MO-NFSA for solving unconstrained multi-objective optimization problems

Abstract

Normative Fish Swarm Algorithm (NFSA) is a novel variant of the Artificial Fish Swarm Algorithm (AFSA) proposed in 2019, and has been proven effective in solving single-objective optimization problems. Inspired by the potential of NFSA, this paper proposes an evolutionary multi-objective optimization algorithm, namely “Multi-Objective Normative Fish Swarm Algorithm (MO-NFSA)”. However, due to the fact that NFSA was originally modeled for single-objective optimization, a certain degree of transformation, modification, and additional strategies (related to multi-objective optimization features) must be integrated into the original NFSA as part of MO-NFSA modeling for further extension. This article adopts a total of 15 multi-objective optimization test cases in any category of fixed-dimensional, non-fixed-dimensional (ZDT set) or scalable multi-objective (DTLZ set) optimization types. These multi-objective optimization test cases are used to compare the performance of MO-NFSA with other comparative algorithms. However, performance evaluation of multi-objective optimization is a daunting task. Their performance results can only be digitized through quality indicators (i.e., performance metrics), which are mainly tested from three different aspects of high-quality approximation: convergence, uniformity, and spread. Here, quality indicators including generation distance (GD), spacing (S), and spread-delta (∆/∆*) are used to check the quality performance of each algorithm based on the corresponding approximation. In the work, 20 simulations are run, and hence, 20 sets of data are collected. The collected results prove that MO-NFSA is superior to other comparison algorithms in all aspects of high-quality approximation. MO-NFSA can solve different types of multi-objective optimization problems.