Objective extraction via fuzzy clustering in evolutionary many-objective optimization

Many-objective optimization problems (MaOPs), which have more than three objectives to optimize simultaneously, have attracted much attention recently in the community of evolutionary computation. Most existing multi-objective evolutionary algorithms (MOEAs) can fail to find a well-representative set of Pareto optimal solutions in dealing with MaOPs. To solve this problem, one methodology is to improve the search ability of existing MOEAs to approximate the Pareto optimal solutions. A variety of such strategies have been proposed. The other methodology is to simplify MaOPs and deal with the simplified ones with existing MOEAs. This paper follows the second methodology by converting an MaOP into a series of multi-objective optimization problems (MOPs) with fewer objectives and solving these MOPs in an online manner. To achieve this goal, new objectives are constructed as linear combinations of the original objectives. The weight vectors are extracted through fuzzy clustering based on the objective values found during the search. Comparing to other dimension reduction based approaches, the new approach constructs new objectives by using all the information of the original objectives. Extensive experimental studies on ill-posed MaOPs are conducted to reveal the performance of our method and to compare with other related algorithms.