# Combinatorial Optimization Problems and Metaheuristics: Review, Challenges, Design, and Development
## 2 Materials and Methods
### Metaheuristic System of Classifications
#### 2.6.4 Solution Creation Strategy  
This dimension also reveals another crucial aspect of the metaheuristics navigation system. In this case, it defines the strategy used to generate and transform solutions during the search process. It also can be considered one of the most important behaviors of a metaheuristic. The solution creation and manipulation strategy can be divided into two main classes of algorithm behavior: (1) combination and (2) movement [12].  
The (1) combination strategy, as the name suggests, is the group of algorithms that are based on operations that are applied to mix the content of some solutions to form other solutions. Additionally, they did not elect a reference solution to be followed. Therefore, any solution of a set of solutions can be used to form the new ones. The Genetic Algorithm (GA) is the most known and symbolic algorithm of this group. They can still be subdivided into two groups, mixture (Section 1.1) and stigmergy (Section 1.2).  
The methods based on \"mixture\" perform a _direct combination_ of existing solutions to form a new one. The Genetic Algorithm (GA) is the most famous metaheuristic that uses the combination strategy. The algorithms based on stigmergy, on another side, use an _indirect combination_ strategy, by using an intermediary structure got from the various solutions used to produce new solutions. Ant Colony Optimization (ACO) is the most known algorithm in this category.  
On the other hand, the algorithms that employ (2) movement strategy use a pattern found in the current set of solutions--by using a differential vector that calculates the intensity and direction of the movement--to generate a new solution. In addition, these algorithms define a solution used as the reference and it is followed by others. The newly developed solutions can replace the reference solution or compete with other followers and replace them. The Particle Swarm Optimization is the most emblematic algorithm of this category.  
The methods based on movement can be further split into three subdivisions, all population (Section 2.1), representative (Section 2.2), and group (Section 2.3). As the name suggests, all population members define the movement in all population (Section 2.1). However, each member has a different level of influence based on the distance of the reference solution. In representative (Section 2.2), each solution is influenced by a reduced representative solution group (PSO is classified in this subdivision). The group-based algorithms (Section 2.3) just consider a subset of solutions to form the new solution. These groups do not use representative criteria. They use neighborhood or subpopulations strategy to define the groups to support the calculation and generate new solutions.  
**Remark 4**.: _It is noteworthy to emphasize, to organize this dimension, we used as the main reference the inputs provided by [PERSON] et al., 2020 [12]. They offered an outstanding critical analysis and recommendations about metaheuristics classification. Essentially, we used Chapter 4 (Taxonomy as Behavior), where they analyzed several metaheuristics and organized them according to the mechanism employed to build and modify solutions. It should be noted that this study adapted the nomenclature to accommodate these inputs with other perspectives. For instance, \"Solution Creation\" was renamed to \"Combination\" (1), and \"Differential Vector movement\" was renamed to \"Movement\" (2). Moreover, the term \"Solution Creation and Manipulation Strategy\" is created to arrange this dimension because the metaheuristics can have many other types of behaviors._