Partially and Fully Constrained Ant Algorithms for the Optimal Solution of Large Scale Reservoir Operation Problems

Abstract

This paper presents a constrained formulation of the ant colony optimization algorithm (ACOA) for the optimization of large scale reservoir operation problems. ACO algorithms enjoy a unique feature namely incremental solution building capability. In ACO algorithms, each ant is required to make a decision at some points of the search space called decision points. If the constraints of the problem are of explicit type, then ants may be forced to satisfy the constraints when making decisions. This could be done via the provision of a tabu list for each ant at each decision point of the problem. This is very useful when attempting large scale optimization problem as it would lead to a considerable reduction of the search space size. Two different formulations namely partially constrained and fully constrained version of the proposed method are outlined here using Max-Min Ant System for the solution of reservoir operation problems. Two cases of simple and hydropower reservoir operation problems are considered with the storage volumes taken as the decision variables of the problems. In the partially constrained version of the algorithm, knowing the value of the storage volume at an arbitrary decision point, the continuity equation is used to provide a tabu list for the feasible options at the next decision point. The tabu list is designed such that commonly used box constraints for the release and storage volumes are simultaneously satisfied. In the second and fully constrained algorithm, the box constraints of storage volumes at each period are modified prior to the main calculation such that ants will not have any chance of making infeasible decision in the search process. The proposed methods are used to optimally solve the problem of simple and hydropower operation of “Dez” reservoir in Iran and the results are presented and compared with the conventional unconstrained ACO algorithm. The results indicate the ability of the proposed methods to optimally solve large scale reservoir operation problems where the conventional heuristic methods fail to even find a feasible solution.