Development of warm initial solution approaches to improve the quality of Pareto optimal solutions in water distribution network design

Water distribution network (WDN) optimization design have been applied various metaheuristic optimization algorithms (i.e., genetic algorithm, particle swarm optimization, harmony search algorithm, and etc.) and have been efforts to improve the final solution quality. In contrast, in multi-objective problem framework, these kinds of efforts are lacking compared to other fields such as mathematics and other civil infrastructure designs. Therefore, in this study, we developed five approaches to improving the quality of the final solution to a WDN design problem: three warm initial solution approaches, collectively referred to as single-multi-optimization approaches (SMO-1, SMO-2, and SMO-3); a post-optimization approach, referred to as multi-single-optimization (MSO); and (3) a guided search approach based on engineering knowledge, referred to as guided search optimization (GSO). The approaches were embedded within the multi-objective harmony search (MOHS) framework and used to find Pareto optimal designs for well-known benchmark networks considering two objectives such as network construction cost and system resilience. The final results were compared using two kinds of performance indices represented the solution diversity and convergence. The application results show that the proposed warm initial solution approaches make better final Pareto solutions and improve performance of optimization compared to other metaheuristic optimization algorithms in terms of computational efficiency.