Multi-Modal Multi-Objective Traveling Salesman Problem and its Evolutionary Optimizer.

A multi-modal multi-objective optimization problem (MMOP) may have equivalent Pareto optimal solutions. These solutions are different in the decision space but correspond to the same objective vector. Searching for equivalent Pareto optimal solutions with evolutionary algorithms is a hot topic in recent years. However, most existing researches are about continuous MMOPs, whereas there are few studies on discrete MMOPs. In this paper, we discuss the property of the multi-modal multi-objective traveling salesman problem and present a set of test problems. Then, we propose an evolutionary optimizer to solve the problem. Experimental results show that our evolutionary optimizer can find more equivalent Pareto optimal solutions than traditional multi-objective evolutionary optimizers on the test problems.