Abstract
The structural and computational aspects of two decomposition algorithms suitable for dynamic optimization of nonlinear interconnected networks are examined. Both methods arise from a decomposition based on Lagrangian duality theory of the addressed dynamic optimization problem, which is the minimization of energy costs over a given time period, subject to the requirement that the network equations and inequality restrictions are satisfied. The first algorithm uses a spatial decomposition of the state space into subgroups of state variables associated with particular network zones. This leads to a number of lower-dimensional optimization problems which can be solved individually at one level and coordinated at a higher level to account for interactions between these zones. The second algorithm uses time decomposition to solve a sequence of static optimization problems, one for each time increment into which the interval is subdivided, which are then coordinated to take account of dynamic interaction between the time increments. Computational results from an actual network in the United Kingdom are presented for both methods.
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References
Lasdon, L. S.,Optimization Theory for Large Systems, Macmillan, London, England, 1970.
Wismer, D. A., Editor,Optimization Methods for Large-Scale Systems with Applications, McGraw-Hill, New York, New York, 1971.
Fallside, F., andPerry, F.,Hierarchical Optimization of a Water Supply Network, Proceedings of the Institution of Electrical Engineers, Vol. 122, pp. 202–208, 1975.
Sterling, M. J. H., andCoulbeck, B.,A Dynamic Programming Solution to Optimization of Pumping Costs, Proceedings of the Institution of Civil Engineers, Part 2, Vol. 59, pp. 813–818, 1975.
Sterling, M. J. H., andCoulbeck, B.,Optimization of Water Pumping Costs by Hierarchical Methods, Proceedings of the Institution of Civil Engineers, Part 2, Vol. 59, pp. 789–797, 1975.
De Moyer, R., Gilman, H. D., andGoodman, M. Y.,Dynamic Computer Simulation and Control Methods for Water Distribution Systems, General Electric, Research Report No. 73SD205, 1973.
Marlow, K. C., andFallside, F.,Minicomputer, Microprocessor, and Telecontrol Applications to a Water Supply Network, Journal of the Institution of Water Engineers and Scientists, Vol. 35, pp. 517–545, 1980.
Javdan, M. R.,Extension of Dual Coordination to a Class of Nonlinear Systems, International Journal of Control, Vol. 24, pp. 551–571, 1976.
Larson, R. E.,State Increment Dynamic Programming, Elsevier, New York, New York, 1968.
Tamura, H.,Decentralized Optimization for Distributed Lag Models of Discrete Systems, Automatica, Vol. 11, pp. 593–602, 1976.
Pearson, J. D.,Dynamic Decomposition Techniques in Optimization Methods for Large-Scale Systems, Edited by D. A. Wismer, McGraw-Hill, New York, New York, 1971.
Fallside, F., andPerry, P. F.,Hierarchical Model for Water Supply System Control, Proceedings of the Institution of Electrical Engineers, Vol. 122, pp. 441–443, 1975.
Perry, P. F.,Demand Forecasting in Water Supply Networks, American Society of Civil Engineers, Journal of the Hydraulics Division, Vol. 107, pp. 1077–1087, 1981.
Mezarovic, M. D., Macko, D., andTakahara, Y.,Theory of Hierarchical Multilevel Systems, Academic Press, New York, New York, 1970.
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Communicated by D. P. Bertsekas
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Perry, P.F. Spatial and time decomposition algorithms for dynamic nonlinear network optimization using duality. J Optim Theory Appl 42, 77–101 (1984). https://doi.org/10.1007/BF00934134
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DOI: https://doi.org/10.1007/BF00934134