A Memetic Algorithm for Water Distribution Network Design R. Baos* , - - PowerPoint PPT Presentation

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A Memetic Algorithm for Water Distribution Network Design

• R. Baños* , C. Gil*, J. I. Agulleiro*, J. Reca†

* Dpt. Computer Architecture and Electronics, University of Almería (Spain)

† Dpt. Rural Engineering, University of Almería (Spain)

11th Online World Conference on Soft Computing in Industrial Applications – September-October , 2006

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Summary

Water distribution network design (WDND) Description of the problem Formulation A new memetic algorithm for WDND MENOME (MEta-Heuristic pipe Network Optimization ModEl)

Flow diagram Interface

Experimental analysis Test networks Parameter settings Results at Alperovits and Shamir’s network Results at Hanoi network Conclusions and future work

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Water distribution network design (WDND)

Goal: find the best way in term of investment cost of conveying water from the sources to the users, satisfying their requirements. Variables imposed in the model:

Network connectivity, Capacity of the tanks, Power of the pumps, Pressure required.

Decision variables:

Pipe diameters.

Description of the problem

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Water distribution network design (WDND)

WDND: minimize fitness function “F”

where: F is the cost function, m is the number of pipe diameters, ci is the cost of the pipe with diameter i per unit of length, Li is the total length of pipe with diameter i in the network, cp is a penalty coefficient, hrj is the required presure head in the node j, hj is the current presure head computed by EPANET for node j.

Formulation

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Linear programming techniques, Non-linear programming techniques, Heuristic methods: Genetic Algorithms, Simulated Annealing, Tabu Search, Ant Colony Optimiation, Scatter Search, …………

A new memetic algorithm for WDND

Techniques for solving WDND

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Get input parameters Obtain children from parents (Reproduction process)

YES YES NO NO

Stop condition?

Return best solution found in the search

Is there convergence?

YES YES

Initialize population of agents (P) Apply Local_Optimizer to P Evaluate convergence of solutions using the Entropy of P

NO NO

A new memetic algorithm for WDND

Flow diagram of the memetic algorithm for WDND

Update P using new children Apply Local_Optimizer to the new children Re-initialize population

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Flow diagram

MENOME (MEta-Heuristic pipe Network Optimization ModEl)

Pipeline Database Network Configuration Reader module of EPANET file formats Database management module (ActiveX Data Object) Network solver EPANET 2.00.07 Main program in Visual Basic (includes meta-heuristic optimizers)

DLL DLL

Graphical interface

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MENOME (MEta-Heuristic pipe Network Optimization ModEl)

MENOME interface

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Experimental Experimental analysis analysis

Test Networks: Alperovits and Shamir network

2 loops, 7 nodes, 8 pipes, 1 reservoir, 0 pumping stations, 14 commercial diameters available 148 = 1,4758·109 possible configurations,

1 2 3 4 5 6 7 8 [1] [2] [3] [4] [5] [6] [7]

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Experimental Experimental analysis analysis

Test Networks: Hanoi network

3 loops, 32 nodes, 34 pipes, 1 reservoir, 0 pumping stations, 6 commercial diameters available 634= 2,8651·1026 possible configurations,

1 32 2 6 21 19 [24] [31] [32] 18 10 12 34 33 26 27 28 15 14 13 29 31 [29] [28] [23] 30 23 [21] [22] 22 20 [20] 24 25 [25] [26] [27] [17] [18] [19] [3] [2] [1] 3 4 [4] [5] 5 [6] [7] 7 [8] 8 [9] [10] [14] [15] 16 17 [16] 9 [12] [13] [11] 11 [30]

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Experimental Experimental analysis analysis

Parameter settings

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Experimental Experimental analysis analysis

Results in Alperovits and Shamir’s network

All the methods reach the minimum cost. On average of 10 runs: MA outperforms to the other methods (all the configurations reach 419.000 monetary units). Difference among methods is, on average, lesser than 1.7%.

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Experimental Experimental analysis analysis

Results in Alperovits and Shamir’s network

All the methods reach 419.000 monetary units, although SA converge faster

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Experimental Experimental analysis analysis

Results in Hanoi network

MA obtains the best investment cost (6295909) while other methods are more expensive. On average of 10 runs: MA outperforms to the other methods Difference among methods is, on average, lesser than 1.95%.

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Experimental Experimental analysis analysis

Results in Hanoi network

MA obtains best results than other methods. Although the difference, in percentage, is small, in layout problems it becomes important.

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Conclusions

New memetic algorithm for Water Distribution Network Design (WDND). Comparative study of memetic algorithms with other heuristic approaches. The memetic algorithm here proposed works better than other heuristics. When the problem instance grows, the memetic algorithm performs better.

Future work

Multi-objective treatment of this problem considering reliability. Extend the formulation to consider other designing aspects (connectivity, etc.)

Conclusions and future work

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QUESTIONS? COMMENTS?

11th Online World Conference on Soft Computing in Industrial Applications – September-October , 2006