1.1 Description of Multi-Objective Optimization Problem
In production activities, multi-objective optimization problems are widespread, such as: RGV dynamic scheduling problem (Li et al., 2020), adaptive parameter estimation problem in wireless networks (Dash et al., 2020). Under normal circumstances, the sub-goals of a multi-objective optimization problem are contradictory to each other, and it is impossible to make all the sub-goals reach the optimal value at the same time. It is often necessary to coordinate and weigh among the sub-goals (Tamaki et al., 1996; Tan et al., 2002). The optimization solution of the multi-objective optimization problem is not unique, but a set of optimal solutions, called the Pareto optimal solution. The decision maker should select the appropriate element from the Pareto optimal solution as the final decision plan according to the needs.
1.2 Research Status of Multi-Objective Optimization Algorithms
The early multi-objective optimization uses linear programming to optimize, but it will become difficult to face complex nonlinear problems. Since the birth of evolutionary algorithm, due to its heuristic search strategy, it has been used in multi-objective problem optimization and has achieved excellent performance. Current multi-objective evolutionary algorithms can be divided into four categories: a. Multi-objective evolutionary algorithms based on Pareto dominance, represented by SPEA, PESA algorithms and their improved algorithms (Zitzler et al., 2001; Lalitesh & Prawendra, 2020); b. Multi-objective evolution based on decomposition Algorithm. In 2007, Zhang first proposed the MOEA/D (Zhang & Li, 2008) algorithm. In recent years, it has become a popular algorithm framework in the field of multi-objective optimization; c. Multi-objective evolutionary algorithm based on indicators, which knows evolution strategies through evaluation indicators, such as SMS-EMOA (Beume et al., 2007), R2-MOGA (Zhu et al., 2017), etc.; d. Hybrid algorithm, combining the advantages of the previous three algorithms to form a hybrid algorithm to solve high-latitude multi-objective complex optimization problems, for instance, a hybrid algorithm HCGA-PSO is proposed based on the global search ability of genetic algorithm and the fast convergence performance of PSO algorithm (Li et al., 2019), while Dang (Dang et al., 2016) proposed an analytical approach based on Newton’s methods and nonlinear barrier method to solve this large-scale joint multi-objective optimization problem.
However, some novel multi-objective optimization algorithms for solving large-scale complex multi-objective optimization problems have been reported recently. Zhou proposed a SIR-DNA algorithm (Zhou, 2020) which was constructed based on the DNA-based SIR (susceptible-infectious) infectious disease model, and the algorithm has the advantages of strong global search ability and has a high convergence speed for solving complex optimization problems. Dang and Kinsner introduced an adaptive multi-objective mimetic optimization algorithms (AMMOA) (Dang & Kinsne, 2016), it guides the process of adaptive selection, clustering and local learning according to the information theory criterion, and adopts the robust stop criterion of AMMOA. These novel algorithms provide more useful alternatives for multi-objective optimization problems.