# A Survey on Search Strategy of Evolutionary Multi-Objective Optimization Algorithms
## 1 Introduction  
As one of the heuristic search optimization algorithms using population, the evolutionary computation algorithm is easy to apply and implement. It does not require highly deterministic mathematical properties for both problems to be solved and the algorithms to solve these. Its application field has expanded steadily up to this point, attracting the interest of several academics and engineers [1]. Evolutionary multi-objective optimization (EMO) has been used successfully in the field of multi-objective optimization problems, and it has developed into a rather popular field of study [2]. EMO has gained widespread attention and adoption in the scope of evolutionary computation research. Optimization problems are a common type of problem encountered in engineering applications and scientific research. These problems involve finding the optimal solution or solutions to a particular problem [3]. The problems of single-objective optimization have a single-objective function, while multi-objective optimization problems (MOP) involve multiple-objective functions, and attempt to satisfy all objective functions simultaneously. One solution may be enough for one objective, but it may not perform well on all objectives at the same time. Therefore, there will be a set of compromise solutions, which is called the Pareto optimal set in multi-objective optimization problems [4]. Conventionally, by giving weights to the various objectives, the MOP was often converted into single-objective problems. These single-objective problems can be solved using mathematical programming techniques, which can only obtain the optimal solution under the condition of one weight at one time. The conventional mathematical programming approaches are frequently ineffective and more susceptible to the weight value or the order provided by the objective because the objective function and constraint function of the MOP may have discontinuous, nonlinear, or non-differentiable characteristics. The population of potential solutions is preserved from generation to generation by an evolutionary computation algorithm to achieve the global optimum. By using this population-to-population strategy, it is possible to find the Pareto optimal solutions set for the multi-objective optimization problem. [PERSON] introduced the vector evaluation genetic algorithm (VEGA) at the beginning of 1985 [4], which is recognized as the evolutionary computation algorithm's groundbreaking contribution to resolving the MOP. The non-dominated sorting genetic algorithm (NSGA) was presented by [PERSON] and [PERSON] [5], and the multi-objective genetic algorithm (MOGA) was suggested by [PERSON] and [PERSON] [6] The niched Pareto genetic algorithm (NPGA) was propounded by [PERSON] et al. [7]. These algorithms are the pioneer works for MOEA in the evolutionary computation community. The original evolutionary multi-objective optimization algorithm is the ordinary name for these algorithms. Individual selection using the Pareto level and population diversity maintenance using the fitness-sharing mechanism are features of the primitive generation of evolutionary multi-objective optimization algorithms [8]. The second-generation evolutionary multi-objective optimization algorithm, which features an elite retention mechanism, was sequentially proposed from 1998 to 2002. In 1998, the strength Pareto evolutionary algorithm (SPEA) was first proposed by [PERSON] and [PERSON] [9], and SPEA-SPEA2 was improved upon three years later [10]. The Pareto archived evolution strategy (PAES) was proposed by [PERSON] and [PERSON] in 2000 [11]; shortly after, they proposed enhanced versions of the algorithm, the Pareto binary-based selection algorithm (PESA) [12] and PESA-II [13]. An enhanced version of NPGA, NPGA2, was proposed by [PERSON] et al. in 2001 [14]. A micro-genetic algorithm (MICRO-GA) was propounded by [PERSON] and [PERSON] [15]. In 2002, [PERSON] et al. suggested a highly conventional algorithm by enhancing NSGA, i.e., NSGA-II [16].