A Convergent Genetic Algorithm for Pipe Network Optimization

Abstract

A highly convergent Genetic Algorithm (GA) for pipe network optimization is presented in this paper. An artificial genotype passing mechanism, an alternative penalty cost calculation method, an iterative setting of the penalty parameters prior to the GA search and, more importantly, a new selection operator, are introduced in the proposed GA. The genotype passing mechanism leads to a monotonically decreasing convergence curve of the GA search and, therefore, paves the way for introducing a logical convergence criterion for genetic algorithms. The use of an alternative penalty cost calculation leads to a better distribution of the fitness function in the search space, compared to conventional methods and, therefore, helps the GA to locate useful genes. Penalty parameters used for the calculation of the penalty cost are determined prior to a GA search, via use of a mathematical programming method, eliminating the possibility of choosing too low or high parameter values. Finally, a new selection operator is designed in an attempt to simulate the process of natural mating more closely, leading to an improvement in the optimality and convergence characteristics of the method. The efficiency of the proposed GA is shown by applying the method to the optimal design of three well-known benchmark networks, namely two-loop, Hanoi and New York networks. The method produces results comparable to the best results presented in the literature with much less computational effort.