List of Figures. List of Tables. Preface. Foreword. 1. Basic Concepts. 2. Evolutionary Algorithm MOP Approaches. 3. MOEA Test Suites. 4. MOEA Testing and Analysis. 5. MOEA Theory and Issues. 3. MOEA Theoretical Issues. 6. Applications. 7. MOEA Parallelization. 8. Multi-Criteria Decision Making. 9. Special Topics. 10. Epilog. Appendix A: MOEA Classification and Technique Analysis. Appendix B: MOPs in the Literature. Appendix C: Ptrue & PFtrue for Selected Numeric MOPs. Appendix D: Ptrue & PFtrue for Side-Constrained MOPs. Appendix E: MOEA Software Availability. Appendix F: MOEA-Related Information. Index. References.

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Evolutionary algorithms for solving multi-objective problems

https://ir.nctu.edu.tw:443/bitstream/11536/26562/1/000220346300012.pdf

Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS

Principles for a new family of outranking methods are given. The main aim of the proposed PROMETHEE approach is to be as easily understood as possible by the decision-maker. It is based on extensions of the notion of criterion. Six possible extensions are considered. These extensions can easily be identified by the decision-maker because the parameters to be defined at most 2 have an economic significance. A valued outranking graph is constructed by using a preference index. Two possibilities are considered to solve the ranking problem by using this valued graph. PROMETHEE I provides a partial preorder and PROMETHEE II a total preorder on the set of the possible actions.

Note-A Preference Ranking Organisation Method: The PROMETHEE Method for Multiple Criteria Decision-Making

In this paper, a new method, called best-worst method (BWM) is proposed to solve multi-criteria decision-making (MCDM) problems. In an MCDM problem, a number of alternatives are evaluated with respect to a number of criteria in order to select the best alternative(s). According to BWM, the best (e.g. most desirable, most important) and the worst (e.g. least desirable, least important) criteria are identified first by the decision-maker. Pairwise comparisons are then conducted between each of these two criteria (best and worst) and the other criteria. A maximin problem is then formulated and solved to determine the weights of different criteria. The weights of the alternatives with respect to different criteria are obtained using the same process. The final scores of the alternatives are derived by aggregating the weights from different sets of criteria and alternatives, based on which the best alternative is selected. A consistency ratio is proposed for the BWM to check the reliability of the comparisons. To illustrate the proposed method and evaluate its performance, we used some numerical examples and a real-word decision-making problem (mobile phone selection). For the purpose of comparison, we chose AHP (analytic hierarchy process), which is also a pairwise comparison-based method. Statistical results show that BWM performs significantly better than AHP with respect to the consistency ratio, and the other evaluation criteria: minimum violation, total deviation, and conformity. The salient features of the proposed method, compared to the existing MCDM methods, are: (1) it requires less comparison data; (2) it leads to more consistent comparisons, which means that it produces more reliable results.

Best-worst multi-criteria decision-making method

How to select and how to rank projects: the promethee method

Abstract In this paper, we present the Promethee methods, a new class of outranking methods in multicriteria analysis. Their main features are simplicity, clearness and stability. The notion of generalized criterion is used to construct a valued outranking relation. All the parameters to be defined have an economic signification, so that the decision maker can easily fix them. Two ways of treatment are proposed: It is possible to obtain either a partial preorder ( Promethee I) or a complete one ( Promethee II), both on a finite set of feasible actions. A comparison is made with the Electre III method. The stability of the results given by the two methods is analysed. Numerical applications are given in order to illustrate the properties of the new methods and some further problems are discussed.

How to select and how to rank projects: the Prométhée method

Prométhée: a new family of outranking methods in multicriteria analysis

A preference ranking organization method

PROMCALC & GAIA is the last development of the interactive decision support system based on the PROMETHEE and GAIA methodology. In the first section, the fundamental characteristics of multicriteria problems are recalled and requisites are formulated for an appropriate multicriteria decision aid methodology. Based on these requisites, the PROMETHEE methods are then introduced, including newer developments such as PROMETHEE V (multicriteria optimization under constraints) and the GAIA visual modelling method. The actual implementation of the proposed methodology in the PROMCALC & GAIA software is then detailed and a numerical example is developed to illustrate the possibilities of the system.

Jean Pierre Brans

Papers

How to select and how to rank projects: the promethee method

How to select and how to rank projects: the Prométhée method

Prométhée: a new family of outranking methods in multicriteria analysis

A preference ranking organization method

The PROMCALC & GAIA decision support system for multicriteria decision aid