Reliability-Based Hybrid Metaheuristic Optimization Model for the Design of Two Loop Network Under Mechanical Uncertain Scenarios

Water distribution network (WDN) is an essential infrastructure for conveying potable water to communities. Constituting different components, it has a complex structure involving significant financial investments for its design. During its life span, the failure of WDN partially or entirely is an inevitable consequence of the network's hydraulic or mechanical uncertainties. Therefore, the WDN design problem naturally involves a tradeoff between the reliability and cost aspects. The present study formulates a reliability-based hybrid metaheuristic optimization model for its robust design. Primarily, the proposed framework is composed of three components, an optimization algorithm, a simulation model, and a reliability assessment model. 
A novel hybrid technique in a combination of differential evolution (DE) and krill herd algorithm (KHA), DE-KHA, is used as the optimization algorithm. The DE-KHA is the computationally efficient algorithm for effortlessly tackling the WDN design problems by balancing the exploration and exploitation features. EPANET 2.0 hydraulic simulator that performs the hydraulic analysis of WDN is used as a simulation model. The hydraulic characteristics of the network, such as flow-through pipes, unit headloss, the actual and total pressure head at the demand nodes, and the demands delivered to the demand nodes, are assessed using EPANET 2.0. The reliability model evaluates the network's performance under mechanical uncertainties. The mechanical failures are the scenarios of networks component failure, which in the present study are considered network pipe outages. The reliability model is based on the minimum cut set method, where the pipe failure combinations that cause the failure of the network are found explicitly considering the minimum pressure head requirement at the demand nodes.
Search for the optimal solution is progressed by the optimization technique, where the constraints of continuity and energy balance equations are explicitly taken care of by the EPANET 2.0 simulation model. Then considering the hydraulic head at the demand node, the minimum cut sets are finalized, and the network’s performance under mechanical failure scenarios is assessed using the reliability model. The DE-KHA and reliability model code is written in MATLAB and linked to EPANEt 2.0 using MATLAB-EPANET toolkit.
The application of the developed framework is validated considering Two loop Network (TLN). It is a hypothetical network studied by many researchers for validating their optimization models. TLN is made up of eight pipes, connected by seven nodes with a single reservoir of 210 m total head that feeds the entire network. Thus, it is a gravity-fed network with no pumps operated. Considering this simple case study, yet a challenging problem with 14⁸ possible solutions in the search space, the reliability-based model is validated. The results present the computational efficiency of the model in yielding the optimal design cost of $ 419,000 with minimal computational effort. Furthermore, the algorithm proposed is efficient in exploring various alternate optimal solutions with considerable reliability, thus, presenting robust design options for TLN. Considering the efficiency of the proposed model, the study suggests it for the robust design of real-life WDNs.

Keywords: Water distribution network design; Reliability; Mechanical uncertainty; Metaheuristic algorithms