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Genetic algorithms for the sequential irrigation scheduling problem

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Abstract

A sequential irrigation scheduling problem is the problem of preparing a schedule to sequentially service a set of water users. This problem has an analogy with the classical single machine earliness/tardiness scheduling problem in operations research. In previously published work, integer program and heuristics were used to solve sequential irrigation scheduling problems; however, such scheduling problems belong to a class of combinatorial optimization problems known to be computationally demanding (NP-hard). This is widely reported in operations research. Hence, integer program can only be used to solve relatively small problems usually in a research environment where considerable computational resources and time can be allocated to solve a single schedule. For practical applications, metaheuristics such as genetic algorithms (GA), simulated annealing, or tabu search methods need to be used. These need to be formulated carefully and tested thoroughly. The current research is to explore the potential of GA to solve the sequential irrigation scheduling problems. Four GA models are presented that model four different sequential irrigation scenarios. The GA models are tested extensively for a range of problem sizes, and the solution quality is compared against solutions from integer programs and heuristics. The GA is applied to the practical engineering problem of scheduling water scheduling to 94 water users.

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Abbreviations

\( \overline{{D_{i - 1} }} \) :

Duration of the job preceding the job at the ith position in the jobs sequence

\( \overline{{D_{j} }} \) :

Duration of job j

E j :

Earliness of job j

F :

Fitness function

G :

Irrigation interval

i :

Index of the job in the jobs sequence i = 1,2,3…J

j :

Index of the job in the jobs sequence i = 1,2,3…J

J :

Total number of outlets

P I :

Penalty for irrigation interval violation

P O :

Penalty for overlap of jobs

R I :

Weighting for interval penalty

R O :

Weighting for overlap penalty

\( \overline{{S_{1} }} \) :

The scheduled start time of the earliest job in the sequence

\( \overline{{S_{i} }} \) :

Scheduled start time of the job at the ith position in the jobs sequence

S i−1 :

Scheduled start time of the job preceding the job at the ith position in the jobs sequence

S int :

Start time of the irrigation interval

S j :

An element of the scheduled start time row vector

t :

Time block index = 1, 2…T

T :

Total number of time blocks

T j :

Tardiness of job j

Z IP :

Value of objective function of the IP

Z GA :

Value of objective function of the GA

Z H :

Value of objective function of the heuristic

α j :

Cost of earliness per unit of time for job j

β j :

Cost of tardiness per unit of time for job j

εIP :

Relative error of the GA to the IP

εH :

Relative error of the heuristic to the IP

δ j :

Binary variable

λ j :

Binary variable

 ψ tj :

Binary variable

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Acknowledgments

The authors would like to acknowledge financial support provided by the Embassy of the Kingdom of Netherlands, Islamabad, Pakistan, through Grant #22294 and also financial support provided through the United Nations University, Institute of Sustainability and Peace Grant# 600UU 848, which supported the revision of this manuscript and the practical application.

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Authors and Affiliations

  1. International Water Management Institute, 12 k Multan Road Chowk, Thokar Niaz Baig, Lahore, 5370, Pakistan

    Arif A. Anwar

  2. NWFP University of Engineering and Technology, Peshawar, Pakistan

    Zia Ul Haq

Authors
  1. Arif A. Anwar
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  2. Zia Ul Haq
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Correspondence to Arif A. Anwar.

Additional information

Communicated by J. Kijne.

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Anwar, A.A., Haq, Z.U. Genetic algorithms for the sequential irrigation scheduling problem. Irrig Sci 31, 815–829 (2013). https://doi.org/10.1007/s00271-012-0364-y

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  • DOI: https://doi.org/10.1007/s00271-012-0364-y

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