Crossover and mutation operators of real coded genetic algorithms for global optimization problems

This study is primarily aimed at investigating two issues in genetic algorithm (GA) and one issue in conformational search (CS) problems. First and foremost, this study examines the proposed crossover and mutation operators on the problems of slow convergence and premature convergence to suboptimal solution. Second of all, this study operates within experimental design with Taguchi method to discover the optimal design factors for the two proposed genetic operators. On the other hand, the CS issue focuses on the effects of the combination of the two proposed genetic operators on two CS problems. Past studies have revealed that GAs are one of the most prevalently used stochastic search techniques to date. The strength of the algorithm lies in the fact that it assists the evolution of a population of individuals who would thrive in the survival of the fittest towards the next generation. GA has been employed in resolving many complex combinatorial optimization problems such as CS problems. However, the lack of diversity in a population and the difficulty to locally exploit the solutions within a population creates a setback for GA. Apart from that, its tuning variables are tricky, as it requires intricate setting properties. On another note, the drawback in CS is in locating the most stable conformation of a molecule with the minimum potential energy based on a mathematical function. The number of local minima grows exponentially with molecular size and this makes it that more difficult to arrive at a solution. As such, this research is aimed at resolving the issues mentioned. The rationale behind developing algorithms using real encoding of chromosome representations is the limitations of binary encoding. In relation to this, Real Coded GA (RCGA) refers to GAs which incorporate real number vector representations of chromosomes. Because the representations of the solutions are similar to the natural formulation, RCGA gets better-customized to the optimization of problems in a continuous domain. Throughout the years, there has been a shift in focus on constructing new crossover and mutation operators to improve the performance of GA in function optimization. GA operators employ two main strategies; that is, exploration and exploitation to locate the optimum solutions. This research employed a new generational GA based on a combination of the proposed Rayleigh Crossover (RX) and proposed Scale Truncated Pareto Mutation (STPM) called RX-STPM. It is applied in optimization problems like CS. While RX displays self-adaptive behavior and possesses exploration capabilities, STPM thrive in its exploitation features. Hence, RX-STPM becomes an optimal equilibrium between exploration and exploitation strategies in leading the system towards global optima. The explorative and exploitative features of the proposed GA are regulated by substantial crossover probability and mutation rate set up using the Taguchi method. Aside from that, tournament selections with proper tournament sizes, used in the design of the proposed operators, also led to strong exploration potentials. As you will see in this study, the performance of all RCGAs is contrasted to the standard criteria used in GA literature, which involves accuracy (judged by average error, mean and standard deviation of the objective function values), efficiency and reliability (judged by success rate and average number of function evaluation). RX and STPM operators were separately tested on a dataset of ten benchmark global optimization problems according to the specified experimental procedure. The numerical findings gathered from performance evaluations for RX and STPM were promising and they have shown significantly better results in comparison to the other crossover and mutation operators found in the literature. An accurate combination of GA operators is pivotal in securing effective resolution to the problem. In this study, the GA was analyzed on a few operators. The numerical results obtained from the performance evaluation indicated that the RX crossover is the most fitting pair to the STPM mutator in competently solving two CS problems i.e. minimizing a molecular potential energy function and finding the most stable conformation of pseudoethane through a molecular model, which involves a realistic energy function.

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