Large scale reservoir operation by Constrained Particle Swarm Optimization algorithms

In this paper two adapted versions of Particle Swarm Optimization (PSO) algorithm are presented for the efficient solution of large scale reservoir operation problems with release volumes taken as the decision variables of the problem. In the first version, exploiting the sequential nature of the solution building procedure of the PSO, the continuity equation is used at each period to define a new set of bounds for the decision variable of the next period which satisfies storage volume constraints of the problem. Particles of the swarm are, therefore, forced to fly in the feasible region of the search space except for very rare cases and hence the name of the Partially Constrained Particle Swarm Optimization (PCPSO) algorithm. In the second, the periods of the operations are treated in a reverse order prior to the PCPSO search to define a new set of bounds for each storage volume such that partially constrained particles are not given any chance of producing infeasible solutions and, hence, the name of Fully Constrained Particle Swarm Optimization (FCPSO) algorithm. These methods are used here to solve two problems of water supply and hydropower operation of “Dez” reservoir in Iran and the results are presented and compared with those of the conventional unconstrained PSO and a genetic algorithm. Three cases of short, medium and long-term operations are considered to illustrate the efficiency and effectiveness of the proposed methods for the solution of large scale operation problems. The methods are shown to be superior to the original PSO and genetic algorithm in locating near optimal solutions and convergence characteristics. Proposed algorithms are also shown to be relatively insensitive to the swarm size and initial swarm compared to the original unconstrained PSO and genetic algorithm.