Hybrid Non-dominated Sorting Differential Evolutionary Algorithm with Nelder-Mead

Non-dominated sorting has been widely applied in many multi-objective evolutionary algorithms, such as NSGA, NSGA-II and NSDE. This paper proposes a novel multi-objective optimization algorithm based on Nelder-Mead (NM) simplex method and non-dominated sorting (NS) approach, NS-simplex. It utilizes NS in simplex procedures and accelerates local search speed. Based on NS-simplex and NSDE, a hybrid technique called NSSDE is proposed, enhancing the overall search capability and efficiency. A variety of benchmark problems are used to test NSSDE. Results show that NSSDE is both robust and suitable for handling multi-objective optimization, and its performance is superior to those of NSDE and NS-simplex applied separately.