Comparison of the Performance of a Surrogate Based Gaussian Process, NSGA2 and PSO Multi-objective Optimization of the Operation and Fuzzy Structural Reliability of Water Distribution System: Case Study for the City of Asmara, Eritrea

Optimal scheduling of pumps in water distribution systems (WDSs) entails reducing operational cost while supplying the required water quality and quantity. The combined use of pumps, however, can increase breakage rate of aging pipes due to high internal pressure. Multi-objective optimization (MO) is crucial in the determination of a trade-off between the two objective functions, minimization of the operational cost and maximization of the velocity reliability index. The velocity reliability index is used as a surrogate metric to quantify the structural performance of the pipes. The optimization process requires repetitive hydraulic simulations resulting in high computational cost. This paper proposes a Gaussian-Process (GP) based sequential approaches that efficiently estimate the optimal Pareto front with reduced computational effort. The technique simultaneously optimizes the two objective functions over a box-constrained domain where each GP model is fitted independently through an infill criterion that balances the space exploration (search of new observations) and exploitation (local improvement around existing observations). The reduced computational cost allows running full hydraulic simulations during the optimization process permitting real time decision making for pumps schedule in large complex WDSs. Utility of the proposed technique was applied for Asmara's WDSs, composed of 9 pumping stations and 12 storage tanks, and showed good performance of the GP based optimization compared to traditional evolutionary optimization techniques (such as NSGA2 and Particle Swarm Optimization). The GP-MO only requires 20 iterations to identify the optimal Pareto front while, even with more than 1000 generations, the NSGA2 is not getting to find a good agreement between the two objective functions.