Offline and Online Objective Reduction in Evolutionary Multiobjective Optimization Based on Objective Conflicts

In recent years, multiobjective problems with many objectives, i.e., more than three, have gained interest. Since the consideration of many objectives cause obvious problems in terms of visualization, decision making and computational cost, the question arises whether objectives can be omitted to avoid or at least diminish the mentioned problems. To answer the question how an objective reduction can help in tackling problems with many objectives, we both theoretically and experimentally investigate how an addition or omission of objectives affects the problem characteristics. Furthermore, we propose a general definition of conflict between objective sets which provides the basis for a relationbased objective reduction method. Exact and heuristic algorithms to reduce the number of objectives under consideration are developed. How a reduction of the objective set can be utilized both offline, i.e., in the decision making step and online, i.e., within the search is demonstrated for a radar waveform application as well as on well-known test problems.