## 1. Introduction

[2] Over the last four decades, significant research has been undertaken to develop techniques to optimize the design of water distribution systems (WDSs). Various optimization techniques including traditional optimization methods and evolutionary algorithms (EAs) have been applied to WDS optimization, and these are summarized in Table 1 (it should be noted that only the first significant paper for each optimization technique applied to WDS optimization is provided in Table 1). Traditional optimization techniques such as linear programming (LP) and nonlinear programming (NLP) often converge at local optimal solutions due to the nonsmoothness properties of the WDS optimization problem [*Eiger et al.,* 1994]. EAs given in Table 1 have been demonstrated to be able to find better quality solutions than traditional optimization methods based on testing on a number of WDS case studies. One major drawback with using EAs, however, is that they require a large number of network evaluations to find optimal solutions, resulting in an expensive computational overhead, especially for relatively large case studies. Thus, it is difficult for these EAs to find good quality optimal solutions for the real-world sized WDSs, as these systems are generally complex, with large numbers of decision variables.

Algorithma | First Reference |
---|---|

^{a}Only the first significant paper for each optimization technique applied to WDS optimization is provided.
| |

Linear programming (LP) | Alperovits and Shamir [1977] |

Nonlinear programming (NLP) | Fujiwara and Khang [1990] |

Standard genetic algorithm (SGA) | Simpson et al. [1994] |

Modified genetic algorithm (MGA) | Dandy et al. [1996] |

Simulated annealing (SA) | Loganathan et al. [1995] |

Tabu search (TS) | Lippai et al. [1999] |

Harmony search (HS) | Geem et al. [2002] |

Shuffled frog leaping algorithm (SFLA) | Eusuff and Lansey [2003] |

Ant colony optimization (ACO) | Maier et al. [2003) |

ANN metamodels | Broad et al. [2005) |

Particle swarm optimization (PSO) | Suribabu and Neelakantan [2006] |

Scatter search (SS) | Lin et al. [2007] |

Cross-entropy algorithm (CE) | Perelman and Ostfeld [2007] |

Hybrid discrete dynamically dimensioned search (HD-DDS) algorithm | Tolson et al. [2009] |

Differential evolution (DE) | Suribabu [2010] |

Honey-Bee Mating Optimization (HB) | Mohan and Babu [2010] |

Genetic Heritage Evolution by Stochastic Transmission (GHEST) | Bolognesi et al. [2010] |

[3] Much research has been done in an attempt to improve the efficiency of EAs applied to large WDS optimization problems [*Bolognesi et al.,* 2010]. Decomposing the original WDS using graph theory to facilitate the optimization process is one of these research lines.