# New Insights into Fuzzy Genetic Algorithms for Optimization Problems
## 1 Introduction  
Fuzzy genetic algorithms (FGAs) are kinds of genetic algorithms (GAs) that employ fuzzy logic (FL) at some point in the process of mutation, crossover, selection, or updating the hyperparameters. The fuzzy reasoning has been exploited by several authors for the complex problem of dynamic control of GA parameters. There is ample literature devoted to the application of FGAs, e.g., in security [1; 2], engineering [3; 4], web applications [5], and manufacturing [6]. Despite the numerous articles of this type, there are not so many that introduce variants of FGAs. In [7], the authors proposed FL-controlled GAs, where mutation and crossover probabilities were dynamically adjusted by FL controllers. The application problem they considered was simulations of economic dispatch and emission dispatch. In [8], the authors presented dynamically controlled GA simulations, with population size and mutation and crossover rates adjusted using the FL controller. Inputs to the controller were genotypic diversity and phenotypic diversity, and outputs of the controller were population size change, mutation rate change, and crossover rate change. At any rate, in [9], it was stated that using a population diversity metric in an FGA can significantly improve premature convergence. Input variables of the fuzzy controller were population diversity, average population diversity divided by the maximum population diversity, and the number of unchanged greatest fitness values. As in some of the previously reviewed works, authors used mutation and crossover probabilities as output variables. An improved version of the FGAs in [8] was presented in [10], modifying some fuzzy inference rules and introducing a scaling factor for normalizing the input variables. In [11], a GA with varying population size (GAvaPS) was enhanced with a fuzzy logic controller byadapting the crossover probability according to a fuzzy rule base. The resulting method was called fuzzy-based lifetime extended GA (LTexGA). A hybrid fuzzy genetic algorithm (HFGA) was developed in [12]. In this FGA variant, the average fitness value and the best fitness value of each generation were adopted for the dynamical tuning of the crossover and mutation probabilities. The HFGA was used to tackle the problem of an optimal grouping of tank crews, based on training time, qualifications, and specialization of soldiers. The authors of [13] tried to improve the adaptive method of [10]. In the proposed improved fuzzy genetic algorithm (IFGA), the average fitness value and standard deviation changes between two consecutive generations were selected as the input variables, using two adaptive scaling factors to normalize the input variables. An interesting variant of FGA was introduced in [14] a few years later. The authors proposed a gendered fuzzy genetic algorithm (GFGA), i.e., GA with gendered selection based on fuzzy rules and age/lifetime formulas. GFGA was successfully used to generate the weights of a neural network (NN). More recently, the elegant fuzzy genetic algorithm (EFGA) was proposed [15] with a min-heap data structure for prioritizing genomes for the optimization of the initial weights of complex-valued NNs. In the EFGA, mutation rate, crossover rate, and reproductive group size were updated using fuzzy rules. In [3], the authors introduced a bilinear fuzzy fitness function in a standard GA to design optimal diagrid structures for tall buildings under engineering design constraints. In [2], the population selection was based on fuzzy clustering, with no explicit mention of fuzzy rules. Here, we focus on FGAs using fuzzy rules. GAs remain largely unexplained to the end-user in terms of their search properties. An attempt to make GAs explainable was made by using surrogate models, which gave a partial understanding of the solutions limited to a single generation [16]. Needing to be trained, such a model comes with an additional computational cost. Fuzzy rules for controlling the GA's search properties bring an enormous advantage: they can add explainability.