The Pipe network design problem is considered by choosing least-cost diameter pipes to satisfy flow demands and minimum head restrictions. Harmony and innovation are brought together as in music to devise a search pattern that can identify a large number of local optima in pipe network design. Improvization is brought in by varying the pitch rate parameter, and harmony is maintained by accumulating improving solutions. Because in pipe networks optimization by its very nature removes any redundancy, a minimum power loss criterion is introduced to enhance feasibility. The efficacy of the algorithm is demonstrated by solving a test nonlinear program and a pipe network problem from the literature to global optimum. Several near-optimal solutions are reported.

Inspired by the observation of the water cycle process and movements of rivers and streams toward the sea, a population-based metaheuristic algorithm, the water cycle algorithm (WCA) has recently been proposed. Lately, an increasing number of WCA applications have appeared and the WCA has been utilized in different optimization fields. This paper provides detailed open source code for the WCA, of which the performance and efficiency has been demonstrated for solving optimization problems. The WCA has an interesting and simple concept and this paper aims to use its source code to provide a step-by-step explanation of the process it follows