The Experts below are selected from a list of 2655 Experts worldwide ranked by ideXlab platform
D. Dangar - One of the best experts on this subject based on the ideXlab platform.
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Duality for a class of fuzzy nonlinear optimization problem under generalized convexity
Fuzzy Optimization and Decision Making, 2014Co-Authors: S. K. Gupta, D. DangarAbstract:In this paper, a Mond-Weir type dual program for a nonlinear primal problem under fuzzy environment is formulated. The Solution concept of primal-dual problems is inspired by the Nondominated Solution. We have considered ordering among fuzzy numbers as a partial ordering and using the concept of Hukuhara difference between two fuzzy numbers and $$H$$ H -differentiability, appropriate duality theorems are established under pseudo/quasi-convexity assumptions. We have also illustrated a numerical example which satisfies the duality relations discussed in the paper.
Jyrki Wallenius - One of the best experts on this subject based on the ideXlab platform.
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evaluation of Nondominated Solution sets for k objective optimization problems an exact method and approximations
European Journal of Operational Research, 2006Co-Authors: Bosun Kim, Esma S Gel, John W Fowler, W M Carlyle, Jyrki WalleniusAbstract:Abstract Integrated Preference Functional (IPF) is a set functional that, given a discrete set of points for a multiple objective optimization problem, assigns a numerical value to that point set. This value provides a quantitative measure for comparing different sets of points generated by Solution procedures for difficult multiple objective optimization problems. We introduced the IPF for bi-criteria optimization problems in [Carlyle, W.M., Fowler, J.W., Gel, E., Kim, B., 2003. Quantitative comparison of approximate Solution sets for bi-criteria optimization problems. Decision Sciences 34 (1), 63–82]. As indicated in that paper, the computational effort to obtain IPF is negligible for bi-criteria problems. For three or more objective function cases, however, the exact calculation of IPF is computationally demanding, since this requires k (⩾3) dimensional integration. In this paper, we suggest a theoretical framework for obtaining IPF for k (⩾3) objectives. The exact method includes solving two main sub-problems: (1) finding the optimality region of weights for all potentially optimal points, and (2) computing volumes of k dimensional convex polytopes. Several different algorithms for both sub-problems can be found in the literature. We use existing methods from computational geometry (i.e., triangulation and convex hull algorithms) to develop a reasonable exact method for obtaining IPF. We have also experimented with a Monte Carlo approximation method and compared the results to those with the exact IPF method.
Maria João Alves - One of the best experts on this subject based on the ideXlab platform.
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MOD - A Differential Evolution Algorithm to Semivectorial Bilevel Problems
Lecture Notes in Computer Science, 2017Co-Authors: Maria João Alves, Carlos Henggeler AntunesAbstract:Semivectorial bilevel problems (SVBLP) deal with the optimization of a single function at the upper level and multiple objective functions at the lower level of hierarchical decisions. Therefore, a set of Nondominated Solutions to the lower level decision maker (the follower) exists and should be exploited for each setting of decision variables controlled by the upper level decision maker (the leader). This paper presents a new algorithmic approach based on differential evolution to compute a set of four extreme Solutions to the SVBLP. These Solutions capture not just the optimistic vs. pessimistic leader’s attitude but also possible follower’s reactions more or less favorable to the leader within the lower level Nondominated Solution set. The differential evolution approach is compared with a particle swarm optimization algorithm. In this experimental comparison we draw attention to pitfalls associated with the interpretation of results and assessment of the performance of algorithms in SVBLP.
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Surrogate Scalar Functions and Scalarizing Techniques
EURO Advanced Tutorials on Operational Research, 2016Co-Authors: Carlos Henggeler Antunes, Maria João Alves, João ClímacoAbstract:The most common procedure to compute efficient/Nondominated Solutions in MOP is using a scalarizing technique, which consists in transforming the original multiobjective problem into a single objective problem that may be solved repeatedly with different parameters. The functions employed in scalarizing techniques are called surrogate scalar functions or scalarizing functions. The optimal Solution to these functions should be anon dominated Solution to the multiobjective problem. These functions temporarily aggregate in a single dimension the p objective functions of the original model and include parameters derived from the elicitation of the DM’s preference information. Surrogate scalar functions should be able to generate Nondominated Solutions only, obtain any Nondominated Solution and be independent of dominated Solutions. In addition, the computational effort involved in the optimization of surrogate scalar functions should not be too demanding (e.g., increasing too much the dimension of the surrogate problem or resorting to nonlinear scalarizing functions when all original objective functions are linear) and the preference information parameters should have a simple interpretation (i.e., not imposing an excessive cognitive burden on the DM). Surrogate scalar functions should not be understood as “true” analytical representations of the DM’s preferences but rather as an operational means to transitorily aggregate the multiple objective functions and generate Nondominated Solutions to be proposed to the DM, which expectedly are in accordance with his/her (evolving) preferences.
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Graphical exploration of the weight space in three-objective mixed integer linear programs
European Journal of Operational Research, 2016Co-Authors: Maria João Alves, João Paulo CostaAbstract:In this paper we address the computation of indifference regions in the weight space for multiobjective integer and mixed-integer linear programming problems and the graphical exploration of this type of information for three-objective problems. We present a procedure to compute a subset of the indifference region associated with a supported Nondominated Solution obtained by the weighted-sum scalarization. Based on the properties of these regions and their graphical representation for problems with up to three objective functions, we propose an algorithm to compute all extreme supported Nondominated Solutions adjacent to a given Solution and another one to compute all extreme supported Nondominated Solutions to a three-objective problem. The latter is suitable to characterize Solutions in delimited Nondominated areas or to be used as a final exploration phase. A computer implementation is also presented.
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OR - A Branch & Cut Algorithm to Compute Nondominated Solutions in MOLFP via Reference Points
Operations Research Proceedings, 2011Co-Authors: João Paulo Costa, Maria João AlvesAbstract:Basedon some previous work ona Branch & Bound algorithm to compute Nondominated Solutions in multiobjective linear fractional programming (MOLFP) problems using reference points, we now present a new algorithm where special cuts are introduced. These cuts stem from some conditions that identify parts of the feasible region where the Nondominated Solution that optimizes the current achievement scalarizing function (ASF) cannot be obtained. Introducing the cuts substantially improves the performance of the previous algorithm. The results of several tests carried out to evaluate the performance of the new Branch & Cut algorithm against the old Branch & Bound are reported.
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motga a multiobjective tchebycheff based genetic algorithm for the multidimensional knapsack problem
Computers & Operations Research, 2007Co-Authors: Maria João Alves, Marla AlmeidaAbstract:This paper presents a new multiobjective genetic algorithm based on the Tchebycheff scalarizing function, which aims to generate a good approximation of the Nondominated Solution set of the multiobjective problem. The algorithm performs several stages, each one intended for searching potentially Nondominated Solutions in a different part of the Pareto front. Pre-defined weight vectors act as pivots to define the weighted-Tchebycheff scalarizing functions used in each stage. Therefore, each stage focuses the search on a specific region, leading to an iterative approximation of the entire Nondominated set. This algorithm, called MOTGA (Multiple objective Tchebycheff based Genetic Algorithm) has been designed to the multiobjective multidimensional 0/1 knapsack problem, for which a dedicated routine to repair infeasible Solutions was implemented. Computational results are presented and compared with the outcomes of other evolutionary algorithms.
S. K. Gupta - One of the best experts on this subject based on the ideXlab platform.
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Duality for a class of fuzzy nonlinear optimization problem under generalized convexity
Fuzzy Optimization and Decision Making, 2014Co-Authors: S. K. Gupta, D. DangarAbstract:In this paper, a Mond-Weir type dual program for a nonlinear primal problem under fuzzy environment is formulated. The Solution concept of primal-dual problems is inspired by the Nondominated Solution. We have considered ordering among fuzzy numbers as a partial ordering and using the concept of Hukuhara difference between two fuzzy numbers and $$H$$ H -differentiability, appropriate duality theorems are established under pseudo/quasi-convexity assumptions. We have also illustrated a numerical example which satisfies the duality relations discussed in the paper.
Bosun Kim - One of the best experts on this subject based on the ideXlab platform.
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evaluation of Nondominated Solution sets for k objective optimization problems an exact method and approximations
European Journal of Operational Research, 2006Co-Authors: Bosun Kim, Esma S Gel, John W Fowler, W M Carlyle, Jyrki WalleniusAbstract:Abstract Integrated Preference Functional (IPF) is a set functional that, given a discrete set of points for a multiple objective optimization problem, assigns a numerical value to that point set. This value provides a quantitative measure for comparing different sets of points generated by Solution procedures for difficult multiple objective optimization problems. We introduced the IPF for bi-criteria optimization problems in [Carlyle, W.M., Fowler, J.W., Gel, E., Kim, B., 2003. Quantitative comparison of approximate Solution sets for bi-criteria optimization problems. Decision Sciences 34 (1), 63–82]. As indicated in that paper, the computational effort to obtain IPF is negligible for bi-criteria problems. For three or more objective function cases, however, the exact calculation of IPF is computationally demanding, since this requires k (⩾3) dimensional integration. In this paper, we suggest a theoretical framework for obtaining IPF for k (⩾3) objectives. The exact method includes solving two main sub-problems: (1) finding the optimality region of weights for all potentially optimal points, and (2) computing volumes of k dimensional convex polytopes. Several different algorithms for both sub-problems can be found in the literature. We use existing methods from computational geometry (i.e., triangulation and convex hull algorithms) to develop a reasonable exact method for obtaining IPF. We have also experimented with a Monte Carlo approximation method and compared the results to those with the exact IPF method.