# CaAIS: Cellular Automata-Based Artificial Immune System for Dynamic Environments
## 1 Introduction
As a result, it is crucial to adequately tackle the extra challenges presented by this scenario to achieve promising results. Reacting to changes is critical to maintaining optimization algorithms' performance in dynamic environments. The first step toward reacting to changes is to detect changes in the first place and then adopt a suitable strategy to deal with them. [PERSON] [15] discussed two major change detection types: population based and sensor based. In population-based detection, statistical hypothesis testing is performed at each generation to see whether the alteration in the fitness of the individuals was not due to their convergence. In sensor-based detection, some measurements (so-called \"fitness landscape sensors\") are placed either randomly or regularly into the landscape. At every generation, the environment changes if any of the sensors detect an altered fitness value. Evolutionary algorithms (EAs) for addressing diverse applications characterized by dynamic behavior have received significant attention in recent years [3]. Conventional population-based algorithms can successfully solve static optimization problems but may fail in dynamic environments since they cannot recognize environmental changes. Different methods have been suggested to detect changes in the dynamic environment. Also, there is no prior knowledge or standard criteria for dealing with changing environments. A simple method can reset the optimization algorithm after detecting any environmental change, which can often be performed correctly [16]. Before reaching optimal regions, another change may occur through the evolution of an optimization algorithm. It is also possible to track the peaks around the optimal instead of locating the optimal using DOP algorithms as an alternative solution. Several techniques and improvements based on the characteristics of each EA are suggested for dynamic optimization [17; 18; 19], among which, the main approaches dealing with the dynamic environment can be categorized into several groups, including: (1) increasing diversity methods [13], (2) diversity maintenance methods [20], (3) memory-based methods [21], (4) predicting the next optimum solution, (5) self-adaptive mechanisms, (6) multi-population methods [22], and (7) hybridization of the methods [23; 24]. This study uses diversity control with parameter adaptation by CAs for the distribution of parameters among the CA cells and their interaction. A cellular automaton (CA) comprises numerous cells, each possessing a state that evolves through a set of feasible states according to a local rule. CA is especially appropriate for simulating natural systems that can be characterized as a vast collection of essential components interacting locally with one another. The cellular automata-based artificial immune system (CaIS) proposed in this paper can be viewed as a stochastic cellular automaton [25], where the size of the state set corresponds to the number of points in the search space, and the cells update their states repeatedly until an appropriate predetermined criterion is met. This paper presents a novel hybrid model of AIS using the cellular automata called cellular automata based on artificial immune system (CaAIS) for dynamic environments. Antibodies are distributed throughout a cellular grid of search space in the proposed model as nominal solutions. They are responsible for different solutions at different times. Based on the local interactions between cells and their local rules, the appropriate parameters and optimal solutions of cells are spread in the cell space. Due to CA properties, the CaAIS inherits the computational power of cellular automata [26] and AIS optimization capability. In summary, our main contributions are highlighted as follows:  
* We proposed a hybrid model of AIS and CA called cellular automata based on the artificial immune system (CaAIS) for dynamic environments. * We proposed the CA local interactions in the CaAIS to adapt the parameters and increase diversity.