Application of an Ant Colony Optimization Algorithm for Optimal Operation of Reservoirs: A Comparative Study of Three Proposed Formulations

Abstract. This paper presents an application of the Max-Min Ant System for optimal operation of
reservoirs using three dierent formulations. Ant colony optimization algorithms are a meta-heuristic
approach initially inspired by the observation that ants can nd the shortest path between food sources and
their nest. The basic algorithm of Ant Colony Optimization is the Ant System. Many other algorithms,
such as the Max-Min Ant System, have been introduced to improve the performance of the Ant System.
The rst step for solving problems using ant algorithms is to dene the graph of the problem under
consideration. The problem graph is related to the decision variables of problems. In this paper, the
problem of optimal operation of reservoirs is formulated using two dierent sets of decision variable, i.e.
storage volumes and releases. It is also shown that the problem can be formulated in two dierent graph
forms when the reservoir storages are taken as the decision variables, while only one graph representation
is available when the releases are taken as the decision variables. The advantages and disadvantages of
these formulation are discussed when an ant algorithm, such as the Max-Min Ant System, is attempted
to solve the underlying problem. The proposed formulations are then used to solve the problem of water
supply and the hydropower operation of the Dez" reservoir. The results are then compared with each
other and those of other methods such as the Ant Colony System, Genetic Algorithms, Honey Bee Mating
Optimization and the results obtained by Lingo software. The results indicate the ability of the proposed
formulation and, in particular, the third formulation to optimally solve reservoir operation problems.