A Hybrid Fuzzy-Probabilistic Bargaining Approach for Multi-objective Optimization of Contamination Warning Sensors in Water Distribution Systems

Water Distribution System (WDS) are strategic infrastructures in all countries. In recent decades, several optimization-based frameworks have been developed to detect potential contaminant events through risk mitigation strategies using the optimal placement of water quality sensors. However, outcomes of the optimization models may not sufficiently represent the priorities of involved stakeholders in real-world case studies where conflicts of interest arise. Therefore, conflict resolution frameworks that consider stakeholder engagement are needed to enhance the security of a WDS through an agreed-upon layout of an optimal number of sensors. In this study, according to the uncertain nature of input contamination into the network, a Fuzzy Transformation Method (FTM) and a Monte-Carlo Simulation (MCS) were employed to address uncertainties in the EPANET simulation model. A fuzzy-based NSGA-II optimization model was developed to determine trade-offs among targets of stakeholders. Social Choice Theories (SCTs) was used to specify the compromise solutions on each trade-off curve. Using the possibility degree method, the obtained fuzzy intervals were ranked based on each stakeholder's point of view. Finally, the most appropriate SCTs were introduced through a negotiation method (unanimity fallback bargaining) at each confidence level. The application of the proposed methodology was evaluated in the WDS of the city of Lamerd in Fars, Iran. The capability of the proposed methodology in selecting socio-optimal sensor placement was compared with the results of previous studies. The obtained results demonstrated that the proposed framework yielded a reliable outcome and enhance the decision-making condition for stakeholders to improve the security of a WDS.