Harmony Search

Optimal cost design of water distribution networks
using harmony search
ZONG WOO GEEM∗
Environmental Planning and Management Program, Johns Hopkins University
729 Fallsgrove Drive #6133, Rockville, MD 20850, USA
Tel: 301-294-3893, Fax: 301-610-4950

Abstract
This study presents a cost minimization model for the design of water distribution
networks. The model uses a recently developedharmony search optimization algorithm
while satisfying all the design constraints. The harmony search algorithm mimics a jazz
improvisation process in order to find better design solutions, in this case pipe diameters
in a water distribution network. The model also interfaces with a popular hydraulic
simulator, EPANET, to check the hydraulic constraints. If the design solution vector
violatesthe hydraulic constraints, the amount of violation is considered in the cost
function as a penalty. The model was applied to five water distribution networks, and
obtained designs that were either the same or cost 0.28 - 10.26% less than those of
competitive meta-heuristic algorithms, such as the genetic algorithm, simulated annealing,
and tabu search under the similar or less favorableconditions. The results show that the
harmony search-based model is suitable for water network design.
Keywords: Water distribution network; Harmony search; Meta-heuristic algorithm

∗

Corresponding author. Email: geem@jhu.edu

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1. Introduction

Today’s highly capitalized societies require ‘maximum benefit with minimum cost.’ In
order to achieve this goal, design engineers depend on costoptimization techniques. In
this study, water distribution networks are optimized. This involves determining the
commercial diameter for each pipe in the network while satisfying the water demand and
pressure at each node. The optimal cost design is the lowest cost design out of numerous
possibilities.
In order to find a low cost design in practice, experienced engineers have traditionallyused trial-and-error methods based on their intuitive ‘engineering sense’. However, their
approaches have not guaranteed ‘optimal’ or ‘near-optimal’ designs, which is why
researchers have been interested in optimization methods [1-2].
Alperovits and Shamir [3] proposed a mathematical approach (a linear programming
gradient method) that reduced the complexity of an original nonlinear problem bysolving
a series of linear sub-problems. They formulated an optimization model with a two-stage
(outer and inner) procedure, in which the outer procedure solved the flow status for a
given network while the inner procedure determined the optimum solution of the network
variables (pipe diameter) for the given flow distribution. This innovative approach was
adopted and further developed bymany researchers, such as Quindry et al. [4], Goulter et
al. [5], Kessler and Shamir [6], and Fujiwara and Kang [7]. Schaake and Lai [8] used
dynamic programming to search for a global optimum, while Su et al. [9] and Lansey and
Mays [10] integrated gradient-based techniques with the hydraulic simulator KYPIPE
[11], and Loganathan et al. [12] and Sherali et al. [13] introduced a lower bound.

2However, Savic and Walters [14] pointed out that the optimum solution obtained by the
aforementioned methods might contain one or two pipe segments of different discrete
sizes between each pair of nodes because the methods are based on a continuous diameter
approach. They asserted that the split-pipe design should be altered into only one
diameter, and that the altered solution shouldthen be checked to ensure that the minimum
head constraints are satisfied. In addition, Cunha and Sousa [15] indicated that the
conversion of the values obtained by the aforementioned methods into commercial pipe
diameters could worsen the quality of the solution and might not even guarantee a
feasible solution.
In order to overcome these drawbacks of mathematical methods, researchers such as...