Fuzzy Programming Approach for Multiobjective Optimization of Water Distribution Systems

Abstract

This paper proposes a fuzzy multiobjective programming model for meeting competing objectives in the optimal design of water distribution systems (WDSs). Fuzzy membership functions for minimizing the pipe network cost and maximizing a number of reliability surrogates are defined, and the model maximizes the degree of satisfaction of these membership functions. Reliability surrogates investigated include: (1) the sum over all nodes of the relative surplus of energy at each node; (2) the minimum surplus head at a critical node; (3) the sum over all nodes of the relative surplus of energy at each node modified by the degree of uniformity of its associated loop; and (4) the minimum uniformity of the associated loops over all nodes. The model is applied to various combinations of objective functions, to identify the design pipe diameters of the water-main network of Farhadgerd, Iran. Optimal solutions of the various model variations, based on inclusion of one or more reliability surrogate(s), show that for this WDS the third surrogate (3) may be a reasonable substitute for the first surrogate (1), and that while the inclusion of the last surrogate (4) may be beneficial, the inclusion of the second surrogate (2) may not. Based on postoptimization cut-set analyses, the model that minimizes cost and maximizes surrogates (3) and (4) exhibits the highest level of mechanical reliability, while the model that minimizes cost and maximizes the second surrogate (2) exhibits the lowest level of mechanical reliability.