Multiobjective Optimization of Water Distribution Networks Using Fuzzy Theory and Harmony Search

Zong Geem

doi:10.3390/w7073613

Abstract

Thus far, various phenomenon-mimicking algorithms, such as genetic algorithm, simulated annealing, tabu search, shuffled frog-leaping, ant colony optimization, harmony search, cross entropy, scatter search, and honey-bee mating, have been proposed to optimally design the water distribution networks with respect to design cost. However, flow velocity constraint, which is critical for structural robustness against water hammer or flow circulation against substance sedimentation, was seldom considered in the optimization formulation because of computational complexity. Thus, this study proposes a novel fuzzy-based velocity reliability index, which is to be maximized while the design cost is simultaneously minimized. The velocity reliability index is included in the existing cost optimization formulation and this extended multiobjective formulation is applied to two bench-mark problems. Results show that the model successfully found a Pareto set of multiobjective design solutions in terms of cost minimization and reliability maximization.

Highlights

Up to date, diverse phenomenon-mimicking algorithms (PMAs) have been proposed for the design optimization of water distribution networks (WDNs)
Diverse phenomenon-mimicking algorithms (PMAs) have been proposed for the design optimization of water distribution networks (WDNs). These algorithms include genetic algorithm [1], simulated annealing [2], tabu search [3], shuffled frog-leaping algorithm [4], ant colony optimization algorithm [5], harmony search [6], cross entropy [7], scatter search [8], hybrid algorithm [9], Water 2015, 7 honey-bee mating optimization [10], differential evolution [11], adaptive cluster covering with local search [12], and Non-Dominated Sorting Genetic Algorithm-II [13]
Various PMAs have been proposed, these were mostly applied to basic bench-mark

Summary

Introduction

Diverse phenomenon-mimicking algorithms (PMAs) have been proposed for the design optimization of water distribution networks (WDNs). These algorithms include genetic algorithm [1], simulated annealing [2], tabu search [3], shuffled frog-leaping algorithm [4], ant colony optimization algorithm [5], harmony search [6], cross entropy [7], scatter search [8], hybrid algorithm [9], Water 2015, 7 honey-bee mating optimization [10], differential evolution [11], adaptive cluster covering with local search [12], and Non-Dominated Sorting Genetic Algorithm-II [13]. Where f (⋅) is cost function which has two arguments of pipe diameter Di and pipe length Li ; and P is total number of pipe i This cost function is to be minimized while satisfying the following constraints: Q − Q in out = Qe (2). This continuity constraint must be satisfied for every node in a network. h f

Methods

Results

Conclusion