Discussion # 6 (03 Aug 2009) : Common Paper

Article Reference
Zoong Woo Geem, Harmony search optimization to the pump included water distributed network design, Environmental Planning and management program, Sept 2009

Introduction
The paper focuses the optimization of the water distribution system along with the pumps which have not been included in the literature of hydrosystems optimization. Optimal solution obtained by the mathematical model is in terms of continuous pipe diameters and in the means of converting those to available commercial diameters might alter the quality of the solution. However meta heuristic optimization techniques like GA, tabu search etc have been used in optimizing distribution network , these algorithms resulted more discrete pipe diameters than the continuous diameters. This paper focuses applying harmony search in optimizing the cost of the water distribution system including the pumps.

Objective function: design cost function
Decision variable: pipe diameters or pump size
HS model most used parameters range: HM range 30-100, HMCR – 0.95-0.99, PAR – 0.05-0.2

Steps followed in HS method are:
1. Initialization of the HM by selecting the vectors randomly
2. Improvisation of the HM by random selection (randomly selecting the decision variable from HM), memory consideration (using the HMCR the next step HM would be choosen), Pitch adjustment (adjusting the pitch i.e selecting the neighboring value based on the given probability) and violated harmony consideration (the new HM is checked by hydraulic analysis to check the nodal pressure, if the nodal pressures are greater than the limit then penalty is added to the design cost)
3. New HM is replaced by the previous HM if the new HM is a better solution than the old HM
4. Stopping criteria is specified by maximum iterations, so the steps 2 and 3 are continued till it reached the maximum iterations

Problem formulation
• Objective function: Pipe capital cost + pump capital cost + pumping energy cost
• Penalty function: squared penalty value + constant penalty value, if the pressure at the nodes do not meet the minimum criteria
• This penalty function is added to the cost objective function

Model
• 10 commercial diameters considered
• L = 2500 m
• 9 commercial pump sizes considered
• Water demand specified at each node
• Minimum pressure at each node should be 30 m above GL
• No. of pipes = 11
• No. of nodes = 9

Conclusions and Discussion
This research explains using meta heuristic technique in distribution optimization along with four different search behaviors. The same problem was solved using Simulated annealing and the cost was identical to that of HS. However HS produced much lower average cost and within less number of function evaluations.