Design of Water Distribution Networks using a Pseudo-Genetic Algorithm and Sensitivity of Genetic Operators

Genetic algorithms (GA) are optimization techniques that are widely used in the design of water distribution networks. One of the main disadvantages of GA is positional bias, which degrades the quality of the solution. In this study, a modified pseudo-genetic algorithm (PGA) is presented. In a PGA, the coding of chromosomes is performed using integer coding; in a traditional GA, binary coding is utilized. Each decision variable is represented by only one gene. This variation entails a series of special characteristics in the definition of mutation and crossover operations. Some benchmark networks have been used to test the suitability of a PGA for designing water distribution networks. More than 50,000 simulations were conducted with different sets of parameters. A statistical analysis of the obtained solutions was also performed. Through this analysis, more suitable values of mutation and crossover probabilities were discovered for each case. The results demonstrate the validity of the method. Optimum solutions are not guaranteed in any heuristic method. Hence, the concept of a “good solution” is introduced. A good solution is a design solution that does not substantially exceed the optimal solution that is obtained from the simulations. This concept may be useful when the computational cost is critical. The main conclusion derived from this study is that a proper combination of population and crossover and mutation probabilities leads to a high probability that good solutions will be obtained.