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Chaos-directed genetic algorithms for water distribution network design: an enhanced search method

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Abstract

The design of a water distribution network (WDN) is an ever-challenging problem. The formulation and application of optimization techniques for WDN design have been an important area of research. Recently, the introduction of chaos theory-based evolutionary algorithms (EAs), in addition to traditional random-based ones, has elevated the scope for further improving the performance of EAs. The present study proposes a chaos-directed genetic algorithm (CDGA) by incorporating chaos ergodicity in GA mechanics for the optimal design of WDNs by introducing two novel frameworks, namely non-sequential approach and sequential approach. In improving the search efficacy of GA, the influence of chaotic systems with high-dimensionality maps is also explored when compared to the low-dimensionality maps. Considering four widely studied WDN benchmark problems ranging from 8 to 454 dimensions, the performance of the proposed GA and CDGA models is evaluated. The results show that the CDGA models outperform GA with better search efficacy, requiring fewer function evaluations to locate the optimal solution. In addition, the CDGA models are found to outperform other optimization techniques reported previously to handle these benchmark problems. Based on the results obtained, the study suggests the use of the chaotic system with other bio-inspired techniques to further improve their searchability and, thus, their computational efficiency.

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Data availability

The benchmark problems considered in the present study are taken from the Centre for Water Systems, Benchmark Problems, University of Exeter (https://emps.exeter.ac.uk/engineering/research/cws/resources/benchmarks/pareto/).

Code availability

All the models or codes that support the findings of this study are available from the corresponding author (written in the MATLAB software and are compiled with the simulation software EPANET using MATLAB-EPANET toolkit).

Abbreviations

\({C}_{j}\) :

Cost of jth pipe

CDS :

Commercially available diameter set

CP :

Crossover point

CS :

Chaotic sequence

D :

Genes or decision variable

\({d}_{j}\) :

Diameter of jth pipe

DL s :

Chaotic sequence data length allocated for a single generation using SA

\({F}_{f}\) :

Fitness function

G s :

Generation size

\({H}_{i}\) :

Head available at the ith node

\({H}_{min}\) :

Minimum head requirement at the ith node

L :

Lower bound of the decision variable

\({l}_{j}\) :

Length of jth pipe

M :

Number of genes that undergo mutation operation

MC :

Mutation chromosome

MV :

Mutation variable

N CD :

Number of commercially available pipe diameter options

\({N}_{D}\) :

Number of decision variables

\({N}_{n}\) :

Number of nodes

\(PC\) :

Parent chromosome

P c :

Crossover probability

P m :

Mutation probability

\(PM\) :

Penalty multiplier

\({P}_{r}\) :

Number of chromosomes retained during trunctation operator

P s :

Population size

\(r\) :

Uniformly distributed random number

SV :

Swapping variable

U :

Upper bound of the decision variable

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, Maharashtra, 400076, India

    S. N. Poojitha, V. Jothiprakash & Bellie Sivakumar

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  1. S. N. Poojitha
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  2. V. Jothiprakash
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  3. Bellie Sivakumar
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Correspondence to Bellie Sivakumar.

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Poojitha, S.N., Jothiprakash, V. & Sivakumar, B. Chaos-directed genetic algorithms for water distribution network design: an enhanced search method. Stoch Environ Res Risk Assess 36, 3377–3393 (2022). https://doi.org/10.1007/s00477-022-02200-7

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