Directed Multiobjective Optimization Based on the Weighted Hypervolume Indicator

• Published in: Journal of multi-criteria decision analysis Vol. 20; no. 5-6; pp. 291 - 317
• Main Authors: Brockhoff, Dimo, Bader, Johannes, Thiele, Lothar, Zitzler, Eckart
• Format: Journal Article
• Language: English
• Published: Chichester Blackwell Publishing Ltd 01.09.2013; Wiley Periodicals Inc; Wiley
• Series: Special Issue: Evolutionary Multiobjective Optimization: Methodologies and Applications
• Subjects: Algorithms; Computer Science; evolutionary algorithm; Genetic algorithms; hypervolume; Monte Carlo simulation; multi objective optimization; Multiple criteria decision making; Neural and Evolutionary Computing; Optimization algorithms; Pareto optimum; preference-based search; Studies; multiobjective optimization; hypervolume; preference-based search; evolutionary algorithm
• ISSN: 1057-9214; 1099-1360
• DOI: 10.1002/mcda.1502

ABSTRACT Recently, there has been a large interest in set‐based evolutionary algorithms for multi objective optimization. They are based on the definition of indicators that characterize the quality of the current population while being compliant with the concept of Pareto‐optimality. It has been shown that the hypervolume indicator, which measures the dominated volume in the objective space, enables the design of efficient search algorithms and, at the same time, opens up opportunities to express user preferences in the search by means of weight functions. The present paper contains the necessary theoretical foundations and corresponding algorithms to (i) select appropriate weight functions, to (ii) transform user preferences into weight functions and to (iii) efficiently evaluate the weighted hypervolume indicator through Monte Carlo sampling. The algorithm W‐HypE, which implements the previous concepts, is introduced, and the effectiveness of the search, directed towards the user's preferred solutions, is shown using an extensive set of experiments including the necessary statistical performance assessment. Copyright © 2013 John Wiley & Sons, Ltd.