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

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

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

Multi-criteria decision analysis (MCDA) methods have become increasingly popular in decision-making for sustainable energy because of the multi-dimensionality of the sustainability goal and the complexity of socio-economic and biophysical systems. This article reviewed the corresponding methods in different stages of multi-criteria decision-making for sustainable energy, i.e., criteria selection, criteria weighting, evaluation, and final aggregation. The criteria of energy supply systems are summarized from technical, economic, environmental and social aspects. The weighting methods of criteria are classified into three categories: subjective weighting, objective weighting and combination weighting methods. Several methods based on weighted sum, priority setting, outranking, fuzzy set methodology and their combinations are employed for energy decision-making. It is observed that the investment cost locates the first place in all evaluation criteria and CO2 emission follows closely because of more focuses on environment protection, equal criteria weights are still the most popular weighting method, analytical hierarchy process is the most popular comprehensive MCDA method, and the aggregation methods are helpful to get the rational result in sustainable energy decision-making.

Review on multi-criteria decision analysis aid in sustainable energy decision-making

The PROMETHEE-GAIA decision support system for multicriteria investigations

In this paper we propose a Decision-Aid procedure to pilot Socio — Economic systems. System Dynamics is used for modelling the complex structure of such systems and the MCDA PROMETHEE-GAIA procedure to select appropriate management strategies. SD long term forecasts provide a view on the possible evolution of the system; they are used to validate strategies and to define possible objectives. Short term forecasts are used to control, to monitor and to pilot the system when the time is evolving. Selected strategies are never fixed forever, they are adapted in function of the observed evolution in order to provide the best possible management. A watchdog procedure allows to reconsider the management of the system in case of chaotic evolution or when a catastrophic event emerge. The computer programme VENSIM is used for SD modelling and PROMCALC and DECISION LAB for the MCDA selection of management strategies. This methodology is now applied in various economic fields. The obtained results are extremely promising.

Management of the Future

The GDSS PROMETHEE procedure: a PROMETHEE-GAIA based procedure for group decision support

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. © 1994.

PROMCALC & GAIA: a new decision support system for multicriteria decision aid

A set of tools for group decision support are presented. Decision problems involving several decision makers, here-after called judges, that have to rank several alternatives, are considered. The toolbox is called JUDGES. It includes the four following procedures: • - a hierarchical representation of the judges allows to display the existing conflicts between groups of judges, • - enhanced box-plots representations of the alternatives are generated in order to detect those that are responsible for the major conflicts, • - specific advice is issued to each judge in order to reach more easily a consensus, • - a general framework for a pairwise group preference structure is proposed, and can be used to finalise the decision. These procedures are embedded in an interactive software, implemented on micro-computer, which currently simulates the use on a network. Actual network implementation is foreseen in the near future. Several applications are presented and future developments are discussed.

Bertrand Mareschal

Papers

The PROMETHEE-GAIA decision support system for multicriteria investigations

Management of the Future

The GDSS PROMETHEE procedure: a PROMETHEE-GAIA based procedure for group decision support

PROMCALC & GAIA: a new decision support system for multicriteria decision aid

JUDGES: a descriptive group decision support system for the ranking of items