A self-adaptive boundary search genetic algorithm and its application to water distribution systems

The success of the application of genetic algorithms (GA) or evolutionary optimization methods to the design and rehabilitation of water distribution systems has been shown to be an innovative approach for the water industry. The optimal design and rehabilitation of water distribution systems is a constrained non-linear optimization problem. Constraints (for example, the minimum pressure requirements) are generally handled within genetic algorithm optimization by introducing a penalty cost function. The optimal or near optimal solution is found when the pressures at some nodes are close to the minimum required pressure or at the boundary of critical constraints. This paper presents a new approach called the self-adaptive boundary search strategy for selection of penalty factor within genetic algorithm optimization. The approach co-evolves and self-adapts the penalty factor such that the genetic algorithm search is guided towards and preserved around constraint boundaries. Thus it reduces the amount of simulation computations within the GA search and enhances the efficacy at reaching the optimal or near optimal solution. To demonstrate its effectiveness, the self-adaptive boundary search strategy is applied to a case study of the optimization of a water distribution system in this paper. It has been shown that the boundary GA search strategy is effective at adapting the feasibility of GA populations for a wide range of penalty factors. As a consequence, the boundary GA has been able to successfully find the least cost solution in the case study more effectively than a GA without the boundary search strategy. Thus a reliable least cost solution is guaranteed for the GA optimization of a water distribution system.