## 2 Materials and Methods  
### Related Work  
Without loss of generality, we can state the classic unconstrained single-objective continuous DOP as follows. \[optimize\ f(\overline{x},\overline{\varphi},t),\ \overline{x}\in F(t)\subseteq S,t\in T \tag{1}\]  
where \(S\in R^{d}\), \(d\) is the search space dimensionality, \(S\) is the search space, \(t\) denotes the time, \(\overline{\varphi}\) is the set of parameters of the current environment, \(f:S\times T\to R\), is the objective function that returns a value \(\left(f(\overline{x},\overline{\varphi},t)\right)\ \in R\) using the feasible solution from the search space at time \(t\), \(F(t)\)--is a set of feasible solutions at time \(t\). There are a lot of approaches that have been proposed to handle DOPs, some of them are described below:  
* Detection-based approaches. This group of methods can be divided into two sub-categories: a solution reevaluation [8; 17] and detection changes in an algorithm's behavior [18; 19]. The solution reevaluation is based on the reevaluation of some solution at a given frequency. If the fitness value of this solution is changed, then the environment is changed too. The second way is based on monitoring the drop in the average performance of an algorithm over several generations. Additionally, some algorithms evaluate the diversity of fitness values. * Introducing diversity when changes are detected. When solving the stationary optimization problem, the population has to converge to an optimum. When solving DOP, if the whole population is converged to some optimum and the environment is changed, the algorithm cannot react to the change quickly and effectively. The following approach has been proposed to diversify the population. In [18], a partial hypermutation step has been proposed. It replaces a predefined percentage of individuals, generated randomly from the feasible search space. The proposed genetic programming approach [19] increases the mutation factor, reduces elitism, and increases the probability of crossover when the environment is changed. * Maintaining diversity during the search. Methods from this group do not detect directly when the environment is changed. They are based on keeping the diversity of the population on the same level. In the random immigrants method [20], a predefined number of randomly generated individuals are added to the population in every generation. The sentinel placement method [21] initializes the predefined number of points that cover the search space. Authors use the proposed method to cover the search space more uniformly. * Memory approaches. If the changes in the environment are periodical, i.e., the landscape of the problem can return, it is useful to contain previous solutions to save computational resources. The previous good solutions are stored in a direct memory [22; 23]. * Prediction approaches. In this case, a heuristic tries to find some patterns that are predictable and use this information to increase the search performance when the environment is changed. A prediction of the optima movement is described in [24]. The prediction model is based on a sequence of optimum positions found in the previous environments. * Multi-population approaches. The idea of the approach is to share responsibilities between populations. For example, the first population may focus on searching for the optimum while the second population focuses on tracking any environmental changes. The approach [25] uses the predefined number of small populations to find better solutions and one big population to track changes. Another method [26] uses the main big population to optimize the current environment and dedicates some small populations to track the changes in the environment. Most of the modern approaches utilize the multi-population concept, for example, in [27], a general adaptive multi-swarm framework is proposed, in which the number of swarms is dynamically adapted and some of the swarms are set to an inactive state to save computational resource.