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.