Preference-based Evolutionary Multiobjective Optimization: Methods, Performance Indicators, and Applications

Abstract

Multiobjective optimization problems (MOPs) involve optimizing multiple conflicting objective functions simultaneously. As a result of this conflict, we have several mathematically incomparable solutions called Pareto optimal solutions with different trade-offs. Typically. in real-world MOPs, a decision maker (DM) is needed to choose one of these solutions based on her/his preferences for implementation. In this thesis, we work with methods incorporating DM’s preferences during the solution process. We call these methods preference-based methods. In this thesis, we develop preference-based evolutionary multiobjective optimization methods and means for assessing their performance. Real-world MOPs come with several challenges. For example, they can have some objectives and constraints with long computation time. In such problems, we can use some surrogate models to replace the expensive functions. However, by utilizing these models, we introduce new challenges: how to incorporate the DM’s preferences during the solution process? How can we satisfy constraints if we have used surrogates? How do we manage the surrogate models? Another challenge we address in this thesis is: how to systematically compare preference-based evolutionary methods? Such comparisons would require quantitative assessments utilizing performance indicators. A handful of performance indicators have been proposed for a priori methods, but no performance indicator has been explicitly designed for interactive methods. This thesis addresses the challenges mentioned above. We propose an a preference-based method called KAEA-C, which is suitable for MOPs involving computationally expensive constraints. It has a novel model management that considers both the DM’s preferences and the feasibility of solutions. We identify 13 desirable properties of indicators designed for interactive evolutionary methods. Based on this foundation, we propose a novel performance indicator called PHI, which we can utilize to assess the performance of interactive evolutionary methods. Finally, we introduce a novel surrogate-assisted interactive method called interactive K-RVEA suitable for computationally expensive problems. We also apply this method to real-world problems. Keywords: Interactive evolutionary multiobjective optimization, Quality indicators, Computationally expensive problems, Decision making, preference information