Abstract
Algorithms to optimise water supply networks are developed and compared when a given set of transfer arcs is constrained to carry the same (or proportional) amounts of flow. Initially, a dynamic multi-period mathematical model is designed as a network flow model. A network simplex-based algorithm, Equalflow, and a subgradient-based algorithm, SUBeqf, are then presented. Both algorithms are characterised by polynomial complexity and can solve large-scale instances that arise when considering water system requirements. A specialised interface for water supply networks provides a data input processor to generate the overall multi-period network model in the implementation of the procedures. The implementation of the algorithms allows the consideration of different types of equal flow instances that take place in water resource system optimisation. The performances of the two algorithms and analysis of their computational efficiency with respect to state-of-the-art mathematical programming software are reported, considering equal-flow instances from a synthetically generated network and two water supply systems in the Sardinia region of Italy.
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References
Ahuja RK, Magnanti T, Orlin JB (1993) Network flows: theory, algorithms, and applications. Prentice Hall, NJ
Ahuja RK, Orlin JB, Sechi GM, Zuddas P (1999) Algorithms for the simple equal flow problem. Manag Sci 45(10):1440–1455
Ali AI, Kennington JL, Shetti B (1988) The equal flow problem. Eur J Oper Res 36:107–115
Brendan LB, Kuczera G (1997) Network linear programming as pipe network hydraulic analysis tool. J Hydraul Eng ASCE 123(6):549–559
Cao C, Sechi GM, Zuddas P (1988) A linear programming algorithm for water resources system planning (in Italian). In: Proceeding of the 21st conference hydraulic and hydraulic works. L’Aquila, pp 59–73
CPLEX Optimization, Inc. (1993) Using the CPLEX callable library and CPLEX mixed integer library. Incline Village, Nevada
DIMACS (1993) The first DIMACS international algorithm implementation challenge. ftp:dimacs.rutgers.edu, in the directory /pub/network
Grigoriadis MD (1986) An efficient implementation of the network simplex method. Math Program Stud 26:83–111
Kennington JL, Helgason RV (1980) Algorithms for network programming. Wiley-Interscience, New York
Klingman D, Napier A, Stutz J (1974) NETGEN: a program for generating large scale capacitated assignment, transportation, and minimum cost flow network problems. Manag Sci 20(5):814–821
Kuczera G (1989) Fast multireservoir multiperiod linear programming models. Water Resour Res 25(2):169–176
Kuczera G (1992) Network linear programming codes for water-supply networks modeling. ASCE J Water Resour Plan Manage 118:412
Kuczera G, Diment G (1988) General water supply system simulation model: WASP. J Water Resour Plan Manage ASCE 114(4):365–382
Ilich N (2008) Shortcomings of linear programming in optimizing river basin allocation. Water Resour Res 44:W02426
Ilich N (2009) Limitations of network flow algorithms in river basin modeling. ASCE J Water Resour Plan Manage 135-1:48–55
Labadie JW (2004) Optimal operation of multireservoir systems: a state-of-the-art review. J Water Resour Plan Manage 130-2:93–111
Loucks DP, Stedingher JR, Haith DA (1981) Water resources system planning and analysis. Prentice-Hall, Englewood Cliffs
Manca A, Sechi GM, Zuddas P (2002) The network simplex equal flow algorithm in dynamic water resources management. In: Proceedings of VI congresso SIMAI 2002. Chia Laguna, Italy
Niedda M, Sechi GM (1996) Mixed optimization technique for large-scale water resource systems. J Water Resour Plan Manage 122(6):387–393
Podda A, Sechi GM, Susnik P, Zuddas P (1994) Network algorithms for water resource systems optimization. In: Proceeding of the hydrosoft ’94, vol 1. Porto Carras, pp 81–88
RAS (2005) Sardinia region water authority. Piano Stralcio di Bacino della Regione Sardegna per l’Utilizzo delle Risorse Idriche. Cagliari, Italy
Sechi GM, Zuddas P (1995) A large scale water resources network optimization algorithm. In: Proceedings of the international conference on optimization ICOTA’95, vol 1. Chengdu, China, pp 378–385
Sechi GM, Zuddas P (2008) Multiperiod hypergraph models for water systems optimization. Water Resour Manage 22:307–320. doi:10.1007/s11269-007-9163-2
Sun YH, Yeh WG, Hsu NS, Louie PWF (1995) Generalized network algorithm for water-supply-system optimization. ASCE J Water Resour Plan Manage 121:392–398
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Manca, A., Sechi, G.M. & Zuddas, P. Water Supply Network Optimisation Using Equal Flow Algorithms. Water Resour Manage 24, 3665–3678 (2010). https://doi.org/10.1007/s11269-010-9625-9
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DOI: https://doi.org/10.1007/s11269-010-9625-9