Very often, real-world applications have several conflicting objectives. Recently, there has been a growing interest in evolutionary multiobjective optimization (EMO) algorithms, which combine two major disciplines: evolutionary computation and the theoretical frameworks of multicriteria decision making. In this paper, the authors propose six different variants of the conventional EMO [1], to solve an optimal pump scheduling problem with four objectives to be minimized.
For any urban infrastructure development, a water distribution system plays a key role, and, as water demand grows in size, the distribution system becomes larger and more complex. The optimization of the scheduling of water pumps is found to be a practical and highly effective method for reducing operational costs, without much change to the actual infrastructure of the whole system. Typically, a pumping station consists of pumps of different capacities, which are used to pump water to one or more reservoirs. A simplified hydraulic model (involving five pumps) was chosen in this research work. The target is to generate optimal hourly schedules during a 24-hour period, so as to minimize electric energy cost, maintenance cost, maximum power peak, and level variation in a reservoir. Results obtained using the six EMO approaches were finally combined using a heuristic algorithm to satisfy the problem constraints. Six performance metrics were used to compare the performance of the EMO methods.
Among the six methods considered, the study revealed that the strength Pareto evolutionary algorithm (SPEA) gave the best performance metrics. An important advantage of the developed schedules is that the pump operators could choose a feasible schedule from a set of optimal solutions. The superiority of the elitism-based EMO techniques, namely SPEA, nondominated sorting genetic algorithm 2 (NSGA2), and controlled elitist nondominated sorting genetic algorithm (CNSGA), is well established. Hence, the performance advantage of these algorithms over the niched Pareto genetic algorithm (NPGA), NSGA, and multiple objective genetic algorithm (MOGA) is not a great surprise. Since the true Pareto front is not known, the authors should have used the well-known c and s metrics [1] for a direct comparison of the six methods. This paper has succeeded in exposing the capabilities of EMO algorithms for real-world problem solving.