A multi-objective differential evolutionary algorithm with angle-based objective space division and parameter adaption for solving sodium gluconate production process and benchmark problems

Abstract

Abstract Convergence and diversity are two main performance indicators in multi-objective evolutionary algorithms. The fitness value in the objective space represents information which guides the evolution. To extract this useful information, a multi-objective differential evolutionary algorithm with angle-based objective space division and parameter adaption is proposed (MODE-ASP). In MODE-ASP, the objective space is split into several subspaces based on angle, and the optimal direction in each subspace is extracted to accelerate the convergence. A probability model is also built to achieve adaption of the parameters along with the evolution of the population. Compared with 5 state-of-the-art algorithms with 20 benchmark functions, MODE-ASP is shown to give a better performance. Moreover, the operating conditions of the sodium gluconate fermentation process are optimized with three proposed objective functions, to improve the utilization rates of equipment and conversion rates effectively. The MODE-ASP is shown to obtain a better Pareto front in this application.