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Optimization of Water Resources Utilization by PSO-GA

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Abstract

The objective of this paper is to present an optimal model to address the water resources utilization of the Tao River basin in China. The Tao River water diversion project has been proposed to alleviate the problem of water shortages in Gansu Province in China. A multi reservoir system is under consideration with multiple objectives including water diversion, ecological water demand, irrigation, hydropower generation, industrial requirements, and domestic uses in the Tao River basin. A multi-objective model for the minimization of water shortages and the maximization of hydro-power production is proposed to manage the utilization of Tao River water resources. An adjustable PSO-GA (particle swarm optimization – genetic algorithm) hybrid algorithm is proposed that combines the strengths of PSO and GA to balance natural selection and good knowledge sharing to enable a robust and efficient search of the solution space. Two driving parameters are used in the adjustable hybrid model to optimize the performance of the PSO-GA hybrid algorithm by assigning a preference to either PSO or GA. The results show that the proposed hybrid algorithm can simultaneously obtain a promising solution and speed up the convergence.

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Abbreviations

c 1 c 2 :

Learning rates in the PSO algorithm

FS :

Frequency of water supply success

gbest :

Global best solution achieved by the swarm

gbest(GA):

Global best solution achieved by the swarm after GA operation

H (i,t):

Effective average turbine head in period t (m)

k 1 :

Influence term for PSO that determines how many individuals in the population can move on to the next generation

k 2 :

Influence term (k 1+k 2=1) for GA that determines how many individuals are replaced in the current generation

k i :

Net efficiency of hydropower station i

k t j :

Position vector of particle j in the tth reproduction step of the PSO algorithm

N(i,t):

Output of reservoir i during period t (kW)

pbest j :

The best solution reached by particle j

pbest j (GA):

The best solution reached by particle j after GA operation

QC (i,t):

Water released through the turbines of hydropower station i in period t (m3/s)

QG(i t):

Water supply of reservoir i in period t (m3/s)

QI(i t):

Inflow of reservoir i during the average period t (m3/s)

QO(i,t):

Release of reservoir i during the average period t (m3/s)

QP(i t):

Water demand of reservoir i in period t (m3/s)

rand 1 rand 2 :

Independent uniformly distributed random variables

θ(t):

Coefficient at time t

V(i,t):

Storage of reservoir i at the beginning of period t (m)

V(i,t+1):

Storage of reservoir i at the end of period t (m3)

v t j :

Speed vector of particle j in the t th reproduction step of the PSO algorithm

w 1,w 2 :

Weighting coefficients set to 0.8 and 0.2, respectively

W :

Inertial weight in the PSO algorithm

WL(i t):

Water loss of reservoir i in period t (m3)

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No: 51190093, 51179149, 51179148); the National Program on Key Basic Research Project (973 Program) in China (2011CB403306-3); and the Program for New Century Excellent Talents in University (NCET-10-0933).

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Authors and Affiliations

  1. Institute of Water Resources and Hydroelectric Power, Xi’an University of Technology, Xi’an, Shaanxi, China

    Jian-xia Chang, Tao Bai, Qiang Huang & Da-wen Yang

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  1. Jian-xia Chang
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  2. Tao Bai
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  3. Qiang Huang
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  4. Da-wen Yang
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Correspondence to Jian-xia Chang.

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Chang, Jx., Bai, T., Huang, Q. et al. Optimization of Water Resources Utilization by PSO-GA. Water Resour Manage 27, 3525–3540 (2013). https://doi.org/10.1007/s11269-013-0362-8

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