Two-Objective Design/Resilience:

Towards the Best-Known Approximation to the True Pareto Front

This webpage presents the best-known Pareto fronts of twelve benchmark design problems of Water Distribution Systems. These problems were collected from the literature and the Pareto fronts were generated using five state-of-the-art multi-objective evolutionary algorithms (MOEAs).

These benchmark problems are categorised into four groups (small, medium, intermediate and large) according to the size of search space. Each problem is formulated to minimise the total cost and to maximise the network resilience. Five MOEAs including two hybrid algorithms (AMALGAM and Borg) were employed to identify the currently best-known Pareto front of each problem given extensive computational budget. The EPANET input file, the associated source code and the data of best-known Pareto front for each benchmark problem are provided in this page.

The aim of this public data is to allow other researchers in the community to have multiple reference points to test new techniques and optimisation algorithms.

Benchmarks

Type Problem Name #LC #WS #DV #PD Search Space Ref
SP Two-Reservoir Network TRN 3 2 8 8* 3.28x107 [1]
Two-Loop Network TLN 1 1 8 14 1.48x109 [2]
BakRyan Network BAK 1 1 9 11 2.36x109 [3]
MP New York Tunnel Network NYT 1 1 21 16 1.93x1025 [4]
Blacksburg Network BLA 1 1 23 14 2.30x1026 [5]
Hanoi Network HAN 1 1 34 6 2.87x1026 [6]
GoYang Network GOY 1 1 30 8 1.24x1027 [7]
IP Fossolo Network FOS 1 1 58 22 7.25x1077 [8]
Pescara Network PES 1 3 99 13 1.91x10110 [8]
LP Modena Network MOD 1 4 317 13 1.32x10353 [8]
Balerma Irrigation Network BIN 1 4 454 10 1.00x10455 [9]
Exeter Network EXN 1 7 567 11 2.95x10590 [10]
Note: SP-Small Problems; MP-Medium Problems; IP-Intermediate Problems; LP-Larger Problems; LC-number of loading conditions; WS-number of water sources; DV-number of decision variables; PD-number of pipe diameter options. *For TRN problem, three existing pipes have 8 diameter options for duplication and 2 extra options, i.e. cleaning and leaving alone.

References

  • [1] Gessler, J., 1985. Pipe network optimization by enumeration, In Proc., Computer Applications for Water Resources. ASCE: New York, N.Y., pp. 572-581.
  • [2] Alperovits, E., Shamir, U., 1977. Design of optimal water distribution systems. Water Resour. Res. 13(6), 885-900.
  • [3] Lee, S.C., Lee, S.I., 2001. Genetic algorithms for optimal augmentation of water distribution networks. J. Korean Water Resour. Assoc. 34(5), 567-575.
  • [4] Schaake, J., Lai, D., 1969. Linear programming and dynamic programming application to water distribution network design, Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts.
  • [5] Sherali, H., Subramanian, S., and Loganathan, G. V. 2001. Effective relaxations and partitioning schemes for solving water distribution network design problems to global optimality. J. Global Optim., 19(1), 1–26.
  • [6] Fujiwara, O., Khang, D., 1990. A two-phase decomposition method for optimal design of looped water distribution networks. Water Resour. Res. 26(4), 539-549.
  • [7] Kim, J.H., Kim, T.G., Kim, J.H., Yoon, Y.N., 1994. A study on the pipe network system design using non-linear programming. J. Korean Water Resour. Assoc. 27(4), 59-67.
  • [8] Bragalli, C., D'Ambrosio, C., Lee, J., Lodi, A., Toth, P., 2012. On the Optimal Design of Water Distribution Networks: a Practical MINLP Approach. Optim. Eng. 13, 219-246.
  • [9] Reca, J., Martínez, J., 2006. Genetic algorithms for the design of looped irrigation water distribution networks. Water Resour. Res. 42(5), W05416.
  • [10] Farmani, R., Savic, D.A., Walters, G.A., 2004. "EXNET" Benchmark Problem for Multi-Objective Optimization of Large Water Systems, Modelling and Control for Participatory Planning and Managing Water Systems, IFAC workshop: Venice, Italy.
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