Cut-and-Price for the Robust Capacitated Vehicle Routing Problem with Knapsack Uncertainty." Operations Research 69, no. 3 (May 2021): 739–54. http://dx.doi.org/10.1287/opre.2020.2035.

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Capacitated vehicle routing problems are widely studied combinatorial optimization problems, and branch-and-cut-and-price algorithms can solve instances harder than ever before. These models, however, neglect that demands volumes are often not known with precision when planning the vehicle routes, thus incentivizing decision makers to significantly overestimate the volumes for avoiding coping with infeasible routes. A robust formulation that models demand uncertainty through a knapsack polytope is considered. A new branch-and-cut-and-price algorithm for the problem is provided, which combines efficient algorithms for the problem with no uncertainty with profound results in robust combinatorial optimization and includes novel heuristics and new valid inequalities. The numerical results illustrate that the resulting approach is two orders of magnitude faster that the best algorithm from the literature, solving twice as many instances to optimality.

23

Buchheim, Christoph, and Marianna De Santis. "An active set algorithm for robust combinatorial optimization based on separation oracles." Mathematical Programming Computation 11, no. 4 (April 24, 2019): 755–89. http://dx.doi.org/10.1007/s12532-019-00160-8.

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24

Yaman, Hande. "Short Paper - A Note on Robust Combinatorial Optimization with Generalized Interval Uncertainty." Open Journal of Mathematical Optimization 4 (June 5, 2023): 1–7. http://dx.doi.org/10.5802/ojmo.23.

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25

Lakhdari, Saliha, and Fateh Boutekkouk. "Optimization Trends for Wireless Network On-Chip." International Journal of Wireless Networks and Broadband Technologies 10, no. 1 (January 2021): 1–31. http://dx.doi.org/10.4018/ijwnbt.2021010101.

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Designing sustainable and high-performance wireless multi-core chips requires a matchless tradeoff between many aspects including scalable and reliable architectures implementation which in its turn implies aware-wideband energy-efficient wireless interfaces and adopting innovative straightforward optimization approaches to achieve the optimal configuration with a minimal cost. This paper focuses on investigating various existing designs and methodologies for wireless network on chip (WiNoC) architectures, as well as the different emerging technologies and optimization tools for the design of a robust and reliable WiNoC infrastructure with a special focus on combinatorial optimization meta-heuristics.

26

McElfresh, Duncan C., Hoda Bidkhori, and John P. Dickerson. "Scalable Robust Kidney Exchange." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 1077–84. http://dx.doi.org/10.1609/aaai.v33i01.33011077.

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In barter exchanges, participants directly trade their endowed goods in a constrained economic setting without money. Transactions in barter exchanges are often facilitated via a central clearinghouse that must match participants even in the face of uncertainty—over participants, existence and quality of potential trades, and so on. Leveraging robust combinatorial optimization techniques, we address uncertainty in kidney exchange, a real-world barter market where patients swap (in)compatible paired donors. We provide two scalable robust methods to handle two distinct types of uncertainty in kidney exchange—over the quality and the existence of a potential match. The latter case directly addresses a weakness in all stochastic-optimization-based methods to the kidney exchange clearing problem, which all necessarily require explicit estimates of the probability of a transaction existing—a still-unsolved problem in this nascent market. We also propose a novel, scalable kidney exchange formulation that eliminates the need for an exponential-time constraint generation process in competing formulations, maintains provable optimality, and serves as a subsolver for our robust approach. For each type of uncertainty we demonstrate the benefits of robustness on real data from a large, fielded kidney exchange in the United States. We conclude by drawing parallels between robustness and notions of fairness in the kidney exchange setting.

27

Buchheim, Christoph. "A note on the nonexistence of oracle-polynomial algorithms for robust combinatorial optimization." Discrete Applied Mathematics 285 (October 2020): 591–93. http://dx.doi.org/10.1016/j.dam.2020.07.002.

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28

Álvarez-Miranda, Eduardo, Ivana Ljubić, and Paolo Toth. "A note on the Bertsimas & Sim algorithm for robust combinatorial optimization problems." 4OR 11, no. 4 (March 2, 2013): 349–60. http://dx.doi.org/10.1007/s10288-013-0231-6.

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29

Lee, Taehan, and Changhyun Kwon. "A short note on the robust combinatorial optimization problems with cardinality constrained uncertainty." 4OR 12, no. 4 (August 8, 2014): 373–78. http://dx.doi.org/10.1007/s10288-014-0270-7.

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30

Huang, Changlong, Ling Pei, and Qi Ouyang. "Research on the Cuckoo Algorithm for Flexible Workshop Scheduling Problems." Frontiers in Computing and Intelligent Systems 3, no. 1 (March 22, 2023): 177–81. http://dx.doi.org/10.54097/fcis.v3i1.6365.

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As a typical combinatorial optimization problem, the essence of the solution to the scheduling problem is to formulate a reasonable scheduling scheme to arrange and allocate production resources, thereby obtaining the optimal scheduling result. The Cuckoo Search Algorithm (CS), a revolutionary meta-heuristic, is based on the cuckoo's breeding behavior and combines Lévy flight and random walk strategies to more efficiently attain the search goal. CS algorithm has been extensively employed in a variety of intricate combinatorial optimization issues, with its few parameters, precise resolution, random search path optimization, robust search aptitude, and uncomplicated implementation leading to satisfactory outcomes. After in-depth research, we found that the cuckoo search algorithm excels in dealing with flexible workshop scheduling problems. We conduct a series of comparative experiments to further confirm the efficacy of this algorithm. The results show that the cuckoo algorithm performs well in global search and can be used to solve complex flexible workshop scheduling models.

31

Montoya, Oscar Danilo, Walter Gil-González, and Jesus C. Hernández. "Optimal Scheduling of Photovoltaic Generators in Asymmetric Bipolar DC Grids Using a Robust Recursive Quadratic Convex Approximation." Machines 11, no. 2 (January 28, 2023): 177. http://dx.doi.org/10.3390/machines11020177.

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This paper presents a robust quadratic convex model for the optimal scheduling of photovoltaic generators in unbalanced bipolar DC grids. The proposed model is based on Taylor’s series expansion which relaxes the hyperbolic relation between constant power terminals and voltage profiles. Furthermore, the proposed model is solved in the recursive form to reduce the error generated by relaxations assumed. Additionally, uncertainties in PV generators are considered to assess the effectiveness of the proposed recursive convex. Several proposed scenarios for the numerical validations in a modified 21-bus test system were tested to validate the robust convex model’s performance. All the simulations were carried out in the MATLAB programming environment using Yalmip and Gurobi solver. Initially, a comparative analysis with three combinatorial optimization methods under three PV generation scenarios was performed. These scenarios consider levels of 0, 50, and 100% capacity of the PV systems. The results demonstrate the effectiveness of the proposed recursively solved convex model, which always achieves the global optimum for three levels of capacity of the PV generators, with solutions of 95.423 kW, 31.525 kW, and 22.985 kW for 0%, 50%, and 100% of the capacity PV rating, respectively. In contrast, the combinatorial optimization methods do not always reach these solutions. Furthermore, the power loss for the robust model is comparable to the deterministic model, increasing by 1.65% compared to the deterministic model.

32

Patish, Uri, and Shimon Ullman. "Cakewalk Sampling." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 03 (April 3, 2020): 2400–2407. http://dx.doi.org/10.1609/aaai.v34i03.5620.

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We study the task of finding good local optima in combinatorial optimization problems. Although combinatorial optimization is NP-hard in general, locally optimal solutions are frequently used in practice. Local search methods however typically converge to a limited set of optima that depend on their initialization. Sampling methods on the other hand can access any valid solution, and thus can be used either directly or alongside methods of the former type as a way for finding good local optima. Since the effectiveness of this strategy depends on the sampling distribution, we derive a robust learning algorithm that adapts sampling distributions towards good local optima of arbitrary objective functions. As a first use case, we empirically study the efficiency in which sampling methods can recover locally maximal cliques in undirected graphs. Not only do we show how our adaptive sampler outperforms related methods, we also show how it can even approach the performance of established clique algorithms. As a second use case, we consider how greedy algorithms can be combined with our adaptive sampler, and we demonstrate how this leads to superior performance in k-medoid clustering. Together, these findings suggest that our adaptive sampler can provide an effective strategy to combinatorial optimization problems that arise in practice.

33

Conde, Eduardo. "Robust minmax regret combinatorial optimization problems with a resource–dependent uncertainty polyhedron of scenarios." Computers & Operations Research 103 (March 2019): 97–108. http://dx.doi.org/10.1016/j.cor.2018.10.014.

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34

Büsing, Christina, and Sabrina Schmitz. "Robust two-stage combinatorial optimization problems under discrete demand uncertainties and consistent selection constraints." Discrete Applied Mathematics 347 (April 2024): 187–213. http://dx.doi.org/10.1016/j.dam.2023.12.028.

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35

Wang, Xinggang, Zhengdong Zhang, Yi Ma, Xiang Bai, Wenyu Liu, and Zhuowen Tu. "Robust Subspace Discovery via Relaxed Rank Minimization." Neural Computation 26, no. 3 (March 2014): 611–35. http://dx.doi.org/10.1162/neco_a_00555.

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This letter examines the problem of robust subspace discovery from input data samples (instances) in the presence of overwhelming outliers and corruptions. A typical example is the case where we are given a set of images; each image contains, for example, a face at an unknown location of an unknown size; our goal is to identify or detect the face in the image and simultaneously learn its model. We employ a simple generative subspace model and propose a new formulation to simultaneously infer the label information and learn the model using low-rank optimization. Solving this problem enables us to simultaneously identify the ownership of instances to the subspace and learn the corresponding subspace model. We give an efficient and effective algorithm based on the alternating direction method of multipliers and provide extensive simulations and experiments to verify the effectiveness of our method. The proposed scheme can also be used to tackle many related high-dimensional combinatorial selection problems.

36

Climent, Laura, Richard J. Wallace, Barry O'Sullivan, and Eugene C. Freuder. "Extrapolating from Limited Uncertain Information in Large-Scale Combinatorial Optimization Problems to Obtain Robust Solutions." International Journal on Artificial Intelligence Tools 25, no. 01 (February 2016): 1660005. http://dx.doi.org/10.1142/s0218213016600058.

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Data uncertainty in real-life problems is a current challenge in many areas, including Operations Research (OR) and Constraint Programming (CP). This is especially true given the continual and accelerating increase in the amount of data associated with real-life problems, to which Large Scale Combinatorial Optimization (LSCO) techniques may be applied. Although data uncertainty has been studied extensively in the literature, many approaches do not take into account the partial or complete lack of information about uncertainty in real-life settings. To meet this challenge, in this paper we present a strategy for extrapolating data from limited uncertain information to ensure a certain level of robustness in the solutions obtained. Our approach is motivated and evaluated with real-world applications of harvesting and supplying timber from forests to mills and the well known knapsack problem with uncertainty.

37

Wang, Fengmin, Dachuan Xu, and Chenchen Wu. "Combinatorial approximation algorithms for the robust facility location problem with penalties." Journal of Global Optimization 64, no. 3 (November 1, 2014): 483–96. http://dx.doi.org/10.1007/s10898-014-0251-6.

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38

Sagban, Rafid, Ku Ruhana Ku-Mahamud, and Muhamad Shahbani Abu Bakar. "ACOustic: A Nature-Inspired Exploration Indicator for Ant Colony Optimization." Scientific World Journal 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/392345.

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A statistical machine learning indicator,ACOustic, is proposed to evaluate the exploration behavior in the iterations of ant colony optimization algorithms. This idea is inspired by the behavior of some parasites in their mimicry to the queens’ acoustics of their ant hosts. The parasites’ reaction results from their ability to indicate the state of penetration. The proposed indicator solves the problem of robustness that results from the difference of magnitudes in the distance’s matrix, especially when combinatorial optimization problems with rugged fitness landscape are applied. The performance of the proposed indicator is evaluated against the existing indicators in six variants of ant colony optimization algorithms. Instances for travelling salesman problem and quadratic assignment problem are used in the experimental evaluation. The analytical results showed that the proposed indicator is more informative and more robust.

39

Zhou, Tao, Liang Luo, Shengchen Ji, and Yuanxin He. "A Reinforcement Learning Approach to Robust Scheduling of Permutation Flow Shop." Biomimetics 8, no. 6 (October 7, 2023): 478. http://dx.doi.org/10.3390/biomimetics8060478.

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The permutation flow shop scheduling problem (PFSP) stands as a classic conundrum within the realm of combinatorial optimization, serving as a prevalent organizational structure in authentic production settings. Given that conventional scheduling approaches fall short of effectively addressing the intricate and ever-shifting production landscape of PFSP, this study proposes an end-to-end deep reinforcement learning methodology with the objective of minimizing the maximum completion time. To tackle PFSP, we initially model it as a Markov decision process, delineating pertinent states, actions, and reward functions. A notably innovative facet of our approach involves leveraging disjunctive graphs to represent PFSP state information. To glean the intrinsic topological data embedded within the disjunctive graph’s underpinning, we architect a policy network based on a graph isomorphism network, subsequently trained through proximal policy optimization. Our devised methodology is compared with six baseline methods on randomly generated instances and the Taillard benchmark, respectively. The experimental results unequivocally underscore the superiority of our proposed approach in terms of makespan and computation time. Notably, the makespan can save up to 183.2 h in randomly generated instances and 188.4 h in the Taillard benchmark. The calculation time can be reduced by up to 18.70 s for randomly generated instances and up to 18.16 s for the Taillard benchmark.

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Zhou, Guangyan, and Rui Kang. "On the Lower Bounds of (1,0)-Super Solutions for Random k-SAT." International Journal of Foundations of Computer Science 30, no. 02 (February 2019): 247–54. http://dx.doi.org/10.1142/s0129054119500035.

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Super solution is a notion introduced to produce robust and stable solutions of combinatorial optimization and decision problems. We consider the [Formula: see text]-super solutions of random instances of [Formula: see text]-SAT, where a clause is satisfied if and only if there are at least two satisfied literals in this clause. By using an enhanced weighting scheme, we obtain better lower bounds that, if a random [Formula: see text]-CNF formula [Formula: see text] is [Formula: see text]-unsatisfiable with probability tending to 1 as [Formula: see text], then [Formula: see text] for [Formula: see text], respectively.

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El Majdouli, Mohamed Amine, and Abdelhakim Ameur El Imrani. "Discrete Fireworks Algorithm for Single Machine Scheduling Problems." International Journal of Applied Metaheuristic Computing 7, no. 3 (July 2016): 24–35. http://dx.doi.org/10.4018/ijamc.2016070102.

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Over the recent years, Fireworks Algorithm has recorded an increasing success on solving continuous optimization problems, due to its efficiency, simplicity and more importantly its rapid convergence to good optimums. Thus, the Fireworks Algorithm performance is now widely comparable with the most popular methods in the optimization field such as evolutionary computation and swarm intelligence techniques. This paper introduces a discrete Fireworks Algorithm for combinatorial single machine scheduling problems. Taking advantage of the robust design of the original Fireworks Algorithm, a new adaptation of sparks generation is proposed with a novel use of the control parameters. To verify the explorative performance of the algorithm, a hybridization with Variable Neighborhood Search heuristic is implemented. To validate it, the proposed method is tested with several benchmarks instances of the single machine total weighted tardiness. A comparison with other optimization algorithms is also included. The obtained results exhibit the high performance of the proposed method.

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Li, Mingguang, Runyi Huang, and Yumiao Yang. "Short-term wind speed prediction based on combinatorial prediction model." Highlights in Science, Engineering and Technology 60 (July 25, 2023): 274–82. http://dx.doi.org/10.54097/hset.v60i.10534.

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Improving the accuracy of wind speed forecast can increase wind power generation and better achieve wind energy grid connection. Therefore, a two-stage wind speed prediction model based on Ensemble Empirical Modal Decomposition (EEMD) and the combination prediction of Recurrent Neural Network (RNN), Long Short Term Memory (LSTM), eXtreme Gradient Boosting (XGBOOST), Gate Recurrent Unit (GRU), Temporal Convolutional Network (TCN) is proposed. First, the original wind speed series is separated into Intrinsic Mode Functions (IMFs) using EEMD. Then, RNN, LSTM, XGBOOST, GRU, TCN multiple prediction models are established to learn features from each subsequence and superimpose the prediction results of subsequences. Finally, Particle Swarm Optimization (PSO) is applied to the results of multiple prediction models to assign weights, combined with weight superimposing sequences to achieve higher accuracy and more robust wind speed prediction. Simulation analysis using data from St. Thomas, Virgin Islands wind measurement station to validate the validity of the combined prediction model. The experimental simulation results show that the model proposed in this paper has a good result on increasing wind speed prediction accuracy.

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Dechter, Rina, Natalia Flerova, and Radu Marinescu. "Search Algorithms for m Best Solutions for Graphical Models." Proceedings of the AAAI Conference on Artificial Intelligence 26, no. 1 (September 20, 2021): 1895–901. http://dx.doi.org/10.1609/aaai.v26i1.8405.

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The paper focuses on finding the m best solutions to combinatorial optimization problems using Best-First or Branchand- Bound search. Specifically, we present m-A*, extending the well-known A* to the m-best task, and prove that all its desirable properties, including soundness, completeness and optimal efficiency, are maintained. Since Best-First algorithms have memory problems, we also extend the memoryefficient Depth-First Branch-and-Bound to the m-best task. We extend both algorithms to optimization tasks over graphical models (e.g., Weighted CSP and MPE in Bayesian networks), provide complexity analysis and an empirical evaluation. Our experiments with 5 variants of Best-First and Branch-and-Bound confirm that Best-First is largely superior when memory is available, but Branch-and-Bound is more robust, while both styles of search benefit greatly when the heuristic evaluation function has increased accuracy.

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Mzili, Toufik, Ilyass Mzili, and Mohammed Essaid Riffi. "Artificial rat optimization with decision-making: A bio-inspired metaheuristic algorithm for solving the traveling salesman problem." Decision Making: Applications in Management and Engineering 6, no. 2 (October 15, 2023): 150–76. http://dx.doi.org/10.31181/dmame622023644.

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In this paper, we present the Rat Swarm Optimization with Decision Making (HDRSO), a hybrid metaheuristic algorithm inspired by the hunting behavior of rats, for solving the Traveling Salesman Problem (TSP). The TSP is a well-known NP-hard combinatorial optimization problem with important applications in transportation, logistics, and manufacturing systems. To improve the search process and avoid getting stuck in local minima, we added a natural mechanism to HDRSO through the incorporation of crossover and selection operators. In addition, we applied 2-opt and 3-opt heuristics to the best solution found by HDRSO. The performance of HDRSO was evaluated on a set of symmetric instances from the TSPLIB library and the results demonstrated that HDRSO is a competitive and robust method for solving the TSP, achieving better results than the best-known solutions in some cases.

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Bernardini, Sara, Fabio Fagnani, Santiago Franco, and Alexandra Neacsu. "A Network Flow Interpretation of Robust Goal Legibility in Path Finding." Proceedings of the International Conference on Automated Planning and Scheduling 32 (June 13, 2022): 668–77. http://dx.doi.org/10.1609/icaps.v32i1.19856.

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In this paper, we define goal legibility in a multi-agent path-finding setting. We consider a set of identical agents moving in an environment and tasked with reaching a set of locations that need to be serviced. An observer monitors their movements from a distance to identify their destinations as soon as possible. Our algorithm constructs a set of paths for the agents, one to each destination, that overlap as little as possible while satisfying a budget constraint. In this way, the observer, knowing the possible agents' destinations as well as the set of paths they might follow, is guaranteed to determine with certainty an agent's destination by looking at the shortest possible fragment of the agent's trajectory, regardless of when it starts observing. Our technique is robust because the observer's inference mechanism requires no coordination with the agents' motions. By reformulating legible path planning into a classical minimum cost flow problem, we can leverage powerful tools from combinatorial optimization, obtaining fast and scalable algorithms. We present experiments that show the benefits offered by our approach.

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Rodriguez-Molins, M., M. A. Salido, and F. Barber. "Robust Scheduling for Berth Allocation and Quay Crane Assignment Problem." Mathematical Problems in Engineering 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/834927.

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Decision makers must face the dynamism and uncertainty of real-world environments when they need to solve the scheduling problems. Different incidences or breakdowns, for example, initial data could change or some resources could become unavailable, may eventually cause the infeasibility of the obtained schedule. To overcome this issue, a robust model and a proactive approach are presented for scheduling problems without any previous knowledge about incidences. This paper is based on proportionally distributing operational buffers among the tasks. In this paper, we consider the berth allocation problem and the quay crane assignment problem as a representative example of scheduling problems. The dynamism and uncertainty are managed by assessing the robustness of the schedules. The robustness is introduced by means of operational buffer times to absorb those unknown incidences or breakdowns. Therefore, this problem becomes a multiobjective combinatorial optimization problem that aims to minimize the total service time, to maximize the buffer times, and to minimize the standard deviation of the buffer times. To this end, a mathematical model and a new hybrid multiobjective metaheuristic is presented and compared with two well-known multiobjective genetic algorithms: NSGAII and SPEA2+.

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MESHOUL, SOUHAM, and MOHAMED BATOUCHE. "COMBINING EXTREMAL OPTIMIZATION WITH SINGULAR VALUE DECOMPOSITION FOR EFFECTIVE POINT MATCHING." International Journal of Pattern Recognition and Artificial Intelligence 17, no. 07 (November 2003): 1111–26. http://dx.doi.org/10.1142/s0218001403002782.

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Feature point matching is a key step for most problems in computer vision. It is an ill-posed problem and suffers from combinatorial complexity which becomes even more critical with the increase in data and the presence of outliers. The work covered in this paper describes a new framework to solve this problem in order to achieve robust registration of two feature point sets assumed to be available. This framework combines the use of extremal optimization heuristic with a clever startup routine which exploits some properties of singular value decomposition. The role of the latter is to produce an interesting matching configuration whereas the role of the former is to refine the initial matching by generating hypothetical matches and outliers using a far-from-equilibrium based stochastic rule. Experiments on a wide range of real data have shown the effectiveness of the proposed method and its ability to achieve reliable feature point matching.

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Flerova, Natalia, Radu Marinescu, and Rina Dechter. "Searching for the M Best Solutions in Graphical Models." Journal of Artificial Intelligence Research 55 (April 12, 2016): 889–952. http://dx.doi.org/10.1613/jair.4985.

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The paper focuses on finding the m best solutions to combinatorial optimization problems using best-first or depth-first branch and bound search. Specifically, we present a new algorithm m-A*, extending the well-known A* to the m-best task, and for the first time prove that all its desirable properties, including soundness, completeness and optimal efficiency, are maintained. Since best-first algorithms require extensive memory, we also extend the memory-efficient depth-first branch and bound to the m-best task. We adapt both algorithms to optimization tasks over graphical models (e.g., Weighted CSP and MPE in Bayesian networks), provide complexity analysis and an empirical evaluation. Our experiments confirm theory that the best-first approach is largely superior when memory is available, but depth-first branch and bound is more robust. We also show that our algorithms are competitive with related schemes recently developed for the m-best task.

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Imabeppu, Takahiro, Shigeru Nakayama, and Satoshi Ono. "Experimental Study on Pair Swap Strategy in Quantum-Inspired Evolutionary Algorithm." Journal of Advanced Computational Intelligence and Intelligent Informatics 13, no. 2 (March 20, 2009): 97–108. http://dx.doi.org/10.20965/jaciii.2009.p0097.

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Quantum-Inspired Evolutionary Algorithm (QEA), a type of stochastic algorithm for solving combinatorial optimization problems, is evolutionary computation using quantum bits and superposition states in quantum computation. Although coarse-grained parallel, QEA has many parameters that must be adjusted manually. The simpler algorithm, Quantum-inspired Evolutionary Computation with Pair Swap operator (QEAPS), the authors propose involves just one population and a simple genetic operation exchanging best solution information between two individuals chosen randomly, instead of the migration operation used in QEA, and thereby fewer parameters to be adjusted. The authors found in experiments that QEAPS finds highly qualified solutions, is more robust against constraint handling, and has a higher search performance of thanks to diversified best solution information.

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Hedayat, A. "Developing a futuristic multi-objective optimization of the fuel management problems for the nuclear research reactors." Kerntechnik 85, no. 1 (December 1, 2020): 26–37. http://dx.doi.org/10.1515/kern-2020-850106.

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Abstract In this paper, at the same time, two separate objectives and two safety and operational constraints are chosen to optimize fuel reloading pattern of a Material Testing Reactor (MTR), independently and coherently. This is one of the most difficult type of engineering problems as a constrained, non-continuous, combinatorial, and fully multi-objective optimization problem. Decision space is a non-continuous multimodal space restricted by both of the combinatorial and safety constraints. A smart software application and a robust hybrid algorithm have been developed to get Pareto optimal set with respect to both of the economy of irradiating utilizations and nuclear safety based on the heuristic soft computing. The hybrid algorithm is composed of a fast and elitist Multi-Objective Genetic Algorithm (MOGA) and a fast fitness function evaluating system based on the semi-deep learning cascade feed forward Artificial Neural Networks (ANNs). The smart software is used to produce database automatically required for the ANN training and test data. It can be also used to revise data accurately, impose further irradiating benefits or Operating Limits and Conditions (OLCs), and to advise the reactor supervisor on the most desire pattern based on the smart searches and filtering. The results are highly promising. For more details, optimization results dominate conventional operating core parameters, significantly. Also chosen OLCs are protected. Furthermore, this is very good practice to reach a fully developed practical application of the complex soft computing for the nuclear fuel management problems.