An Evolutionary Algorithm for Multi and Many-Objective Optimization With Adaptive Mating and Environmental Selection

Abstract

Multi-objective evolutionary algorithms (MOEAs) have received immense recognition due to their effectiveness and efficiency in tackling multi-objective optimization problems (MOPs). Recently, numerous studies on MOEAs revealed that when handling many-objective optimization problems (MaOPs) that have more than three objectives, MOEAs encounter challenges and the behavior of MOEAs resembles a random walk in search space as the proportion of nondominated solutions increases subsequently. This phenomenon is commonly observed in most classical Pareto-dominance-based MOEAs (PDMOEAs) such as NSGA-II, SPEAII, as these algorithms face difficulties in guiding the search process towards the optimal Pareto front due to lack of selection pressure. From the literature, it is evident that incorporating sum of normalized objectives into the framework of MOEAs would enhance the converging capabilities. Hence, in this work, we propose a novel multi-objective optimization algorithm with adaptive mating and environmental selection (ad-MOEA) which effectively incorporates the concept of sum of objectives in the mechanisms of mating and environmental selection to control the convergence and diversity adaptively. To demonstrate the effectiveness of the proposed ad-MOEA, we have conducted experiments on 26 test problems that includes DTLZ, WFG and MaOP test suites. Along with the benchmark problem, we have analyzed the performance of the proposed approach on real-world problems. The experimental results demonstrate the effectiveness of the proposed method with respect to the state-of-art methods.

Keywords

• Evolutionary computation
• multi-objective optimization
• many-objective optimization
• Pareto-dominance
• sum of normalized objectives
• crowding distance