Multi-objective optimisation of the pump scheduling problem using SPEA2

Significant operational cost and energy savings can be achieved by optimising the schedules of pumps, which pump water from source reservoirs to storage tanks, in water distribution networks. Despite the fact that pump scheduling problem involves several conflictive objectives, few studies have considered multi-objective optimisation in terms of Pareto optimality. Our approach links a well-known multi-objective optimiser, SPEA2, with a hydraulic simulator, EPANET, in order to provide a Pareto set of explicit schedules. Since only fixed speed pumps and fixed time intervals are considered, we use a natural binary representation and simple and straightforward initialisation and recombination operators. Unlike earlier studies, feasibility constraints are handled by a methodology based on the dominance relation rather than using penalty functions or reparation mechanisms. We test the proposed approach using a network instance and an assessment of the results is carried out by means of empirical attainment surfaces. The results show that the proposed approach is able to obtain better schedules than the state-of-the-art single-objective algorithm for this network instance and within the same number of function evaluations