This paper deals with multiobjective optimization programs in which the objective functions are ordered by their degree of priority. A number of approaches have been proposed (and several implemented) for the solution...
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This paper deals with multiobjective optimization programs in which the objective functions are ordered by their degree of priority. A number of approaches have been proposed (and several implemented) for the solution of lexicographic (preemptive priority) multiobjective optimization programs. These approaches may be divided into two classes. The first encompasses the development of algorithms specifically designed to deal directly with the initial model. Considered only for linear multiobjective programs and multiobjective programs with a finite discrete feasible region, the second one attempts to transform, efficiently, the lexicographic multiobjective model into an equvivalent model, i.e. a single objective programming problem. In this paper, we deal with the second approach for lexicographic nonlinear multiobjective programs.
The Pareto (or nondominated set) for a multiobjective optimization problem is often of nontrivial size, and the decision maker may have a difficult time establishing objective criterion weights to select a solution. I...
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The Pareto (or nondominated set) for a multiobjective optimization problem is often of nontrivial size, and the decision maker may have a difficult time establishing objective criterion weights to select a solution. In light of these issues, clustering or partitioning methods can be of considerable value for pruning the Pareto set and limiting the decision to a few choice exemplars. A three-stage approach is proposed. In stage one, a variance-to-range measure is used to normalize the criterion function values. In stage two, maximum split partitioning and p-median partitioning are each applied to the normalized measures, thus producing two partitions of the Pareto set and two sets of exemplars. Finally, in stage three, the union of the exemplars obtained by the two partitioning methods is accepted as the final set of exemplars. The partitioning methods are compared within the context of multiobjective allocation of a cross-trained workforce to achieve both operational and human resource objectives. (C) 2017 Elsevier Ltd. All rights reserved.
With the number of alternative systems increasing, the system portfolio selection problem for large-scale complex systems is an non-deterministic polynomial (NP)-hard problem. The time cost of the classification selec...
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With the number of alternative systems increasing, the system portfolio selection problem for large-scale complex systems is an non-deterministic polynomial (NP)-hard problem. The time cost of the classification selection algorithm used for the portfolio selection is intolerable;thus, improving the algorithm is necessary. In this paper, first, the weapon system portfolio selection (WSPS) model is categorized into two types: single objective and multiobjective;the optimization difficulties are analyzed;and the feasible solution space reduction strategy is given. Second, a portfolio selection optimization algorithm based on the difference evolution technique for order preference by similarity to ideal solution (DE-TOPSIS) is proposed where the weapon system weighting method TOPSIS is integrated with the DE algorithm. Finally, considering different weapon system scales, the advantages of the proposed algorithm are illustrated by comparing it with two other algorithms in a single-target case and two other algorithms in a multiobjective case. The results indicate that the DE algorithm always has better performance with regard to optimal solution quality, convergence speed, and algorithm stability.
A pair of Wolfe type multiobjective second order symmetric dual programs with cone constraints is formulated and usual duality results are established under second order invexity assumptions. These results are then us...
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A pair of Wolfe type multiobjective second order symmetric dual programs with cone constraints is formulated and usual duality results are established under second order invexity assumptions. These results are then used to investigate symmetric duality for minimax version of multiobjective second order symmetric dual programs wherein some of the primal and dual variables are constrained to belong to some arbitrary sets, i.e., the sets of integers. This paper points out certain omissions and inconsistencies in the earlier work of Mishra [S.K. Mishra, multiobjective second order symmetric duality with cone constraints, European journal of Operational Research 126 (2000) 675-682] and Mishra and Wang [S.K. Mishra, S.Y. Wang, Second order symmetric duality for nonlinear multiobjective mixed integer programming, European journal of Operational Research 161 (2005) 673-682]. (C) 2009 Elsevier B.V. All rights reserved.
In this paper, the so-called eta-approximation approach is used to obtain the sufficient conditions for a nonlinear multiobjective programming problem with univex functions with respect to the same function eta. In th...
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In this paper, the so-called eta-approximation approach is used to obtain the sufficient conditions for a nonlinear multiobjective programming problem with univex functions with respect to the same function eta. In this method, an equivalent eta-approximated vector optimization problem is constructed by a modification of both the objective and the constraint functions in the original multiobjective programming problem at the given feasible point. Moreover, to find the optimal solutions of the original multiobjective problem, it sufficies to solve its associated eta-approximated vector optimization problem. Finally, the description of the eta-approximation algorithm for solving a nonlinear multiobjective programming problem involving univex functions is presented.
This study is devoted to constraint qualifications and strong Kuhn-Tucker necessary optimality conditions for nonsmooth multiobjective optimization problems. The main tool of the study is the concept of convexificator...
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This study is devoted to constraint qualifications and strong Kuhn-Tucker necessary optimality conditions for nonsmooth multiobjective optimization problems. The main tool of the study is the concept of convexificators. Mangasarian-Fromovitz type constraint qualification and several other qualifications are proposed and their relationships are investigated. In addition, sufficient optimality conditions are studied. (C) 2011 Elsevier Ltd. All rights reserved.
This article presents a methodological approach for the formulation of control strategies capable of reducing atmospheric pollution at the standards set by European legislation. The approach was implemented in the gre...
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This article presents a methodological approach for the formulation of control strategies capable of reducing atmospheric pollution at the standards set by European legislation. The approach was implemented in the greater area of Thessaloniki and was part of a project aiming at the compliance with air quality standards in five major cities in Greece. The methodological approach comprises two stages: in the first stage, the availability of several measures contributing to a certain extent to reducing atmospheric pollution indicates a combinatorial problem and favors the use of Integer programming. More specifically, Multiple Objective Integer programming is used in order to generate alternative efficient combinations of the available policy measures on the basis of two conflicting objectives: public expenditure minimization and social acceptance maximization. In the second stage, these combinations of control measures (i.e., the control strategies) are then comparatively evaluated with respect to a wider set of criteria, using tools from Multiple Criteria Decision Analysis, namely, the well-known PROMETHEE method. The whole procedure is based on the active involvement of local and central authorities in order to incorporate their concerns and preferences, as well as to secure the adoption and implementation of the resulting solution.
Often decision makers have to cope with a programming problem with unknown quantitities. Then they will estimate these quantities and solve the problem as it then appears-the 'approximate problem'. Thus there ...
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Often decision makers have to cope with a programming problem with unknown quantitities. Then they will estimate these quantities and solve the problem as it then appears-the 'approximate problem'. Thus there is a need to establish conditions which will ensure that the solutions to the approximate problem will come close to the solutions to the true problem in a suitable manner. Confidence sets, i.e. sets that cover the true sets with a given prescribed probability, provide useful quantitative information. In this paper we consider multiobjective problems and derive confidence sets for the sets of efficient points, weakly efficient points, and the corresponding solution sets. Besides the crucial convergence conditions for the objective and/or constraint functions, one approach for the derivation of confidence sets requires some knowledge about the true problem, which may be not available. Therefore also another method, called relaxation, is suggested. This approach works without any knowledge about the true problem. The results are applied to the Markowitz model of portfolio optimization.
In this paper, the problem of the determination of Pareto optimal solutions for certain large-scale systems with multiple conflicting objectives is considered. As a consequence, a two-level hierarchical method is prop...
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In this paper, the problem of the determination of Pareto optimal solutions for certain large-scale systems with multiple conflicting objectives is considered. As a consequence, a two-level hierarchical method is proposed, where the global problem is decomposed into smaller multiobjective problems (lower level) which are coordinated by an upper level that has to take into account the relative importance assigned to each subsystem. The scheme that has been developed is an iterative one, so that a continuous information exchange is carried out between both levels in order to obtain efficient solutions for the initial global problem. The practical implementation of the developed scheme allows us to prove its efficiency in terms of processing time.
This paper presents three algorithms for solving linear programming problems in which some or all of the objective function coefficients are specified in terms of intervals. Which algorithm is applicable depends upon ...
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This paper presents three algorithms for solving linear programming problems in which some or all of the objective function coefficients are specified in terms of intervals. Which algorithm is applicable depends upon (a) the number of interval objective function coefficients, (b) the number of nonzero objective function coefficients, and (c) whether or not the feasible region is bounded. The algorithms output all extreme points and unbounded edge directions that are “multiparametrically optimal” with respect to the ranges placed on the objective function coefficients. The algorithms are most suitable to linear programs in which the objective function coefficients are deterministic but are likely to vary from time period to time period (as for example in blending problems).
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