A non-dominated sorting based evolutionary algorithm for many-objective optimization problems

Abstract

The optimization problems with more than three objectives are Manyobjective Optimization Problems (MaOPs) that exist in various scientific and engineering domains. The existing multi-objective evolutionary algorithms are not found effective in addressing the MaOPs. Its limitations initiated the need to develop an algorithm that efficiently solves MaOPs. The proposed work presents the design of the Many-Objective Hybrid Differential Evolution (MaOHDE) algorithm to address MaOPs. Initially, two multi-objective evolutionary algorithms viz. Non-dominated Sorting based Multi-Objective Differential Evolution (NS-MODE) and Non-dominated Sorting based Multi-Objective Particle Swarm Optimization (NS-MOPSO) algorithms were designed. These algorithms were developed by incorporating the non-dominated sorting approach from Non-dominated Sorting-based Genetic Algorithm II (NSGA-II), the ranking approach, weight vector, and reference points. Tchebycheff a decomposition-based approach, was applied to decompose the MaOPs. The MaOHDE algorithm was developed by hybridizing the NS-MODE with the NS-MOPSO algorithm. The strength of the presented approach was determined using 20 instances of DTLZ functions, and its effectiveness and efficiency were verified upon its comparison with the recently developed state of algorithms existing in the literature. From the results, it is observed that the MaOHDE responds better than its competitors or is competitive for most of the test instances and the convergence rate is also good.