# A Selection Process for Genetic Algorithm Using Clustering Analysis
## 3 Problem Definition  
In essence, the basic objective of any clustering algorithm is to find a global or approximate optimal for combinatorial optimization problems which are NP-hard [47]. The \(k\)-means algorithm is very likely to converge to a suboptimal partition. The main advantage of stochastic optimization techniques over deterministic-methods is that they are able to avoid convergence to a local optimal solution. Therefore, stochastic approaches have been employed to solve clustering problems; algorithms such as simulated annealing, genetic algorithms, evolution strategies and evolutionary programming. Inspired by the principles of natural selection and biological evolution, evolutionary algorithms seek to optimize a population of individuals by applying a set of evolutionary operators. They are population-based meta-heuristic optimization algorithms that make use of biological evolution operators such as selection, recombination and mutation. In order to demonstrate the novelty in the use of clustering analysis in the selection process of the genetic algorithm, the performance of the proposed KGA techniques will be compared with existing GA methods. They were originally proposed by [PERSON] [48], inspired by the principle of natural selection of biological systems or 'Darwinian evolution'. GAs have demonstrated their capability to solve a wide range of optimization problems such as revenue management, optimal engineering  
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system designs, scheduling applications, image processing, quality control etc. [PERSON] essentially laid the foundation of modern evolutionary computing by fundamentally defining three key genetic operators: crossover, mutation, and selection. These evolutionary operators provide a way to generate offspring from parent solutions. We summarize the fundamental steps of genetic algorithms in Algorithm 1. In genetic algorithms, each individual (or solution vector) is encoded as either a binary bit string or a real-value vector, both referred to as a chromosome. The standard representation of each individual is a binary array of bits, to facilitate the crossover and mutation operations. ```



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improve the probability of discovering the global optimum by sufficiently covering the solution space (exploration) yet ensuring sufficient pressure to obtain even better solutions from current individuals (exploitation). Furthermore, in practical multimodal domains problems, it is desirable to evaluate several global optima or some local optima that might be suitable alternatives to the global optima. Traditional genetic algorithms perform well on single optimum problems but fail to provide multiple solutions. By combining the strength of clustering analysis and genetic search, the proposed KGA techniques permit the evaluation of multimodal functions. A detailed explanation of the proposed KGA technique is considered in the next section. ## 4 The Proposed Algorithm

The following section presents a brief description of the proposed \(k\)-means genetic selection processes. We are interested in the unconstrained optimization problems in which we attempt to find \(\overset{\rightarrow}{x^{*}}\) which optimizes \(f(\overset{\rightarrow}{x})\) using GA-based algorithms. Therefore, only the standard GA will be used to test the performance of the proposed KGA algorithms. Below, two distinct selection techniques KGA\({}_{f}\) and KGA\({}_{o}\) are presented. ### Kga\({}_{f}\)

The proposed KGA is different to the standard GA in several ways. Primary, the chromosomes of the population are partitioned into groups in such a way that all individuals inside the same cluster are similar. This offers a novel approach to solve the two important issues in the evolution process of the genetic search: exploitation and exploration. Exploration is responsible for population diversity by exploring the search space, while exploitation attempts to reduce the diversity by focusing on individuals with higher fitness scores.