Article Preview
Top1. Introduction
In most science, business, and engineering fields, global optimization problems often arise with the purpose of locating the global optimum. Many approaches have been proposed to deal with global optimization problems. Nevertheless, when the objective of global optimization problems is nonlinear, non-convex or non-differentiable, traditional mathematical approaches may become inefficient, or even fail to work. Evolutionary algorithm (EA) is a kind of population based iterative heuristic optimization paradigm. Over the last two decades, EAs have been widely studied and applied for many scientific and real-world optimization problems with promising results (Del, Osaba, & Molina, 2019). However, the basic EAs are easy to fall into some local optima when tackling complicated global optimization problems with a large number of local optima. Apparently, the key to solving global optimization problems using EAs is how to handle the relationship between the exploration and exploitation.
The exploration refers to the capability of an EA to investigate undiscovered regions in the decision space to find more potential solutions, while the exploitation means the ability of an EA to apply the knowledge of discovered promising solutions to further improve their fitness. A loss of exploration might result in stagnation in suboptimal areas, producing the effect known as premature convergence. By contrast, a low exploitation rate cannot make the population convergence to the global optimum. In practice, exploration and exploitation are conflicting with each other. Thus, in order to achieve good performances on global optimization problems, the exploration and exploitation abilities should be well balanced (Singh & Deep, 2019). It is extensively recognized that an EA should put more emphasis on exploration at the early stage of the evolution and high exploitation at the later stage of the evolution.
To balance the exploration and exploitation in EAs, this paper makes an attempt to adopt decomposition-based dynamic MOEA to solve complicated global optimization problems. Firstly, a global optimization problem is converted to a dynamic bi-objective optimization problem by taking the niche count function as a helper objective. Subsequently, a decomposition-based MOEA: MOEA/D-M2M (Liu, Gu, & Zhang, 2014), with DE operator (Storn & Price, 1997) is employed to solve the transformed dynamic bi-objective optimization problem. The dynamic version of MOEA/D-M2M is named DMOEA/D-M2M. DMOEA/D-M2M decomposes the converted bi-objective optimization problem into a number of bi-objective optimization subproblems which are easier to solve. In DMOEA/D-M2M, optimization of the original objective is beneficial to the population convergence while minimization of the niche-count objective is helpful to the population diversity. Throughout the entire evolution stage, the gradually-decreasing-to-zero niche radius is capable of achieving a tradeoff between exploration and exploitation.
The remainder of the paper is organized as follows. Section 2 briefly reviewed related works. Section 3 depicts some preliminary. Section 4 presents the dynamic multi-objective technique, which a global optimization problem is converted to a dynamic bi-objective optimization problem. Section 5 shows the detailed of proposed DMOEA/D-M2M algorithm. Section 6 conducts the experiments and makes a comparison of DMOEA/D-M2M with four competitors. Section 7 makes some further discussions. At last, Section 8 draws conclusions.