Multiobjective Evolutionary Algorithms and Applications

Tan, Kay Chen; Lee, Tong Heng; k-c-tan,; Khor, E. F.

doi:10.1007/1-84628-132-6

Cited by 38 publications

(1 citation statement)

References 126 publications

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“…Decision-making methods based on optimality were introduced by Pareto in 1896 and applied to a wide range of problems. The Multi-Objective Evolutionary Algorithm (MOEA) [24] is used to find the optimal Pareto solutions for specific problems [25]. Keeney and Raiffa [26] and Fishburn [27] introduced the Multi-Attribute Value Theory (MAVT), the Multi-Attribute Value Analysis (MAVA) and Multi-Attribute Utility Theory (MAUT) methods.…”

Section: Literature Reviewmentioning

confidence: 99%

Multi-Attribute Decision-Making Methods as a Part of Mathematical Optimization

Vinogradova

2019

Mathematics

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Optimization problems are relevant to various areas of human activity. In different cases, the problems are solved by applying appropriate optimization methods. A range of optimization problems has resulted in a number of different methods and algorithms for reaching solutions. One of the problems deals with the decision-making area, which is an optimal option selected from several options of comparison. Multi-Attribute Decision-Making (MADM) methods are widely applied for making the optimal solution, selecting a single option or ranking choices from the most to the least appropriate. This paper is aimed at providing MADM methods as a component of mathematics-based optimization. The theoretical part of the paper presents evaluation criteria of methods as the objective functions. To illustrate the idea, some of the most frequently used methods in practice—Simple Additive Weighting (SAW), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Complex Proportional Assessment Method (COPRAS), Multi-Objective Optimization by Ratio Analysis (MOORA) and Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE)—were chosen. These methods use a finite number of explicitly given alternatives. The research literature does not propose the best or most appropriate MADM method for dealing with a specific task. Thus, several techniques are frequently applied in parallel to make the right decision. Each method differs in the data processing, and therefore the results of MADM methods are obtained on different scales. The practical part of this paper demonstrates how to combine the results of several applied methods into a single value. This paper proposes a new approach for evaluating that involves merging the results of all applied MADM methods into a single value, taking into account the suitability of the methods for the task to be solved. Taken as a basis is the fact that if a method is more stable to a minor data change, the greater importance (weight) it has for the merged result. This paper proposes an algorithm for determining the stability of MADM methods by applying the statistical simulation method using a sequence of random numbers from the given distribution. This paper shows the different approaches to normalizing the results of MADM methods. For arranging negative values and making the scales of the results of the methods equal, Weitendorf’s linear normalization and classical and author-proposed transformation techniques have been illustrated in this paper.

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Section: Literature Reviewmentioning

confidence: 99%