Enhanced directed search: a continuation method for mixed-integer multi-objective optimization problems

Multi-objective optimization problems (MOPs) commonly arise in various applications of engineering and management fields. Many real-world MOPs are mixed-integer multiobjective optimization problems (MMOP), where the solution space consists of real and integer decision variables. The research regarding MMOPs is still scarce due to the mixture nature of the solution space and difficulty of finding the set of trade-off solutions. In this work we propose a continuation based method that efficiently solves MMOP problems. Our method, called Enhanced Directed Search (EDS), is capable of steering the search along a predefined direction along the Pareto front in the objective function space. EDS traces the Pareto front by following closest predictor and corrector solutions in the course of optimization. By searching around the objective function boundary, EDS can solve problems with k > 2 objectives. With five example problems widely studied in the literature, we demonstrate that EDS outperforms the recently developed Direct Zig Zag algorithm and the popular NSGA-II method.