An Interactive Algorithm for Solving Multiple Objective Nonlinear Programming Problems

Narula, Subhash C.; Kirilov, Leoneed; Vassilev, Vassil

doi:10.1007/978-1-4612-2666-6_13

Cited by 8 publications

(7 citation statements)

References 6 publications

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“…This approach based on the combined with the Reference Direction method introduced by Narula et al [14], and the Attainable Reference Point (ARP) method introduced by Wang et al [19], and adapted the Lexicographic Weighted Tcheycheff program. The main development we made constitutes in using the weak efficient solution obtained from the initial step of the reference direction method to improve the weights in the Lexicographic Weighted Tcheycheff program.…”

Section: Discussionmentioning

confidence: 99%

“…On the basis of this transformation(s) he (she) is used to classify the objective functions into three classes: the unacceptable objective function whose values he(she) wants to improve ) ( ). The reference direction method presented by Narula et al [14] is based on a reference directions , and it needs to minimize a series of achievement scalarizing problems at each iteration according to several values of the parameters α ( ) 1 0 ≤ ≤α according to the DM wishes. The solution of each achievement scalarizing problem is weakpareto optimal solution.…”

Section: Introductionmentioning

confidence: 99%

“…The approach is combined with the Reference Direction (RD) introduced by Narula et al [14] and the Attainable Reference Point (ARP) method introduced by Wang et al [19] In the unified approach, we still starting with a weak efficient solution as the first step and use the corresponding objective values to improve the weighting coefficients of the augmented Lexicographic Weighted Tchebycheff problem and hence modify the reference point in the case of an unsatisfactory solution for the decision maker (DM) he (she) wishes.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, unified approach for solving multi-objective optimization problem is introduced. The approach is based on the Reference Direction (RD) method introduced by Narula et al [14], and the Attainable Reference Point (ARP) method introduced by Wang et al [19]. This approach improves the performance of the ARP method by using the initial weak efficient solution of the RD method that is to improve the weights in the Lexicographic weighted Techebycheff program.…”

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confidence: 99%

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Solving Multi-Objective Optimization Problems through Unified Approach

Khalifa¹,

AL-harbi²

2017

APAM

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Abstract. In this paper, unified approach for solving multi-objective optimization problem is introduced. The approach is based on the Reference Direction (RD) method introduced by Narula et al. [14], and the Attainable Reference Point (ARP) method introduced by Wang et al. [19]. This approach improves the performance of the ARP method by using the initial weak efficient solution of the RD method that is to improve the weights in the Lexicographic weighted Techebycheff program. The weights in the unified approach are constructed through the ARP and the weak efficient solution. A numerical example is given in the sake of the paper to clarify the obtained results.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Solving Multi-Objective Optimization Problems through Unified Approach

Khalifa¹,

AL-harbi²

2017

APAM

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“…In the classification based reference direction (RD) method [177,178], a current objective vector z h is presented to the decision maker and (s)he is asked to specify a reference pointz h consisting of desired levels for the objective functions. However, as the idea is to move around the weakly Pareto optimal set, some objective functions must be allowed to increase in order to attain lower values for some other objectives.…”

Section: Reference Direction Methodsmentioning

confidence: 99%

Interactive Nonlinear Multiobjective Optimization Methods

Miettinen

Hakanen

Podkopaev

2016

International Series in Operations Research &Amp; Management Science

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Interactive Nonlinear Multiobjective Procedures

Miettinen

International Series in Operations Research &Amp; Management Science

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Keywords:An overview of the interactive methods for solving nonlinear multiple criteria decision making problems is given. In interactive methods, the decision maker progressively provides preference information so that the most satisfactory compromise can be found. The basic features of several methods are introduced and some theoretical results are provided. In addition, references to modifications and applications as well as to other methods are indicated.Multiple criteria decision making, Multiobjective optimization, Nonlinear optimization, Interactive methods. IntroductionNonlinear multiobjective optimization means multiple criteria decision making involving nonlinear functions of continuous decision variables. In these problems, the best possible compromise is to be found from an infinite number of alternatives represented by decision variables restricted by constraint functions.Solving multiobjective optimization problems usually requires the participation of a human decision maker who is supposed to have better insight into the problem and to express preference relations between alternative solutions. The methods can be divided into four classes according to the role of the decision maker in the solution process. If the decision maker is not involved, we use methods where no articulation of preference information is used, in other words, no-preference methods. If the decision maker expresses preference information after the solution process, we speak about a posteriori methods whereas a priori methods require articulation of preference information before the solution process. The most extensive method class is interactive methods where the decision maker specifies preference information progressively during the solution process. Here we concentrate on this last-mentioned class and introduce several examples of interactive methods.Many real-world phenomena behave in a nonlinear way. Besides, linear problems can always be solved using methods created for nonlinear problems but not vice versa. For these reasons, we here devote ourselves to nonlinear problems. We assume that all the information involved is deterministic and that we have a single decision maker. Further information about the topics treated here can be found in [105]. 228 MULTIPLE CRITERIA OPTIMIZATION ConceptsLet us begin by introducing several concepts and definitions. We study multiobjective optimization problems of the form involving objective functions that we want to minimize simultaneously. The decision (variable) vectors belong to the (nonempty) feasible regionThe feasible region is formed by constraint functions but we do not fix them here.We denote the image of the feasible region by and call it a feasible objective region. Objective (function) values form objective vectorsNote that if is to be maximized, it is equivalent to minimizeWe call a multiobjective optimization problem convex if all the objective functions and the feasible region are convex. On the other hand, the problem is nondifferentiable if at least one o...

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An Interactive Algorithm for Solving Multiple Objective Nonlinear Programming Problems

Cited by 8 publications

References 6 publications

Solving Multi-Objective Optimization Problems through Unified Approach

Solving Multi-Objective Optimization Problems through Unified Approach

Interactive Nonlinear Multiobjective Optimization Methods

Interactive Nonlinear Multiobjective Procedures

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