Optimization difficulty indicator and testing framework for water distribution network complexity

In the last three decades, benchmark water distribution networks (WDNs) have provided a common testbed for new optimization algorithms and design approaches. However, deriving generalized and reliable conclusions from such benchmark WDNs is difficult because their optimization difficulty levels (ODLs) are either too low or too high (i.e., biased). Final solutions do not consistently converge to a global optimum for a WDN problem with a high ODL. In addition, little effort has been given to quantifying and comparing the ODLs of WDNs with different characteristics and conditions. In this study, an ODL indicator was developed for WDNs: the coefficient of variation of the final solution fitness values. An ODL quantification framework was also developed with two phases: (1) generating network layouts with various topological characteristics, and (2) quantifying the statistics of the final solution quality and ODL by using a global parallel genetic algorithm. The proposed indicator and framework were applied to the design of a dense-grid B-city network and large C network, and the results demonstrated their applicability to generating a WDN benchmark problem with the target ODL.