# A Selection Process for Genetic Algorithm Using Clustering Analysis
## 1 Introduction  
The fields of computational intelligence and optimization algorithms have grown rapidly in the past few decades. Classical methods are not efficient in solving current problems in engineering such as energy, transportation and management [1]. The development of these optimization algorithms can be mainly divided into deterministic and stochastic approaches [2].  
Most conventional algorithms are deterministic, such as gradient-based algorithms that use the function values and their derivatives. These methods work extremely well for smooth unimodal problems, but in the case of some discontinuities, non-gradient algorithms are preferred [3]. Nelder-Mead downhill simplex [4] and Hooke-Jeeves pattern search technique [5] are a few examples of deterministic gradient-free algorithms. For stochastic algorithms, we have two types: heuristic and meta-heuristic. Although there is no agreed definition of each type in the literature, the aim of stochastic methods is to find feasible solutions in a satisfactory timescale. There is no guarantee that the best solutions can be found; however, it is expected that the algorithm will provide nearly optimal solutions most of the time.  
In this paper, we propose a genetic algorithm (GA)-based algorithm that uses clustering analysis to organize the population and select the parents for recombination. Cluster analysis is the study of techniques and algorithms to organize data into sensible groupings (clusters) according to measured or apparent similarities [6]. Clustering has been successfully applied in various engineering andscientific disciplines such as biology, medicine, machine learning, pattern recognition, image analysis and data mining [7; 8]. The performance of a newly proposed selection process named the \(k\)-means genetic algorithm selection process is investigated on a class of unconstrained optimization problems. The KGA technique is composed of four essential stages: clustering, membership phase, fitness scaling and selection. The authors postulate that clustering the evolving population can help preserve a continuous selection pressure throughout the evolution process. A membership probability index is allocated to each individual following the clustering phase. Fitness scaling alters the membership scores into a range suitable for the selection function, which selects the parents of the succeeding generation. Two versions of the KGA technique are examined: using a fixed number of clusters \(K\) (KGA\({}_{\vartheta}\)) and via an optimal number of clusters \(K_{opt}\) (KGA\({}_{\vartheta}\)). The performance of each method is tested on eight benchmark problems. The numerical simulations reveal that the proposed selection process is superior to or competitive with the standard GA for the given problems.  
The remainder of the paper is organized as follows: The next section summarizes some relevant studies that have explored clustering analysis in optimization algorithms. Section 3 presents important definitions on genetic algorithm. Section 4 presents the selection processes (KGA\({}_{\vartheta}\) and KGA\({}_{\vartheta}\)) proposed in this paper. Section 5 contains the numerical simulations where the performance of the proposed approaches is demonstrated. Finally, Section 6 concludes with some final remarks and possible future contributions.