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IEEE/PES Transmission and Distribution Conference - Latin America

作者： Hashimoto, K Kagan, N Sao Paulo State Energy Regulatory Commiss CSPE Sao Paulo SP Brazil

ISBN: (纸本)0780387759

This paper aims at contributing for the estimation of electrical performance in the distribution of electric energy. Electrical performance is assumed to be the evaluation of network congestion parameters, losses and voltage level. The electrical performance estimation is formulated according to an optimization problem where the objective functions correspond to an evaluation of occurrence probability, and also correspond to a proximity evaluation of calculated parameters with values obtained by measurement. Load values are discretized according to ocurrence probabilities within each interval, so that formulation results in a multiobjective combinatorial optimization of exponential dimension. Network reduction procedures to substantially reduce Decision Domain and network expansion procedures to rebuild it are proposed. Specific heuristics are also proposed to get solutions with load diversity and unbalanced. In order to adequately apply these heuristics, a metaheuristic evolutionary method to build feasible solutions is proposed and applied, and ranked according to Pareto's concept. The mathematical formulation of optimization is flexible enough to be effectively applied taking into account different levels of supervisory systems developed in the utilities. The metaheuristic evolutionary model proposed was applied to a representative case with main potentialities and weak points to be improved.

关键词： electrical performance estimation. multiobjective combinatorial optimization evolutionary method. metaheuristics

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A greedy hypervolume polychotomic scheme for multiobjective combinatorial optimization

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Computers & Operations Research 2025年 183卷

作者： Gonçalo Lopes Kathrin Klamroth Luís Paquete CISUC Department of Informatics Engineering University of Coimbra Pólo II 3030-290 Coimbra Portugal School of Mathematics and Natural Sciences University of Wuppertal 42119 Wuppertal Germany

The usual goal in multiobjective combinatorial optimization is to find the complete set of nondominated points. However, in general, the nondominated set may be too large to be enumerated under a tight time budget. In these cases, it is preferable to rapidly obtain a concise representation of the nondominated set that satisfies a given property of interest. This work describes a generic greedy approach to compute a representation of the nondominated set for multiobjective combinatorial optimization problems that approximately maximizes the dominated hypervolume. The representation is built iteratively by solving a sequence of hypervolume scalarized problems, each of which with respect to k reference points, which is a parameter of our approach. We present a mixed-integer formulation of the hypervolume scalarization function for k reference points as well as a combinatorial branch-and-bound for the m -objective knapsack problem. We empirically analyse the functional relationship between k and its running-time and representation quality. Our results indicate that the branch-and-bound is a much more efficient approach and that increasing k does not directly translate into much better representation quality.

关键词： multiobjective combinatorial optimization Hypervolume scalarization Representation of the nondominated set Greedy hypervolume algorithm Local bounds

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Identifying preferred solutions in multiobjective combinatorial optimization problems

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TURKISH JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES 2019年第3期27卷 1970-1981页

作者： Lokman, Banu Koksalan, Murat Univ Portsmouth Portsmouth Business Sch Portsmouth Hants England Middle East Tech Univ Dept Ind Engn Fac Engn Ankara Turkey

We develop an evolutionary algorithm for multiobjective combinatorial optimization problems. The algorithm aims at converging the preferred solutions of a decision-maker. We test the performance of the algorithm on the multiobjective knapsack and multiobjective spanning tree problems. We generate the true nondominated solutions using an exact algorithm and compare the results with those of the evolutionary algorithm. We observe that the evolutionary algorithm works well in approximating the solutions in the preferred regions.

关键词： Evolutionary algorithm preferred region nondominated frontier multiobjective combinatorial optimization

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Effective anytime algorithm for multiobjective combinatorial optimization problems

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INFORMATION SCIENCES 2021年 565卷 210-228页

作者： Angel Dominguez-Rios, Miguel Chicano, Francisco Alba, Enrique Univ Malaga ITIS Software Malaga Spain

In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the search algorithm has to be stopped prematurely to analyze the solutions found so far. A set of efficient solutions that are well-spread in the objective space is preferred to provide the decision maker with a great variety of solutions. However, just a few exact algorithms in the literature exist with the ability to provide such a well-spread set of solutions at any moment: we call them anytime algorithms. We propose a new exact anytime algorithm for multiobjective combinatorial optimization combining three novel ideas to enhance the anytime behavior. We compare the proposed algorithm with those in the state-of-the-art for anytime multiobjective combinatorial optimization using a set of 480 instances from different well-known benchmarks and four different performance measures: the overall non-dominated vector generation ratio, the hypervolume, the general spread and the additive epsilon indicator. A comprehensive experimental study reveals that our proposal outperforms the previous algorithms in most of the instances. (c) 2021 Elsevier Inc. All rights reserved.

关键词： multiobjective combinatorial optimization Anytime algorithm Well-spread non-dominated points

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An interactive evolutionary metaheuristic for multiobjective combinatorial optimization

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MANAGEMENT SCIENCE 2003年第12期49卷 1726-1738页

作者： Phelps, S Köksalan, M Middle E Tech Univ Ind Engn Dept TR-06531 Ankara Turkey

We propose an evolutionary metaheuristic for multiobjective combinatorial optimization problems that interacts with the decision maker (DM) to guide the search effort toward his or her preferred solutions. Solutions are presented to the DM, whose pairwise comparisons are then used to estimate the desirability or fitness of newly generated solutions. The evolutionary algorithm comprising the skeleton of the metaheuristic makes use of selection strategies specifically designed to address the multiobjective nature of the problem. Interactions With the DM are triggered by a probabilistic evaluation of estimated fitnesses, while memory structures with indifference thresholds restrict the presentation of solutions resembling those that have already been rejected. The algorithm has been tested on a number of random instances of the multiobjective Knapsack Problem (MOKP) and the multiobjective Spanning Tree Problem (MOST). Simulation results indicate that the algorithm requires only a small number of comparisons to be made for satisfactory solutions to be found.

关键词： evolutionary algorithm multiobjective combinatorial optimization metaheuristic

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Cross entropy for multiobjective combinatorial optimization problems with linear relaxations

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第2期243卷 362-368页

作者： Caballero, Rafael Hernandez-Diaz, Alfredo G. Laguna, Manuel Molina, Julian Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain Pablo de Olavide Univ Dept Econ Quantitat Methods & Econ Hist Seville Spain Univ Colorado Leeds Sch Business Boulder CO 80309 USA

While the cross entropy methodology has been applied to a fair number of combinatorial optimization problems with a single objective, its adaptation to multiobjective optimization has been sporadic. We develop a multiobjective optimization cross entropy (MOCE) procedure for combinatorial optimization problems for which there is a linear relaxation (obtained by ignoring the integrality restrictions) that can be solved in polynomial time. The presence of a relaxation that can be solved with modest computational time is an important characteristic of the problems under consideration because our procedure is designed to exploit relaxed solutions. This is done with a strategy that divides the objective function space into areas and a mechanism that seeds these areas with relaxed solutions. Our main interest is to tackle problems whose solutions are represented by binary variables and whose relaxation is a linear program. Our tests with multiobjective knapsack problems and multiobjective assignment problems show the merit of the proposed procedure. (C) 2014 Elsevier B.V. All rights reserved.

关键词： multiobjective combinatorial optimization Cross entropy EMO Linear relaxation

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On local optima in multiobjective combinatorial optimization problems

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ANNALS OF OPERATIONS RESEARCH 2007年第1期156卷 83-97页

作者： Paquete, Luis Schiavinotto, Tommaso Stuetzle, Thomas Univ Algarve Ctr Sistemas Inteligentes Fac Econ P-8005139 Faro Portugal Scuola Normale Super Pisa I-56126 Pisa Italy Univ Libre Bruxelles IRIDIA CoDE B-1050 Brussels Belgium

In this article, local optimality in multiobjective combinatorial optimization is used as a baseline for the design and analysis of two iterative improvement algorithms. Both algorithms search in a neighborhood that is defined on a collection of sets of feasible solutions and their acceptance criterion is based on outperformance relations. Proofs of the soundness and completeness of these algorithms are given.

关键词： multiobjective combinatorial optimization local search local optima

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Easy to say they are Hard, but Hard to see they are Easy-Towards a Categorization of Tractable multiobjective combinatorial optimization Problems

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JOURNAL OF MULTI-CRITERIA DECISION ANALYSIS 2017年第1-2期24卷 82-98页

作者： Figueira, Jose Rui Fonseca, Carlos M. Halffmann, Pascal Klamroth, Kathrin Paquete, Luis Ruzika, Stefan Schulze, Britta Stiglmayr, Michael Willems, David Univ Lisbon Inst Super Tecn CEG IST Lisbon Portugal Univ Coimbra Dept Informat Engn CISUC Coimbra Portugal Univ Koblenz Landau Math Inst Koblenz Germany Univ Wuppertal Sch Math & Nat Sci Gaussstr 20 D-42119 Wuppertal Germany

multiobjective combinatorial optimization problems are known to be hard problems for two reasons: their decision versions are often NP-complete, and they are often intractable. Apart from this general observation, are there also variants or cases of multiobjective combinatorial optimization problems that are easy and, if so, what causes them to be easy? This article is a first attempt to provide an answer to these two questions. Thereby, a systematic description of reasons for easiness is envisaged rather than a mere collection of special cases. In particular, the borderline of easy and hard multiobjective optimization problems is explored. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： multiobjective combinatorial optimization tractability complexity theory bottleneck objective binary coefficients dynamic programming

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Interactive resolution of multiobjective combinatorial optimization problems by incremental elicitation of criteria weights

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EURO JOURNAL ON DECISION PROCESSES 2018年第3-4期6卷 283-319页

作者： Benabbou, Nawal Perny, Patrice Natl Univ Singapore COM1 NUS Sch Comp 13 Comp Dr Singapore 117417 Singapore Sorbonne Univ CNRS LIP6 F-75005 Paris France

We propose an introduction to the use of incremental preference elicitation methods in the field of multiobjective combinatorial optimization. We consider three different optimization problems in vector-valued graphs, namely the shortest path problem, the minimum spanning tree problem and the assignment problem. In each case, the preferences of the decision-maker over cost vectors are assumed to be representable by a weighted sum but the weights of criteria are initially unknown. We then explain how to interweave preference elicitation and search to quickly determine a near-optimal solution with a limited number of preference queries. This leads us to successively introduce an interactive version of dynamic programming, greedy search, and branch and bound to solve the problems under consideration. We then present numerical tests showing the practical efficiency of these algorithms that achieve a good compromise between the number of queries asked and the solution times.

关键词： multiobjective combinatorial optimization Preference elicitation Imprecise weights Minimax regret

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Balancing profits and costs on trees

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NETWORKS 2013年第3期61卷 200-211页

作者： Coene, Sofie Filippi, Carlo Spieksma, Frits C. R. Stevanato, Elisa Katholieke Univ Leuven Operat Res Grp B-3000 Louvain Belgium Univ Brescia Dept Quantitat Methods I-25122 Brescia Italy

We consider a rooted tree graph with costs associated with the edges and profits associated with the vertices. Every subtree containing the root incurs the sum of the costs of its edges, and collects the sum of the profits of its nodes;the goal is the simultaneous minimization of the total cost and maximization of the total profit. This problem is related to the TSP with profits on graphs with a tree metric. We analyze the problem from a biobjective point of view. We show that finding all extreme supported efficient points can be done in polynomial time. The problem of finding all efficient points, however, is harder;we propose a practical FPTAS for solving this problem. Some special cases are considered where the particular profit/cost structure or graph topology allows the efficient points to be found in polynomial time. Our results can be extended to more general graphs with distance matrices satisfying the Kalmanson conditions. (c) 2012 Wiley Periodicals, Inc. NETWORKS, 2013

关键词： multiobjective combinatorial optimization trees traveling salesman problem with profits Kalmanson conditions complexity

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