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Solving discrete multi-objective optimization problems using modified augmented weighted Tchebychev scalarizations

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第2期271卷 436-449页

作者： Holzmann, Tim Smith, J. C. Clemson Univ Dept Ind Engn 100B Freeman Hall Clemson SC 29634 USA

In this paper we present the modified augmented weighted Tchebychev norm, which can be used to generate a complete efficient set of solutions to a discrete multi-objective optimization problem. We contribute a generating algorithm that will, without supervision, generate the entire non-dominated set for any number of objectives. To our knowledge, this is the first generating method for general discrete multi objective problems that uses a variant of the Tchebychev norm. In a computational study, our algorithm's running times are comparable to previously proposed algorithms. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Tchebychev norm Computational optimization Generating methods

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A normal boundary intersection approach to multiresponse robust optimization of the surface roughness in end milling process with combined arrays

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PRECISION ENGINEERING-JOURNAL OF THE INTERNATIONAL SOCIETIES FOR PRECISION ENGINEERING AND NANOTECHNOLOGY 2014年第3期38卷 628-638页

作者： Brito, T. G. Paiva, A. P. Ferreira, J. R. Gomes, J. H. F. Balestrassi, P. P. Univ Fed Itajuba Inst Ind Engn BR-37500903 Itajuba MG Brazil

Robust parameter design (RPD) has recently been applied in modern industries in a large deal of processes. This technique is occasionally employed as a multiobjective optimization approach using weighted sums as a trade-off strategy;in such cases, however, a considerable number of gaps have arisen. In this paper, the use of normal boundary intersection (NBI) method coupled with mean-squared error (MSE) functions is proposed. This approach is capable of generating equispaced Pareto frontiers for a bi-objective robust design model, independent of the relative scales of the objective functions. To verify the adequacy of this proposal, a central composite design (CCD) is developed with combined arrays for the AISI 1045 steel end milling process. In this case study, a CCD with three noise factors and four control factors are used to create the mean and variance equations for MSE of two quality characteristics. The numerical results indicate the NBI-MSE approach is capable of generating a convex and equispaced Pareto frontier to MSE functions of surface roughness, thus nullifying the drawbacks of weighted sums. Moreover, the results show that the achieved optimum lessens the sensitivity of the end milling process to the variability transmitted by the noise factors. (C) 2014 Elsevier Inc. All rights reserved.

关键词： multiple objective programming Robust parameter design (RPD) Normal boundary intersection (NBI) End milling process Surface roughness

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PROMISE/scenarios: An interactive method for multiobjective stochastic linear programming under partial uncertainty

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第2期155卷 361-372页

作者： Urli, B Nadeau, R Univ Quebec Dept Econ & Gest Rimouski PQ G5L 3A1 Canada Univ Laval St Foy PQ G1K 7P4 Canada

In many real contexts where the multiobjective stochastic linear programming can be used as a modelling approach, the decision maker is in general placed in a situation of incomplete information concerning the uncertain parameters of the problem. A good way to express that incomplete information consists in resorting to the idea of scenarios relatively to the objectives and constraints of the stochastic program. While the authors who have suggested methods based on scenarios suppose that the probabilities of those scenarios are known, in this paper we propose a scenarios approach where the probabilities of scenarios is only incompletely specified according to a ranking. That interactive method, called PROMISE/scenarios, is presented and is illustrated by a didactic example. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： multiple objective programming stochastic programming scenarios interactive method partial uncertainty

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Biobjective route planning of an unmanned air vehicle in continuous space

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2023年第1期168卷 151-169页

作者： Ozturk, Diclehan Tezcaner Koksalan, Murat Hacettepe Univ Dept Ind Engn TR-06800 Ankara Turkiye Univ Michigan Ross Sch Business Ann Arbor MI 48104 USA Middle East Tech Univ Dept Ind Engn TR-06800 Ankara Turkiye

We consider the route planning problem of an unmanned air vehicle (UAV) in a continuous space that is monitored by radars. The UAV visits multiple targets and returns to the base. The routes are constructed considering the total distance traveled and the total radar detection threat ob-jectives. The UAV is capable of moving to any point in the terrain. This leads to infinitely many efficient trajectories between target pairs and infinitely many efficient routes to visit all targets. We use a two stage approach in solving the complex problem of finding all efficient routes. In the first stage, we structure the nondominated frontiers of the efficient trajectories between all target pairs. For this, we first identify properties shared by efficient trajectories between target pairs that are protected by a radar. This helps to structure the nondominated frontier between any target pair by identifying at most four specific efficient trajectories. We develop a search-based algo-rithm that finds these efficient trajectories effectively. For the second stage, we develop a mixed integer nonlinear program that exploits the structured nondominated frontiers between target pairs to construct the efficient routes. We compare the nondominated front we generate in the continuous space with its counterpart in a terrain discretized with three different grid fidelities. The continuous space representation outperforms all discrete representations in terms of solution quality and computational times.

关键词： multiple objective programming UAV routing Continuous space

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Integration of electromagnetism with multi-objective evolutionary algorithms for RCPSP

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2016年第1期251卷 22-35页

作者： Xiao, Jing Wu, Zhou Hong, Xi-Xi Tang, Jian-Chao Tang, Yong S China Normal Univ Sch Comp Sci Guangzhou 510631 Guangdong Peoples R China

As one of the most challenging combinatorial optimization problems in scheduling, the resource-constrained project scheduling problem (RCPSP) has attracted numerous scholars' interest resulting in considerable research in the past few decades. However, most of these papers focused on the single objective RCPSP;only a few papers concentrated on the multi-objective resource-constrained project scheduling problems (MORCPSP). Inspired by a procedure called electromagnetism (EM), which can help a generic population based evolutionary search algorithm to obtain good results for single objective RCPSP, in this paper we attempt to extend EM and integrate it into three reputable state-of-the-art multi-objective evolutionary algorithms (MOEAs) i.e. non-dominated sorting based multi-objective evolutionary algorithm (NSGA-II), strength Pareto evolutionary algorithm (SPEA2) and multi-objective evolutionary algorithm based on decomposition (MOEA/D), for MORCPSP. We aim to optimize makespan and total tardiness. Empirical analysis based on standard benchmark datasets are conducted by comparing the versions of integrating EM to NSGA-II, SPEA2 and MOEND with the original algorithms without EM. The results demonstrate that EM can improve the performance of NSGA-II and SPEA2, especially for NSGA-II. (C) 2015 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Heuristics Resource-constrained project scheduling Electromagnetism Evolutionary algorithms

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Pareto solutions in multicriteria optimization under uncertainty

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期281卷 357-368页

作者： Engau, Alexander Sigler, Devon Univ Lancaster Management Sch Lancaster LA1 4YX England Dalhousie Univ Rowe Sch Business Kenneth C Rowe Management Bldg6100 Univ Ave Halifax NS B3H 4R2 Canada Univ Colorado Dept Math & Stat Sci Campus Box 170POB 173364 Denver CO 80217 USA Natl Renewable Energy Lab 15013 Denver West Pkwy Golden CO 80401 USA

We present and analyze several definitions of Pareto optimality for multicriteria optimization or decision problems with uncertainty primarily in their objective function values. In comparison to related notions of Pareto robustness, we first provide a full characterization of an alternative efficient set hierarchy that is based on six different ordering relations both with respect to the multiple objectives and a possibly finite, countably infinite or uncountable number of scenarios. We then establish several scalarization results for the generation of the corresponding efficient points using generalized weighted-sum and epsilon-constraint techniques. Finally, we leverage these scalarization results to also derive more general conditions for the existence of efficient points in each of the corresponding optimality classes, under suitable assumptions. (C) 2019 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Pareto solutions Optimization under uncertainty Efficient set hierarchy Scalarization methods

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Redistribution of funds for teaching and research among universities: The case of North Rhine-Westphalia

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2001年第1期130卷 111-120页

作者： Fandel, G Gal, T Fern Univ Hagen Dept Econ D-58084 Hagen Germany

This paper reports on a real application of a performance and success based system for redistribution of funds for teaching and research among universities in North Rhine-Westphalia, After a precise description of the decision situation, we show how goal programming and distance minimization were applied in order to find a solution on the basis of real data. Some comments on the results and the quality of the redistribution process conclude the paper. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： group decisions and negotiations multiple criteria analysis multiple objective programming resource allocation

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A multi-objective Monte Carlo tree search for forest harvest scheduling

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第3期282卷 1115-1126页

作者： Neto, Teresa Constantino, Miguel Martins, Isabel Pedroso, Joao Pedro Inst Politecn Viseu Escola Super Tecnol & Gestao P-3504510 Viseu Portugal Univ Lisbon Fac Ciencias Ctr Matemat Aplicacoes Fundamentals & Invest Oper P-1749016 Lisbon Portugal Univ Lisboa Tapada Ajuda Inst Super Agron Ctr Matemat Aplicacoes Fundamentals & Invest Oper P-1349017 Lisbon Portugal Univ Porto INESC TEC Fac Ciencias Rua Campo Alegre P-4169007 Porto Portugal

While the objectives of forest management vary widely and include the protection of resources in protected forests and nature reserves, the primary objective has often been the production of wood products. However, even in this case, forests play a key role in the conservation of living resources. Constraining the areas of clearcuts contributes to this conservation, but if it is too restrictive, a dispersion of small clearcuts across the forest might occur, and forest fragmentation might be a serious ecological problem. Forest fragmentation leads to habitat loss, not only because the forest area is reduced, but also because the core area of the habitats and the connectivity between them decreases. This study presents a Monte Carlo tree search method to solve a bi-objective harvest scheduling problem with constraints on the clearcut area, total habitat area and total core area inside habitats. The two objectives are the maximization of both the net present value and the probability of connectivity index. The method is presented as an approach to assist the decision maker in estimating efficient alternative solutions and the corresponding trade-offs. This approach was tested with instances for forests ranging from some dozens to over a thousand stands and temporal horizons from three to eight periods. In general, multi-objective Monte Carlo tree search was able to find several efficient alternative solutions in a reasonable time, even for medium and large instances. (C) 2019 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Forest planning Core area Connectivity Tree search

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A fuzzy hybrid integrated framework for portfolio optimization in private banking

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EXPERT SYSTEMS WITH APPLICATIONS 2018年 92卷 350-362页

作者： Ferreira, Luciano Borenstein, Denis Righi, Marcelo Brutti de Almeida Filho, Adiel Teixeira Univ Fed Rio Grande do Sul Management Sch Porto Alegre RS Brazil Univ Fed Pernambuco CDSID Recife PE Brazil

Decision-making processes in private banking must comply with standards for risk management and transparency enforced by banking regulations. Therefore, investors must be supported throughout a risk informed decision process. This paper contributes to the literature by presenting a hybrid integrated framework that considers personal features of the investor and additional characteristics imposed by regulations, for which linguistic evaluations are used with regard to risk exposure. The proposed approach for personal investment portfolios considers legal aspects and investor's preferences as an input to the novel fuzzy multiple-attribute decision making approach for sorting problems proposed in this paper, called FTOPSIS-Class. Then, the next step of the proposed framework uses the sorting results for a fuzzy multi-objective optimization model that considers the risk and return associated with the investor's profile over three objectives. The contributions of this paper are illustrated and validated by using a numerical application in line with a new trend for modern portfolio theory which enables a real world investor's characteristics to be considered throughout the decision-making process. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： OR in banking Investment analysis Fuzzy sets multiple attribute decision making multiple objective programming

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A multiplicative version of Promethee II applied to multiobjective optimization problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第2期183卷 729-740页

作者： Parreiras, R. O. Vasconcelos, J. A. Univ Fed Minas Gerais Dept Elect Engn BR-31270010 Belo Horizonte MG Brazil

The method Promethee II has produced attractive results in the choice of the most satisfactory optimal solution of convex multiobjective problems. However, according to the current literature, it may not work properly with nonconvex problems. A modified version of this method, called multiplicative Promethee, is proposed in this paper. Both versions are applied to some analytical problems, previously optimized by an evolutionary algorithm. The multiplicative Promethee got much better results than the original Promethee II, being capable of solving convex and nonconvex problems, with continuous and discontinuous Pareto fronts. (c) 2006 Elsevier B.V. All rights reserved.

关键词： multiple criteria analysis multiple objective programming decision analysis

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