Multiobjective Differential Evolution with Application to Reservoir System Optimization

Abstract

Many water resources systems are characterized by multiple objectives. For multiobjective optimization, typically there can be no single optimal solution which can simultaneously satisfy all the goals, but rather a set of technologically efficient noninferior or Pareto optimal solutions exists. Generating those Pareto optimal solutions is a challenging task and often difficulties arise in using the conventional methods. In the optimization of reservoir systems, most of the times there is interdependence among one or more decision variables. Recently, it is emphasized that the evolutionary operators used in differential evolution algorithms are very much suitable for problems having interdependence among the decision variables. This paper utilizes this aspect and presents an efficient and effective approach for multiobjective optimization, namely multiobjective differential evolution (MODE) algorithm with an application to a case study in reservoir system optimization. The developed MODE algorithm is first tested on a few benchmark test problems and validated with standard performance measures by comparing them with the nondominated sorting genetic algorithm-II. On achieving satisfactory performance for test problems, it is applied to generate Pareto optimal solutions to a multiobjective reservoir operation problem. It is found that MODE provides many alternative Pareto optimal solutions with uniform coverage and convergence to true Pareto optimal fronts. The results obtained show that the proposed MODE can be a viable alternative for generating optimal trade-offs in multiobjective optimization of water resources systems.