Comparing the Real-Time Searching Behavior of Four Differential-Evolution Variants Applied to Water-Distribution-Network Design Optimization

Abstract

Differential evolution (DE) algorithms have been successfully used to handle a wide range of water resource optimization problems in recent years. The relative performance of various DE variants has been typically assessed based on the quality of the final solutions for the selected problems within the given computational budget. Such a comparative analysis, however, provides limited understanding on how various operational mechanisms alter the DE algorithms’ searching behavior and what searching properties lead to improved performance. To improve research in this area, this study aims to characterize and compare the searching behavior of four DE variants using a range of measure metrics, mainly focusing on real-time statistics of the algorithm’s search quality, search progress, and convergence manner. The utility of the metrics is demonstrated using the four DE variants (SDE, dDE, MdDE, and SADE) applied to three water distribution network (WDN) design problems with significantly increased complexity (scales). The behavioral results offer an appreciably improved understanding of the searching characteristics associated with each DE variant, thereby providing guidance for choosing the most suitable DE algorithm to solve a particular WDN optimization problem as well as offering knowledge to develop new advanced algorithms. For real-world problems, the SDE algorithm is more suitable if a limited computational budget is allowed, whereas the SADE and MdDE variants are respectively more appealing when moderate and large computational budgets are available. A new solution with a cost of $12.62 million for the large-scale problem (1,278 decision variables) is presented.