A preference modified inverted generational distance indicator guided algorithm for evolutionary multi-objective optimization

Preference-based evolutionary multi-objective optimization algorithms have attracted much attention in the area of evolutionary computation. However, there are only a few researchers incorporating performance indicators for designing preference-based evolutionary algorithm. In this paper, we propose a preference modified inverted generational distance indicator guided algorithm, named PIGA, for evolutionary multi-objective optimization. The main purpose is that decision-makers provide their preferences, ultimately identifying the portion of Pareto optimal solutions where are located in region of interest. A new preference construction strategy based on coordinate transformation is first proposed. The reference points in the whole objective space can be projected into the preference space, obtaining the preferred reference points. The non-preferred reference points remain in the original objective space, outside the specified preference region. In addition, we define the distance between the candidate solution and preferred reference points as the preference distance and the distance to non-preferred reference points as the penalty distance. Finally, a preference-based modified inverted generational distance indicator is formulated to obtain the preferred optimal solutions according to the preferences and penalty distances. The comparative results are comprehensively analyzed by comparing it with some related preference-based evolutionary algorithms on some test instances. Experimental results have validated the effectiveness and feasibility of the proposed algorithm under different scenarios with the given preference range.