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A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第3期169卷 943-959页

作者： Paquete, L Stützle, T Tech Univ Darmstadt Dept Comp Sci Intellect Grp D-64283 Darmstadt Germany

This paper studies the performance of two stochastic local search algorithms for the biobjective Quadratic Assignment Problem with different degrees of correlation between the flow matrices. The two algorithms follow two fundamentally different ways of tackling multiobjective combinatorial optimization problems. The first is based on the component-wise ordering of the objective value vectors of neighboring solutions, while the second is based on different scalarizations of the objective function vector. Our experimental results suggest that the performance of the algorithms with respect to solution quality and computation time depends strongly on the correlation between the flow matrices. In addition, some variants of these stochastic local search algorithms obtain very good solutions in short computation time. (c) 2004 Elsevier B.V. All rights reserved.

关键词： combinatorial optimization stochastic local search multiple objective programming

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Trade-off preservation in inverse multi-objective convex optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第1期270卷 25-39页

作者： Chan, Timothy C. Y. Lee, Taewoo Univ Toronto Mech & Ind Engn 5 Kings Coll Rd Toronto ON M5S 3G8 Canada Univ Houston Ind Engn 4722 Calhoun Rd Houston TX 77204 USA

Given an input solution that may not be Pareto optimal, we present a new inverse optimization methodology for multi-objective convex optimization that determines a weight vector producing a weakly Pareto optimal solution that preserves the decision maker's trade-off intention encoded in the input solution. We introduce a notion of trade-off preservation, which we use as a measure of similarity for approximating the input solution, and show its connection with minimizing an optimality gap. We propose a linear approximation to the inverse model and a successive linear programming algorithm that balance between trade-off preservation and computational efficiency, and show that our model encompasses many of the existing inverse optimization models from the literature. We demonstrate the proposed method using clinical data from prostate cancer radiation therapy. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Convex programming Inverse optimization OR in cancer therapy

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A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第3期180卷 1011-1027页

作者： Sylva, John Crema, Alejandro Cent Univ Venezuela Escuela Computac Fac Ciencias Caracas 1041A Venezuela Cent Univ Venezuela Fac Ingn Dept Matemat Aplicada Caracas 1041A Venezuela

We present an algorithm for generating a subset of non-dominated vectors of multiple objective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a new one that maximizes the infinity-norm distance from the set dominated by the previously found solutions. When all variables are integer, it can generate the whole set of non-dominated vectors. (c) 2006 Elsevier B.V. All rights reserved.

关键词： integer programming multiple objective programming parametric programming

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Resource allocation in dynamic PERT networks with finite capacity

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2011年第3期215卷 670-678页

作者： Yaghoubi, Saeed Noori, Siamak Azaron, Amir Tavakkoli-Moghaddam, Reza Univ Coll Dublin Michael Smurfit Grad Sch Business Dublin 2 Ireland Iran Univ Sci & Technol Dept Ind Engn Tehran Iran Univ Tehran Dept Ind Engn Fac Engn Tehran Iran Reykjavik Univ Dept Financial Engn & Engn Management Sch Sci & Engn Reykjavik Iceland

This article models the resource allocation problem in dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)), where activity durations are independent random variables with exponential distributions, and the new projects are generated according to a Poisson process. The system is represented as a queuing network with finite concurrent projects, where each activity of a project is performed at a devoted service station with one server located in a node of the network. For modeling dynamic PERT networks with CONPIP, we first convert the network of queues into a stochastic network. Then, by constructing a proper finite-state continuous-time Markov model, a system of differential equations is created to solve and find the completion time distribution for any particular project. Finally, we propose a multi-objective model with three conflict objectives to optimally control the resources allocated to the servers, and apply the goal attainment method to solve a discrete-time approximation of the original multi-objective problem. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Project management Markov processes multiple objective programming

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Computing all efficient solutions of the biobjective minimum spanning tree problem

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COMPUTERS & OPERATIONS RESEARCH 2008年第1期35卷 198-211页

作者： Steiner, Sarah Radzik, Tomasz Kings Coll London Dept Comp Sci London WC2R 2LS England

A common way of computing all efficient (Pareto optimal) solutions for a biobjective combinatorial optimisation problem is to compute first the extreme efficient solutions and then the remaining, non-extreme solutions. The second phase, the computation of non-extreme solutions, can be based on a "k-best" algorithm for the single-objective version of the problem or on the branch-and-bound method. A k-best algorithm computes the k-best solutions in order of their objective values. We compare the performance of these two approaches applied to the biobjective minimum spanning tree problem. Our extensive computational experiments indicate the overwhelming superiority of the k-best approach. We propose heuristic enhancements to this approach which further improve its performance. (C) 2006 Elsevier Ltd. All rights reserved.

关键词： multiple objective programming combinatorial optimisation minimum spanning tree k-best algorithm

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Pareto uncertainty index for evaluating and comparing solutions for stochastic multiple objective problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期284卷 644-659页

作者： Selcuklu, Saltuk Bugra Coit, David W. Felder, Frank A. Erciyes Univ Energy Syst Engn Kayseri Turkey Rutgers State Univ Ind & Syst Engn Piscataway NJ USA Tsinghua Univ Ind Engn Dept Beijing Peoples R China Rutgers State Univ Ctr Energy Econ & Environm Policy Piscataway NJ USA

Many engineering problems have multiple conflicting objectives, and they are also stochastic due to inherent uncertainties. One way to represent the multi-objective nature of problems is to use the Pareto optimality to show the trade-off between objectives. Pareto optimality involves the identification of solutions that are not dominated by other solutions based on their respective objective functions. However, the Pareto optimality concept does not contain any information about the uncertainty of solutions. Evaluation and comparison of solutions becomes difficult when the objective functions are subjected to uncertainty. A new metric, the Pareto Uncertainty Index (PUI), is presented. This metric includes uncertainty due to the stochastic coefficients in the objective functions as part of the Pareto optimality concept to form an extended probabilistic Pareto set, we define as the p-Pareto set. The decision maker can observe and assess the randomness of solutions and compare the promising solutions according to their performance of satisfying objectives and any undesirable uncertainty. The PUI is an effective and convenient decision-making tool to compare promising solutions with multiple uncertain objectives. (C) 2020 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Uncertainty modeling Pareto

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Locating series FACTS devices for multi-objective congestion management improving voltage and transient stability

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2014年第2期236卷 763-773页

作者： Esmaili, Masoud Shayanfar, Heidar Ali Moslemi, Ramin Islamic Azad Univ Dept Elect Engn West Tehran Branch Tehran Iran Iran Univ Sci & Technol Ctr Excellence Power Syst Automat & Operat Tehran Iran

Transmission congestion management is a vital task in electricity markets. Series FACTS devices can be used as effective tools to relieve congestion mostly employing Optimal Power Flow based methods, in which total cost as the objective function is minimized. However, power system stability may be deteriorated after relieving congestion using traditional methods leading to a vulnerable power system against disturbances. In this paper, a multi-objective framework is proposed for congestion management where three competing objective functions including total operating cost, voltage and transient stability margins are simultaneously optimized. This leads to an economical and robust operating point where enough levels of voltage and transient security are included. The proposed method optimally locates and sizes series FACTS devices on the most congested branches determined by a priority list based on Locational Marginal Prices. Individual sets of Pareto solutions, resulted from solving multi-objective congestion management for each location of FACTS devices, are merged together to create the comprehensive Pareto set. Results of testing the proposed method on the well-known New-England test system are discussed in details and confirm efficiency of the proposed method. (C) 2014 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Congestion management FACTS devices Electricity markets Power system stability margin

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Post design modeling for cellular manufacturing system with cost uncertainty

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 1998年第1期55卷 97-109页

作者： Shanker, R Vrat, P Indian Inst Technol Dept Mech Engn New Delhi 110016 India

Post-design decisions in a cellular manufacturing system are modeled in this paper as an interval programming model in which the coefficients of the objective function are expressed in range rather than a point estimate. Uncertainties in estimations for costs related to exceptional elements and bottleneck machines have been modeled. The interval objective function involves order relations, which represents the decision makers' preference between interval costs. The objective function is minimized by converting it into a multi-objective problem using order relations. A quantitative estimate of 'risk by gain ratio' is proposed to understand the model behavior and to facilitate the selection of appropriate strategies. (C) 1998 Elsevier Science B.V. All rights reserved.

关键词： cellular manufacturing system interval analysis multiple objective programming

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On the computational efficiency of multiple objective metaheuristics. The knapsack problem case study

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第2期158卷 418-433页

作者： Jaszkiewicz, A Poznan Univ Tech Inst Comp Sci PL-60965 Poznan Poland

The paper describes a computational experiment which goal is to evaluate computational efficiency of three multiple objective evolutionary metaheuristics on the multiple objective multiple constraints knapsack problem. The relative efficiency of the multiple objective algorithms is evaluated with respect to a single objective evolutionary algorithm (EA). We use a methodology that allows consistent evaluation of the quality of approximately Pareto-optimal solutions generated by both multiple and single objective metaheuristics. Then, we compare computational efforts needed to generate solutions of approximately the same quality by the two kinds of methods. The results indicate that computational efficiency of multiple objective EAs deteriorates with the growth of the number of objectives. Furthermore, significant differences in the performance of the three algorithms are observed. (C) 2003 Elsevier B.V. All rights reserved.

关键词： multiple objective programming combinatorial optimization metaheuristics

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A study of interval metric and its application in multi-objective optimization with interval objectives

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COMPUTERS & INDUSTRIAL ENGINEERING 2014年第1期74卷 169-178页

作者： Bhunia, Asoke Kumar Samanta, Subhra Sankha Univ Burdwan Dept Math Burdwan 713104 W Bengal India

The aim of this paper is to discuss the optimality of interval multi-objective optimization problems with the help of different interval metric. For this purpose, we have proposed the new definitions of interval order relations by modifying the existing definitions and also modified different definitions of interval mathematics. Using the definitions of interval order relations and interval metric, the multi-objective optimization problem is converted into single objective optimization problem by different techniques. Then the corresponding problems have been solved by hybrid Tournament Genetic Algorithm with whole arithmetic crossover and double mutation (combination of non-uniform and boundary mutations). To illustrate the methodology, five numerical examples have been solved and the computational results have been compared. Finally, to test the efficiency of the proposed hybrid Tournament Genetic Algorithm, sensitivity analyses have been carried out graphically with respect to genetic algorithm parameters. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： multiple objective programming Interval objective Interval order relations Pareto optimality Tournament Genetic Algorithm

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