Preference ranking schemes in multi-objective evolutionary algorithms

In recent years, multi-objective evolutionary algorithms have diversified their goal from finding an approximation of the complete efficient front of a multi-objective optimization problem, to integration of user preferences. These user preferences can be used to focus on a preferred region of the efficient front. Many such user preferences come from so called proper Pareto-optimality notions. Although, starting with the seminal work of Kuhn and Tucker in 1951, proper Pareto-optimal solutions have been around in the multi-criteria decision making literature, there are (surprisingly) very few studies in the evolutionary domain on this. In this paper, we introduce new ranking schemes of various state-of-the-art multi-objective evolutionary algorithms to focus on a preferred region corresponding to proper Pareto-optimal solutions. The algorithms based on these new ranking schemes are successfully tested on extensive benchmark test problems of varying complexity, with the aim to find the preferred region of the efficient front. This comprehensive study adequately demonstrates the efficiency of the developed multi-objective evolutionary algorithms in finding the complete preferred region for a large class of complex problems.