Reference direction approach for solving multiple objective nonlinear programming problems

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

doi:10.1109/21.293497

Cited by 21 publications

(5 citation statements)

References 9 publications

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“…Among them are the interactive reference direction algorithm for convex nonlinear integer problems (Vassilev et al, 2001) which uses three classes I ≤ , I ≥ and I = and the reference direction approach for nonlinear problems (Narula et al, 1994) using the same three classes and generating several solutions in the reference direction (pointing from the current solution towards the reference point). Furthermore, the interactive decision making approach NIDMA (Kaliszewski and Michalowski, 1999) asks for both a classification and maximal acceptable global trade-offs from the DM.…”

Section: Other Classification-based Methodsmentioning

confidence: 99%

Introduction to Multiobjective Optimization: Interactive Approaches

Miettinen

Ruiz

Wierzbicki

2008

Lecture Notes in Computer Science

210

197

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Abstract. We give an overview of interactive methods developed for solving nonlinear multiobjective optimization problems. In interactive methods, a decision maker plays an important part and the idea is to support her/him in the search for the most preferred solution. In interactive methods, steps of an iterative solution algorithm are repeated and the decision maker progressively provides preference information so that the most preferred solution can be found. We identify three types of specifying preference information in interactive methods and give some examples of methods representing each type. The types are methods based on trade-off information, reference points and classification of objective functions. IntroductionSolving multiobjective optimization problems typically means helping a human decision maker (DM) in finding the most preferred solution as the final one. By the most preferred solution we refer to a Pareto optimal solution which the DM is convinced to be her/his best option. Naturally, finding the most preferred solution necessitates the participation of the DM who is supposed to have insight into the problem and be able to specify preference information related to the objectives considered and different solution alternatives, as discussed in Chapter 1. There we presented four classes for multiobjective optimization methods according to the role of the DM in the solution process.

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Section: Other Classification-based Methodsmentioning

confidence: 99%

Introduction to Multiobjective Optimization: Interactive Approaches

Miettinen

Ruiz

Wierzbicki

2008

Lecture Notes in Computer Science

210

197

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“…The following scalarizing problems can be derived from the above scalarizing problem (we use notations to make difference between them): the MinMax or Chebyshev scalarizing problem (Steuer & Choo, 1983), the weighted sum scalarizing problem WS (Gass & Saaty, 1955;Zadeh, 1963), the scalarizing problem of ε-constraint method EC (Haimes et al, 1971), STEM scalarizing problem (Benayoun et al, 1971), STOM scalarizing problem (Nakayama & Sawaragi, 1984), the scalarizing problem of the reference point RP (Wierzbicki, 1980), GUESS scalarizing problem (Buchanan, 1997), the scalarizing problem of the modified reference point MRP , the scalarizing problem of VIG method (Korhonen & Laakso, 1986;Korhonen, 1997), the scalarizing problem of reference direction method RD (Vassilev et al, 1992); Narula et al, 1992Narula et al, , 1994, the scalarizing problem of reference direction RD2 (Vassilev & Narula, 1993), the classification-oriented scalarizing problem NIMBUS (Miettinen, 1999;Miettinen & Mäkelä 2002;Miettinen & Mäkelä 2006) the classification-oriented scalarizing problem DALDI (Vassileva et al, 2001).…”

Section: Generalized Scalarizing Problemmentioning

confidence: 99%

Generalized Scalarizing Model GENS in DSS WebOptim

Kirilov

Guliashki

Genova

et al. 2013

International Journal of Decision Support System Technology

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A web-based Decision Support System WebOptim for solving multiple objective optimization problems is presented. Its basic characteristics are: user-independent, multisolver-admissibility, method-independent, heterogeneity, web-accessibility. Core system module is an original generalized interactive scalarizing method. It incorporates a number of thirteen interactive methods. Most of the known scalarizing approaches (reference point approach, reference direction approach, classification approach etc.) could be used by changing the method’s parameters. The Decision Maker (DM) can choose the most suitable for him/her form for setting his/her preferences: objective weights, aspiration levels, aspiration directions, aspiration intervals. This information could be changed interactively by the DM during the solution process. Depending on the DM’s preferences form the suitable scalarizing method is chosen automatically. In this way the demands on the DM’s knowledge and experience in the optimization methods area are minimized.

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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%