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.
Similar content being viewed by others
References
Abbaspour KC, Schlin R, Van Genuchten MT (2001) Estimating unsaturated soil hydraulic parameters using ant colony optimization. Adv Water Resour 24(8):827–933
Afshar MH (2005) A new transition rule for ant colony optimisation algorithms: application to pipe network optimisation problems. Eng Optim 37(5):525–540
Afshar MH (2006a) Improving the efficiency of ant algorithms using adaptive refinement: application to storm water network design. Adv Water Resour 29:1371–1382
Afshar MH (2006b) Application of an Max–Min Ant System to joint layout and size optimization of pipe networks. Eng Optim 38(3):299–317
Afshar MH, Marino MA (2006) Application of an ant algorithm for layout optimization of tree networks. Eng Optim 38(3):353–369
Afshar MH, Mariño MA (2007) A parameter free self-adapting boundary genetic search for pipe network optimization. Comput Optim Appl 37(1):83–102
Bäck T, Hoffmeister F, Schwell HP (1991) A Survey of evolution strategies. Proceedings of the Fourth International Conference on Genetic Algorithms, Morgan Kaufmann, pp. 2–9
Becker L, Yeh W (1974) Optimization of real-time operation of a multiple reservoir system. Water Resour Res 10(6):1107–1112
Box MJ (1965) A new method of constrained optimisation and a comparison with other methods. Computer 8:42
Bozorg Haddad O, Afshar A, Marino MA (2006) Honey-bees mating optimization (HBMO) algorithm: a new heuristic approach for water resources optimization. Water Resour Manag 20:661–680
Chang FJ, Chen L (1998) Real-coded genetic algorithm for rule-based flood control reservoir management. Water Resour Manag 12(3):185–198
Colorni A, Dorigo M, Maniezzo V (1991) The ant system: ant autocatalytic optimization process. Technical Report TR 91-016, politiecnico di Milano
Costa D, Hertz A (1997) Ants can color graphs. J Operate Res Soc 48:295–305
Di Caro G, Dorigo M (1998) Two ant colony algorithms for best-effort quality of service routing. unpublished at ANTS’98-From Ant colonies to Artificial Ants: First International Workshop on Ant Colony Optimization
Dorigo M, Gambardella LM (1997) Ant colonies for the traveling salesman problem. Biosystems 43:73–81
Dorigo M, Maniezzo V, Colorni A (1996) The ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B Cybern 26:29–41
Dorigo M, Bonabeau E, Theraulaz G (2000) Ant algorithms and stigmergy. Future Gener Comput Syst 16:851–887
East V, Hall MJ (1994) Water resource system optimization using genetic algorithms. Hydro informatics’94, 1st Int. Conf. on Hydro informatics, Balkerma, Rotterdam, The Netherlands, pp. 225–231
Fahmy HS, King JP, Wentzle MW, Seton JA (1994) Economic optimization of river management using genetic algorithms. Int. summer Meeting, AM. Soc Agric Engrs, paper no.943034, St. Joseph, Mich
Jalali MR (2005) Optimal design and operation of hydro systems by ant colony algorithms: new heuristic approach. Ph.D. Thesis, Department of Civil Engineering, Iran University of Science and Technology
Jalali MR, Afshar A, Marino MA (2007) Multi-colony ant algorithm for continuous multi-reservoir operation optimization problems. Water Resour Manag 21:1429–1447
Kumar DN, Baliarsingh F (2003) Folded dynamic programming for optimal operation of multireservoir system. Water Resour Manag 17:337–353
Kumar DN, Reddy MJ (2006) Ant colony optimization for multi-purpose reservoir operation. Water Resour Manag 20:879–898
Kumar DN, Reddy MJ (2007) Multipurpose reservoir operation using particle swarm optimization. J Water Resour plan Manage 133(3):192–201
Marino MA, Loaiciga HA (1985) Dynamic model for multi reservoir operation. Water Resour Res 21(5):619–630
Maier HR, Simpson AR, Zecchin AC, Foong WK, Phang KY, Seah HY, Tan CL (2003) Ant colony optimization for design of water distribution systems. J Water Resour Plan Manage, ASCE 129(3):200–209
Michalewicz Z, Schouenauer M (1996) Evolutionary algorithms for constrained parameter optimization problems. Evol Comput 4:1–32
Oliveira R, Loucks D (1997) Operation rules for multi reservoir systems. Water Resour Res 33(4):839–852
Schoenauer M, Michalewicz Z (1996) Evolutionary computation at the edge of feasibility. Proceedings of the Fourth International Conference on Parallel Problem Solving from Nature. Springer, Berlin, pp. 22–27
Simpson AR, Maier HR, Foong WK, Phang KY, Seah HY, Tan CL (2001) Selection of parameters for ant colony optimization applied to the optimal design of water distribution systems. Proc., Int. Congress on Modeling and Simulation, Canberra, Australia, pp. 1931–1936
Stutzle T, Hoos H (2000) MAX-MIN ant system. Future Gener Comput Syst 16(8):889–914
Wardlaw R, Sharif M (1999) Evaluation of genetic algorithms for optimal reservoir system operation. J Water Resour Plan Manage 125:25–33
Wu ZY, Simpson AR (2002) A self-adaptive boundary search genetic algorithm and its application to water distribution systems. J Water Res 40(2):191–203
Wu ZY, Wang YT (1992) Arch dam optimisation design under strength fuzziness and fuzzy safety measure. Proc. of Int. Conf. on Arch Dam, Hehai University, Nanjing, China, pp. 129–131
Yakowitz S (1982) Dynamic programming application in water resources. Water Resour Res 18(4):673–696
Zecchin AC, Maier HR, Simpson AR, Roberts A, Berrisford MJ, Leonard M (2003) Max-Min ant system applied to water distribution system optimization. MODSIM 2003, International Congress on Modeling and Simulation, Modeling and Simulation Society of Australia and New Zealand Inc, Townsville, Australia, 14-17 July, Vol. 2, pp.795-800
Zecchin AC, Simpson AR, Maier HR (2005) Parametric study for an ant algorithms applied to water distribution system optimization. IEEA Trans Evol Comput 9(2):175–191
Zhu BF, Li ZM, Zhang BC (1984) Structural optimal design: theory and applications. Hydro-electrical Press, Beijing, China
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Afshar, M.H., Moeini, R. Partially and Fully Constrained Ant Algorithms for the Optimal Solution of Large Scale Reservoir Operation Problems. Water Resour Manage 22, 1835–1857 (2008). https://doi.org/10.1007/s11269-008-9256-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-008-9256-6