Solving Interval Multi-objective Optimization Problems Using Evolutionary Algorithms with Preference Polyhedron

Multi-objective optimization (MOO) problems with interval parameters are popular and important in real-world applications. Previous evolutionary optimization methods aim to find a set of well-converged and evenly-distributed Pareto-optimal solutions. We present a novel evolutionary algorithm (EA) that interacts with a decision maker (DM) during the optimization process to obtain the DMEs most preferred solution. First, the theory of a preference polyhedron for an optimization problem with interval parameters is built up. Then, an interactive evolutionary algorithm (IEA) for MOO problems with interval parameters based on the above preference polyhedron is developed. The algorithm periodically provides a part of non-dominated solutions to the DM, and a preference polyhedron, based on which optimal solutions are ranked, is constructed with the worst solution chosen by the DM as the vertex. Finally, our method is tested on two biobjective optimization problems with interval parameters using two different value function types to emulate the DMEs responses. The experimental results show its simplicity and superiority to the posteriori method.