Real-coded Crossover Operators Research Articles

Enhancing probabilistic based real-coded crossover genetic algorithms with authentication of VIKOR multi-criteria optimization method

<p> To improve the performance of genetic algorithms (GAs) in complex optimization settings, this work offered two novel real-coded crossover operators: one based on the Gumbel distribution (GX) and the other on the Rayleigh distribution (RX). These innovative operators, when combined with three different mutation techniques, created a significant improvement in GA methodology. Our meticulous simulations showed that the GX operator significantly outperformed RX and other traditional operators, demonstrating its superior capacity to address complex optimization problems. The GX operator's unusual robustness was further validated through detailed performance analysis utilizing the VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) multi-criteria decision-making technique, setting a new standard in crossover operator design and significantly improving the state of the art in GAs.</p>

Mixture distribution based real-coded crossover: A hybrid probabilistic approach for global optimization

In the present simulation-based study, a novel parent-centric real-coded crossover operator is introduced with a unique probabilistic aspect of the mixture distribution. Moreover, the mixture distribution is a co-integration of double Pareto and Laplace probability distributions with various parameters. The key objective of the newly proposed methodology is to obtained optimal solutions for complex multimodal optimization problems. Hence, for its global comparison, the newly proposed mixture distribution crossover operator (MDX) is compared with double Pareto (DPX), Laplace (LX), and simulated binary (SBX) crossover operators within the conjunction of three mutation operators (MTPM, PM, and NUM). After a descriptive comparison, a Quade multiple comparison test is also administered to examine its statistical significance. Furthermore, the performance of the genetic algorithm (GA) is also examined on a set of twenty-one unconstraint benchmark functions with diverse features. The empirical results of the simulation-based study reveal that the mixture-based crossover operator obtained a substantial dominance over all considered crossover operators in terms of computational complexity, robustness, scalability, and capability of exploration and exploitation. Moreover, the Quade multiple comparison test also showed a significant superiority with graphical authentication of the performance index (PI).

A Novel Parent Centric Crossover with the Log-Logistic Probabilistic Approach Using Multimodal Test Problems for Real-Coded Genetic Algorithms

In this paper, a comprehensive empirical study is conducted to evaluate the performance of a new real-coded crossover operator called Fisk crossover (FX) operator. The basic aim of the proposed study is to preserve population diversity as well as to avoid local optima. In this context, a new crossover operator is designed and developed which is linked with Log-logistic probability distribution. For its global performance, a realistic comparison is made between FX versus double Pareto crossover (DPX), Laplace crossover (LX), and simulated binary crossover (SBX) operators. Moreover, these crossover operators are also used in conjunction with three mutation operators called power mutation (PM), Makinen, Periaux, and Toivanen mutation (MPTM), and nonuniform mutation (NUM) for inclusive evaluation. The performance of probabilistic-based algorithms is tested on a set of twenty-one well-known nonlinear optimization benchmark functions with diverse features. The empirical results show a substantial dominance of FX over other crossover operators with authentication of performance index (PI). Moreover, we also examined the significance of the proposed crossover scheme by administrating ANOVA and Gabriel pairwise multiple comparison test. Finally, the statistically significant results of the proposed crossover scheme have a definite edge over the other schemes, and it is also expected that FX has a great potential to solve complex optimization problems.

A Novel Genetic Algorithm for Global Optimization

This paper presents a novel genetic algorithm for globally solving un-constraint optimization problem. In this algorithm, a new real coded crossover operator is proposed firstly. Furthermore, for improving the convergence speed and the searching ability of our algorithm, the good point set theory rather than random selection is used to generate the initial population, and the chaotic search operator is adopted in the best solution of the current iteration. The experimental results tested on numerical benchmark functions show that this algorithm has excellent solution quality and convergence characteristics, and performs better than some algorithms.

A new compound arithmetic crossover-based genetic algorithm for constrained optimisation in enterprise systems

ABSTRACTIn many real industrial applications, the integration of raw data with a methodology can support economically sound decision-making. Furthermore, most of these tasks involve complex optimisation problems. Seeking better solutions is critical. As an intelligent search optimisation algorithm, genetic algorithm (GA) is an important technique for complex system optimisation, but it has internal drawbacks such as low computation efficiency and prematurity. Improving the performance of GA is a vital topic in academic and applications research. In this paper, a new real-coded crossover operator, called compound arithmetic crossover operator (CAC), is proposed. CAC is used in conjunction with a uniform mutation operator to define a new genetic algorithm CAC10-GA. This GA is compared with an existing genetic algorithm (AC10-GA) that comprises an arithmetic crossover operator and a uniform mutation operator. To judge the performance of CAC10-GA, two kinds of analysis are performed. First the analysis of the convergence of CAC10-GA is performed by the Markov chain theory; second, a pair-wise comparison is carried out between CAC10-GA and AC10-GA through two test problems available in the global optimisation literature. The overall comparative study shows that the CAC performs quite well and the CAC10-GA defined outperforms the AC10-GA.

Real-coded Crossovers as a Role of Kernel Density Estimator Proposal of Crossover Kernels based on Unimordal Normal Distribution Crossover

This paper presents a kernel density estimation method by means of real-coded crossovers. Functions of real-coded crossover operators are composed of probabilistic density estimation from parental populations and sampling from estimated models. Real-coded Genetic Algorithm (RCGA) does not explicitly estimate probabilistic distributions, however, probabilistic model estimation is implicitly included in algorithms of real-coded crossovers. Based on this understanding, we exploit the implicit estimation of probabilistic distribution of crossovers as a kernel density estimator. We also propose an application of crossover kernels to Expectation-Maximization estimation (EM) of Gaussian mixtures.

A new crossover operator for real coded genetic algorithms

In this paper, a new real coded crossover operator, called the Laplace Crossover (LX) is proposed. LX is used in conjunction with two well known mutation operators namely the Makinen, Periaux and Toivanen Mutation (MPTM) and Non-Uniform Mutation (NUM) to define two new generational genetic algorithms LX–MPTM and LX–NUM respectively. These two genetic algorithms are compared with two existing genetic algorithms (HX–MPTM and HX–NUM) which comprise of Heuristic Crossover operator and same two mutation operators. A set of 20 test problems available in the global optimization literature is used to test the performance of these four genetic algorithms. To judge the performance of the LX operator, two kinds of analysis is performed. Firstly a pair wise comparison is performed between LX–MPTM and HX–MPTM, and then between LX–NUM and HX–NUM. Secondly the overall comparison of performances of all the four genetic algorithms is carried out based on a performance index (PI). The comparative study shows that Laplace crossover (LX) performs quite well and one of the genetic algorithms defined (LX–MPTM) outperforms other genetic algorithms.