Extension of the Constrained Gravitational Search Algorithm for Solving Multi-Reservoir Operation Optimization Problem

In this paper the proposed constrained gravitational search algorithm (CGSA) is extended and used to solve multi-reservoir operation optimization problem. Tow constrained versions of GSA named partially constrained GSA (PCGSA) and fully constrained GSA (FCGSA) are outlined to solve this optimization problem. In the PCGSA, the problem constraints are partially satisfied, however, in the FCGSA, all the problem constraints are implicitly satisfied by providing the search space for each agent which contains only feasible solution and hence leading to smaller search space for each agent. These proposed constrained versions of GSA are very useful when they are applied to solve large scale multi-reservoir operation optimization problem. The constrained versions of GSA are formulated here for both possible variables of the problem means considering water release or storage volumes as the decision variables of the problem and therefore first and second formulations of these algorithms are proposed. The proposed algorithms are used to solve the well-known four and ten reservoir operation optimization problems and the results are presented and compared with those of original form of the GSA and any available results in the literature. The results indicate the superiority of the proposed algorithms and especially FCGSA over existing methods to optimally solve large scale multi-reservoir operation optimization problem.