Reference Point Approaches

Wierzbicki, Andrzej P.

doi:10.1007/978-1-4615-5025-9_9

Cited by 63 publications

(36 citation statements)

References 34 publications

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“…Reference point approaches have a long history and multiple practical applications (Wierzbicki, 1977(Wierzbicki, , 1980(Wierzbicki, , 1999Wierzbicki et al, 2000). However, we shall limit the description here to their fundamental philosophy, a short indication of their basic features and of some contemporary, new developments related to this class of approaches.…”

Section: Fundamental Assumptions Of Reference Point Approachesmentioning

confidence: 99%

“…Another basic assumption of reference point approaches is that reference (aspiration, reservation) levels and points are treated not as a fixed expression of preferences but as a tool of adaptive, holistic learning about the decision situation as described by the substantive model. Thus, even if the convergence of reference point approaches to a solution most preferred by the DM can be proved (Wierzbicki, 1999), this aspect is never stressed. More important aspects relate to other properties of these approaches.…”

Section: K)mentioning

confidence: 99%

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Introduction to Multiobjective Optimization: Interactive Approaches

Miettinen

Ruiz

Wierzbicki

2008

Lecture Notes in Computer Science

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217

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: Fundamental Assumptions Of Reference Point Approachesmentioning

confidence: 99%

Section: K)mentioning

confidence: 99%

Introduction to Multiobjective Optimization: Interactive Approaches

Miettinen

Ruiz

Wierzbicki

2008

Lecture Notes in Computer Science

Self Cite

217

197

View full text Add to dashboard Cite

show abstract

“…The approach adopted was thus based on sampling the efficient frontier by optimizing an aggregate measure of performance subject to the constraints on x, for each of a number of different aggregations. The aggregation chosen was that of the scalarizing function introduced by Wierzbicki (1999) in the context of his reference point methodology, except that we chose a smoother function than that based on the maximum operator. Thus for any given reference point (which can be viewed as a set of goals or aspiration levels for each objective), say g 1 , g 2 , .…”

Section: Methodsmentioning

confidence: 99%

Real-World Applications of Multiobjective Optimization

Stewart

Bandte

Braun

et al. 2008

Multiobjective Optimization

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Abstract. This chapter presents a number of illustrative case studies of a wide range of applications of multiobjective optimization methods, in areas ranging from engineering design to medical treatments. The methods used include both conventional mathematical programming and evolutionary optimization, and in one case an integration of the two approaches. Although not a comprehensive review, the case studies provide evidence of the extent of the potential for using classical and modern multiobjective optimization in practice, and opens many opportunities for further research. IntroductionThe intention with this chapter is to provide illustrations of real applications of multiobjective optimization, covering both conventional mathematical programming approaches and evolutionary multiobjective optimization. These illustrations do cover a broad range of application, but do not attempt to provide a comprehensive review of applications.

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“…But most of them are developed based on the classical optimization methods. Some of the most popular ones are Interactive Surrogate Worth Tradeoff (ISWT) method [3], Reference Point method [12], the NIMBUS approach [10] etc. Each method is different from each other, but uses a single solution in each iteration.…”

Section: Related Workmentioning

confidence: 99%

I-EMO: An Interactive Evolutionary Multi-objective Optimization Tool

Deb

Chaudhuri

2005

Lecture Notes in Computer Science

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Abstract. With the advent of efficient techniques for multi-objective evolutionary optimization (EMO), real-world search and optimization problems are being increasingly solved for mulitple conflicting objectives. During the past decade of research and application, most emphasis has been spent on finding the complete Pareto-optimal set, although EMO researchers were always aware of the importance of procedures which would help choose one particular solution from the Pareto-optimal set for implementation. This is also one of the main issues on which the classical and EMO philosophies are divided on. In this paper, we address this long-standing issue and suggest an interactive EMO procedure which, for the first time, will involve a decision-maker in the evolutionary optimization process and help choose a single solution at the end. This study is the culmination of many year's of research on EMO and would hopefully encourage both practitioners and researchers to pay more attention in viewing the multi-objective optimization as a aggregate task of optimization and decision-making.

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Reference Point Approaches

Cited by 63 publications

References 34 publications

Introduction to Multiobjective Optimization: Interactive Approaches

Introduction to Multiobjective Optimization: Interactive Approaches

Real-World Applications of Multiobjective Optimization

I-EMO: An Interactive Evolutionary Multi-objective Optimization Tool

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