Interactive multiobjective evolutionary algorithm based on decomposition and compression

Many real-world optimization problems involve multiple conflicting objectives. Such problems are called multiobjective optimization problems (MOPs). Typically, MOPs have a set of so-called Pareto optimal solutions rather than one unique optimal solution. To assist the decision maker (DM) in finding his/her most preferred solution, we propose an interactive multiobjective evolutionary algorithm (MOEA) called iDMOEA-εC, which utilizes the DM’s preferences to compress the objective space directly and progressively for identifying the DM’s preferred region. The proposed algorithm employs a state-of-the-art decomposition-based MOEA called DMOEA-εC as the search engine to search for solutions. DMOEA-εC decomposes an MOP into a series of scalar constrained subproblems using a set of evenly distributed upper bound vectors to approximate the entire Pareto front. To guide the population toward only the DM’s preferred part on the Pareto front, an adaptive adjustment mechanism of the upper bound vectors and two-level feasibility rules are proposed and integrated into DMOEA-εC to control the spread of the population. To ease the DM’s burden, only a small set of representative solutions is presented in each interaction to the DM, who is expected to specify a preferred one from the set. Furthermore, the proposed algorithm includes a two-stage selection procedure, allowing to elicit the DM’s preferences as accurately as possible. To evaluate the performance of the proposed algorithm, it was compared with other interactive MOEAs in a series of experiments. The experimental results demonstrated the superiority of iDMOEA-εC over its competitors.