Evolutionary algorithms with preference polyhedron for interval multi-objective optimization problems

Multi-objective optimization problems (MOPs) with interval parameters are ubiquitous in real-world applications. Existing evolutionary optimization methods, however, aim to obtain a set of well-converged and evenly-distributed Pareto-optimal solutions. In this paper, we presented a novel evolutionary algorithm (EA) that interacts with a decision maker (DM) during the optimization process to obtain the most preferred solution. The theory of preference polyhedron for the optimization problem with interval parameters was developed first. An interactive evolutionary algorithm (IEA) for MOPs with interval parameters was then proposed based on the theory of preference polyhedron. The algorithm periodically provides a set of non-dominated solutions to the DM; a preference polyhedron is constructed in the objective space by taking the worst solution chosen by the DM as the vertex. The solutions with the same rank are sorted based on the polyhedron constructed. Finally, our method was empirically evaluated on several MOPs with interval parameters where the value functions were used to simulate the DM's responses. The numerical results indicated that our method is simpler and more efficient than the a posteriori method.