Use of multiobjective particle swarm optimization in water resources management

Water resources management presents a large variety of multiobjective problems that require powerful optimization tools in order to fully characterize the existing trade-offs. Different optimization methods, based on mathematical programming at first and on evolutionary computation more recently, have been applied with various degrees of success. This paper explores the use of a relatively recent heuristic technique called particle swarm optimization (PSO), which has been found to perform very well in a wide spectrum of optimization problems. Many extensions of the single-objective PSO to handle multiple objectives have been proposed in the evolutionary computation literature. This paper presents an implementation of multiobjective particle swarm optimization (MOPSO) that evaluates alternative solutions based on Pareto dominance, using an external repository to store nondominated solutions, a fitness sharing approach to promote diversity, and a mutation operator to improve global search. The MOPSO solver is used on three applications: (1) test function for comparison with results of other MOPSO and other evolutionary algorithms reported in the literature; (2) multipurpose reservoir operation problem with up to four objectives; and (3) problem of selective withdrawal from a thermally stratified reservoir with three objectives. In the test function application, standard performance metrics were used to measure closeness to the true Pareto front and evenness of coverage of the nondominated set. Results for the other two applications are compared to Pareto solutions obtained using the epsilon-constraint method with nonlinear optimization (epsilon-NLP). MOPSO performed very well when compared with other evolutionary algorithms for the test function and also provided encouraging results on the water management applications with the advantage of being much simpler than the epsilon-NLP approach.