Bargaining Models for Optimal Design of Water Distribution Networks

Optimal design of water distribution networks (WDN) involves an evaluation of both consumers’ pressure benefits and investors’ economic objectives. The aforementioned objectives often conflict, so finding the optimal solution for one of those objectives reduces the other objective’s utility. In such situations, there are many nondominated solutions, each solution denoting an alternative that cannot be preferred over another in terms of both objectives. Thus, an appropriate alternative to fulfill both objectives and satisfy decision makers’ criteria and meet the design purposes within a desirable range necessitates the use of bargaining models that are called conflict-resolution models. This paper considers two urban WDN optimization design problems having different objectives, including initial costs and hydraulic performance improvement of the network by satisfying given hydraulic constraints. First, a set of alternatives are drawn out by a fast messy genetic algorithm (FMGA), then the appropriate alternative design is achieved by using Nash’s and Young’s bargaining models. Thus, the methodology presented in this paper can be employed by designers of WDNs to simultaneously consider the utilities of both consumers and investors that are the main beneficiaries of such infrastructures. Results show that in almost all the alternatives obtained by the proposed methodology, at least 80% of the most probable utility of both beneficiaries is obtained at the same time, which indirectly indicates the low vulnerability of the design alternative by the considered methodology in meeting the goals of each beneficiary. Moreover, results also indicate that when using the same utility functions, decision points obtained from the two models coincide.