Hybrid metaheuristics for multi-objective design of water distribution systems

Multi-objective design of Water Distribution Systems (WDSs) has received considerable attention in the past. Multi-objective evolutionary algorithms (MOEAs) are popular in tackling this problem due to their ability to approach the true Pareto-optimal front (PF) in a single run. Recently, several hybrid metaheuristics based on MOEAs have been proposed and validated on test problems. Among these algorithms, AMALGAM and MOHO are two noteworthy representatives which mix their constituent algorithms in contrasting fashion. In this paper, they are employed to solve a wide range of benchmark design problems against another state-of-the-art algorithm, namely NSGA-II. The design task is formulated as a bi-objective optimisation problem taking cost and network resilience into account. The performance of three algorithms is assessed via normalised hypervolume indicator. The results demonstrate that AMALGAM is superior to MOHO and NSGA-II in terms of convergence and diversity on the networks of small-to-medium size; however, for larger networks, the performance of hybrid algorithms deteriorates as they lose their adaptive capabilities. Future improvement and/or redesign on hybrid algorithms should not only adopt the strategies of adaptive portfolios of sub-algorithms and global information sharing, but also prevent the deterioration mainly caused by imbalance of constituent algorithms.