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 ...
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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.
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 solut...
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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.
We present an algorithm for generating a subset of non-dominated vectors of multipleobjective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a n...
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We present an algorithm for generating a subset of non-dominated vectors of multipleobjective 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.
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 rand...
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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.
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...
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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.
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 t...
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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.
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 co...
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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.
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 estima...
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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.
The paper describes a computational experiment which goal is to evaluate computational efficiency of three multipleobjective evolutionary metaheuristics on the multipleobjectivemultiple constraints knapsack problem...
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The paper describes a computational experiment which goal is to evaluate computational efficiency of three multipleobjective evolutionary metaheuristics on the multipleobjectivemultiple constraints knapsack problem. The relative efficiency of the multipleobjective 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 multipleobjective 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.
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...
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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.
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