An improved firefly algorithm with harmony search scheme for optimization of water distribution systems

In this study, a new hybrid method based on Firefly Algorithm (FA) and Harmony Search (HS) techniques, is presented for solving the least-cost design problem of water distribution systems (WDS). This algorithm is designed to improve the performance of the FA as a recently developed meta-heuristic that mimics the natural behaviour of fireflies. The use of such a nature–inspired optimization method to solve the optimal design problem of WDS needs particular modifications to produce high quality solutions. Therefore, a modification is proposed to the movement stage of artificial fireflies and based on the HS strategy a memory is utilized to save a number of the best solutions. Another improvement in this algorithm contains the addition of pitch adjustment operation in the FA as a mutation operator.The presented method is applied to optimal design of some well-known benchmark problems taken from literature, and the results confirm its validity. In addition, a sensitivity analysis is performed on the parameters of the algorithm.