Indicator-based Selection in Evolutionary Multiobjective Optimization Algorithms Based On the Desirability Index

• Published in: Journal of multi-criteria decision analysis 2013-09, Vol.20 (5-6), p.319-337
• Main Authors: Trautmann, Heike, Wagner, Tobias, Biermann, Dirk, Weihs, Claus
• Format: Article
• Language: English
• Subjects: Algorithms; archive; Complexity theory; decision making; desirability function; desirability index; evolutionary multiobjective optimization; Genetic algorithms; hypervolume; Multiple criteria decision making; Optimization; Optimization techniques; Pareto optimum; preferences; Studies; ε-MOEA
• ISSN: 1057-9214; 1099-1360
• DOI: 10.1002/mcda.1503

ABSTRACT In multiobjective optimization, the identification of practically relevant solutions on the Pareto‐optimal front is an important research topic. Desirability functions (DFs) allow the preferences of the decision maker to be specified in an intuitive way. Recently, it has been shown for continuous optimization problems that an a priori transformation of the objectives by means of DFs can be used to focus the search of a hypervolume‐based evolutionary algorithm on the desired part of the front. In many‐objective optimization, however, the computational complexity of the hypervolume can become a crucial part. Thus, an alternative to this approach will be presented in this paper. The new algorithm operates in the untransformed objective space, but the desirability index (DI), that is, a DF‐based scalarization, will be used as the second‐level selection criterion in the non‐dominated sorting. The diversity and uniform distribution of the resulting approximation are ensured by the use of an external archive. In the experiments, different preferences are specified as DFs, and their effects are investigated. It is shown that trade‐off solutions are generated in the desired regions of the Pareto‐optimal front and with a density adaptive to the DI. The efficiency of the approach with respect to increasing objective space dimension is also analysed using scalable test functions. The convergence speed is superior to other set‐based and preference‐based evolutionary multiobjective algorithms while the approach is of low computational complexity due to cheap DI evaluations. Copyright © 2013 John Wiley & Sons, Ltd.