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

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.

Statistical Dependence of Pipe Breaks on Explanatory Variables

“…Canal de Isabel II is the company commissioned for the integral water cycle in Madrid's region. The urban water network managed by the company covers more than 8000 km 2 and supplies water to more than 177 municipalities. It is composed of a set of trunk mains and a set of distribution lines.…”

“…If there is additional information (i.e., we know that for the pipe segment the explanatory variable takes a value in the interval [x, x + ∆x]), we can estimate the probability of occurrence of the explanatory event as defined in Equation (2).…”

“…For developed countries, aging infrastructure is a current concern but it is likely to become an important issue worldwide in the future [1]. Water distribution networks are large scale systems which demand continuous improvements for their design optimization or to achieve appropriate levels of efficiency [2]. Likewise, increasing asset investment is required for rehabilitation or repairing to maintain the level of service.…”

Optimization of Intelligent Controllers Using a Type-1 and Interval Type-2 Fuzzy Harmony Search Algorithm

“…This article focuses on the optimization of parameters to achieve the tracking of a trajectory applied to benchmark control problems. The proposed method is based on the original harmony search algorithm, which mimics the process of music improvisation, which has been widely used to solve different problems, as shown in [5][6][7][8][9]. The proposed method is called fuzzy harmony search algorithm (FHS) that performs an adaptation of parameters with Type-1 and interval Type-2 fuzzy logic and it is used to optimize fuzzy tracking controllers so that they follow desired trajectories for benchmark control problems.…”

Fuzzy Dynamic Parameter Adaptation in the Harmony Search Algorithm for the Optimization of the Ball and Beam Controller

“…The granular term is used herein to indicate the number of membership functions to be used in the fuzzy system. The proposed method called fuzzy harmony search algorithm (FHS) uses Type 1, interval Type 2, and generalized Type 2 fuzzy systems for dynamic parameter adaptation while other works have made different methods based on this algorithm such as [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The main contribution of this work is to perform dynamic parameter adaptation using Type 1, interval Type 2, and generalized Type 2 fuzzy system in the harmony search algorithm applied to optimization of the membership functions of a fuzzy controller for a benchmark problem.…”