Extension of the constrained particle swarm optimization algorithm to optimal operation of multi-reservoirs system

Three constrained versions of Particle Swarm Optimization (PSO) algorithm are presented in this paper for the efficient optimal operation of multi-reservoir systems using storage/release volumes as decision variables of the problem. Proposed algorithms are based on identifying and excluding the infeasible region of the search space before and during the search which has already proposed and used by the author for the operation of single reservoirs [5]. In the first version named Partially Constrained Particle Swarm Optimization I (PCPSO1), the sequential nature of the solution building procedure of PSO is used to explicitly enforce the release/storage constraints of the problem during solution construction. For this, the continuity equation is used at each period of the operation of each reservoir to define a new set of bounds for decision variable of the next period which satisfy release/storage constraints of the problem. Particles of the swarm are, therefore, forced to fly in the feasible region of the search space except for some rare cases. In the second version named Partially Constrained Particle Swarm Optimization Two (PCPSO2), the periods of the operations for upstream reservoirs, reservoirs with known inflow, are treated in a reverse order prior to the PCPSO1 search to define new set of bounds for storage volumes such that PCPSO1 algorithm is not given any chance of producing infeasible operations regarding upstream reservoirs. In the third version, the PCPSO2 search is augmented with a mechanism similar to that used in PCPSO2 for all downstream reservoirs by which all the infeasible operation of the downstream dams are also excluded from the search process and, hence, the name of Fully Constrained Particle Swarm Optimization (FCPSO) algorithm. Proposed methods are used to solve two benchmark problems of hydro-power operations of multi-reservoir system namely Four and Ten reservoir systems and the results are presented and compared with those of the conventional unconstrained PSO and other methods in the literature. The methods are shown to be very effective in locating optimal or near optimal solutions and efficient in terms of the convergence characteristics of the resulting algorithms. Proposed algorithms are also shown to be relatively insensitive to the swarm size and initial swarm compared to the original algorithm. (C) 2013 Elsevier Ltd. All rights reserved.