Modified crowding distance and mutation for multimodal multi-objective optimization

Many real-world applications contain complex optimization problems with several conflicting objectives. Finding a solution which can satisfy all the objectives is usually a challenging task for optimization algorithms. When dealing with these complex multi-objective problems, decision-makers want to find the best tradeoff between the conflicting objectives. Another challenge occurs in problems where multiple configurations of the input variables might yield the same objective function values. Such problems are called multimodal problems. For a decision maker, it might be of importance to obtain enough information about all the alternative optimal solutions that reach the same objective value. Traditionally, Evolutionary Algorithms make use selection processes based only on objective function values, which might be a disadvantage when faced with multimodal problems. In this article, we present two operators to use in multimodal multi-objective algorithms, namely a modified crowding distance operator and a neighbourhood Polynomial mutation, which take into account the distribution of solution in the decision space at run-time. Our experimental results demonstrate that the proposed operators are able to outperform the performance of a state-of-the-art method on six current multimodal benchmark functions.