# A Survey on Search Strategy of Evolutionary Multi-Objective Optimization Algorithms
## 3 Classification of Multi-Objective Evolutionary Algorithms from the View of Search Strategy
### High-Dimensional MOEA  
In multi-objective optimization studies, the difficulty of optimization increases exponentially with the increasing number of objective dimensions. Usually, optimization problems with four or more objectives are called high-dimensional multi-objective optimization problems. In recent years, high-dimensional MOEA has become a highly popular research topic in the field of evolutionary multi-objective optimization. Classical MOEAs, such as NSGA-II and SPEA2, have good results in solving two-dimensional or three-dimensional optimization problems. However, as the number of objective dimensions increases, these classical MOEAs based on Pareto dominance relations face many difficulties.  
1. Degradation of the search capability. As the number of objective dimensions increases, the number of non-dominated individuals in the population increases exponentially, thus reducing the selection pressure of the evolutionary process.
2. The number of non-dominated solutions used to cover the entire Pareto front increases exponentially.
3. Difficulties in visualizing the optimal solution set.
4. The computational overhead for evaluating the distributivity of the solution set increases.
5. The efficiency of the recombination operation decreases. In a larger high-dimensional space, the children resulting from the recombination of two distant parents may be far away from the parents, making the ability of the local search of the population weaker. Therefore, designing and implementing algorithms that can efficiently solve high-dimensional multi-objective optimization problems is one of the current and future challenges in the field of evolutionary multi-objective optimization.  
In recent years, scholars have proposed some effective methods for solving high-dimensional multi-objective optimization problems. One type of algorithm is based on Pareto dominance relations, which reduce the number of non-dominated individuals by extending the Pareto dominance region, such as \(\epsilon\)-MOEA [95] and control the dominance area of solutions (CDAS) [96]. An aggregation function can also be used to aggregate multiple objectives into a single objective for optimization, such as MOEA/D, NSGA-III [97], and MSOPS-II [98]. Finally, there are metric-based algorithms that use performance evaluation metrics to compare the merits of two populations or between two individuals, such as IBEA, SMS-EMOA, and Hyp [99]. In 2013, [PERSON] proposed a shift-based density estimation method (SDE) from the perspective of a diversity retention mechanism and integrated it into SPEA2 with good results [100]. In addition, one scholar dealt with the high-dimensional multi-objective optimization problem by trying to reduce the number of objectives, and the treatment methods mainly include the principal component analysis method [101], the redundant objective elimination algorithm based on the minimum objective subset [102]. Reducing redundant objectives or unimportant objectives is also an important direction for high-dimensional MOEA research.