# A Survey on Search Strategy of Evolutionary Multi-Objective Optimization Algorithms
## 3 Classification of Multi-Objective Evolutionary Algorithms from the View of Search Strategy
### Decomposition-Based MOEA Algorithms
#### 3.1.2 MOEA/D Search Strategy  
The MOEA/D algorithm leverages a collaborative optimization approach to solve a single objective or a collection of multiple multi-objective sub-problems, which are derived from the original MOP [70]. The algorithm simultaneously solves all of the sub-problems to identify the entire Pareto front surface. Typically, weight vectors are used to define the sub-problems, and the Euclidean distance between the weight vectors is used to determine the neighborhood relations between sub-problems. The MOEA/D algorithm stands out from other MOEA algorithms due to its focus on selecting parent individuals from the neighborhood, producing new individuals through crossover operations, and carrying out neighborhood population updates by predetermined regulations [71]. Therefore, the neighborhood-based optimization strategy is an integral feature in guaranteeing the search efficiency of MOEA/D. During the evolutionary process, once a high-quality solution for a sub-problem is searched, its good genetic information is rapidly spread to the rest of the individuals in the neighborhood, and it accelerates the rate of algorithm convergence.  
The MOEA/D algorithm provides a basic framework using a decomposition strategy, whose most important feature is decomposition and cooperation. Currently, many different versions of the MOEA/D algorithm have been created to address MOP with different difficulty characteristics. In this paper, fundamental MOEA/D algorithms using [PERSON]'s method are presented [72], and its basic data structure is as follows.  
1. The Chebyshev sub-problem is defined by the set of weight vectors \(\left\{\lambda^{1},\cdots,\lambda^{N}\right\}\) with reference points \(z\).
2. Each sub-problem is assigned an individual, and all individuals \(\left\{x^{1},\cdots,x^{N}\right\}\) form a current evolutionary population \(P\).
3. The elite population used to save the Pareto solution is EP.
4. The sub-problem neighborhood is \(NS_{1},\cdots,NS_{N}\).  
Unlike other MOEA algorithms, MOEA/D represents an open class of decomposition-based algorithms. Based on MOEA/D, it is easy to combine existing optimization techniques to design efficient algorithms to deal with various problems [46]. For different levels of difficulty that may occur in sub-problems, [PERSON] et al. presented MOEA/D-DRA with the adaptation of computational resources [73]. MOEA/D considers the simultaneous optimization of multiple single-objective sub-problems, and different sub-problems are responsible for approximating different parts of the Pareto surface, so MOEA/D can be easily parallelized. [PERSON] and [PERSON] developed a parallel line-based MOEA/D that can be performed in parallel on multicore computers [74]. Combining the advantages of different aggregation functions, [PERSON] et al. proposed using different aggregation functions in unused search phases [75]. When dealing with combinatorial optimization  
Figure 2: The contour of weighted sum approach. Concerning convex problems, several isometries can be drawn to discover the shortest distance points that together produce a different set of Pareto optimal vectors. For non-convex problems, the vertical line of each reference vector cannot be tangent to its leading edge. This figure is adopted from [20].  
problems, optimization for sub-problems can be combined with classical heuristics, e.g., [PERSON] et al. combined MOEA/D with ant colony optimization techniques and suggested the MOEA/D-ACO [76].