An improved Firefly algorithm with harmony search scheme for optimiziation of water distribution systems

In this study, a new hybrid method based on Fire y 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 re ies. The use of such a nature-inspired optimization method to solve the optimal design problem of WDS needs particular modications to produce high quality solutions. Therefore, a modication is proposed to the movement stage of articial re ies, and based on the HS strategy a memory is utilized to save a number of the best solutions. Another improvement in this algorithm includes the addition of pitch adjustment operation in the FA as a mutation operator. The presented method is applied to the optimal design of some well-known benchmark problems taken from literature, and the results conrm its validity. In addition, a sensitivity analysis is performed on the parameters of the algorithm.