Two competitive hybridization approaches based on combining of Giza Pyramids Construction with Particle Swarm Optimization for solving global optimization problems

Abstract

Optimization problems are complex problems that are very difficult to solve. Although these types of problems are solved in the real world using exact methods, these methods are very time-consuming and costly. By using soft computing methods, the time and cost of problem-solving can be reduced to some extent. Engineering problems are among the complex real-world problems that can be solved through soft computing methods. One of these methods is the use of metaheuristic algorithms to optimize the solution of these types of problems. The Particle Swarm Optimization (PSO) algorithm is a common and state-of-the-art metaheuristic algorithm used to solve engineering optimization problems. This algorithm is known as swarm-based optimization techniques and has a very powerful mathematical basis. Another recently published algorithm is the Giza Pyramids Construction (GPC) algorithm. The GPC algorithm models the technological advancements of construction in ancient times. Both algorithms have many advantages through which optimization problems can be solved effectively. To increase the power of metaheuristic algorithms and solve optimization problems more effectively through them, the idea of competitive hybridization algorithms has been proposed. In this paper, two competitive hybrid approaches of combining PSO and GPC algorithms are presented. These two competitive hybridization approaches have been first applied to 45 benchmark functions and have been evaluated and analyzed statistically. Then they have been applied to six classic engineering problems. Algorithms presented in each step have been compared with Genetic Algorithm (GA) and PSO algorithms and their combined approaches. The results of experiments and statistical analysis show that the solution to engineering problems has been done more effectively by using the two proposed combinations.