pp 1–34 | Cite as

An intelligent computing technique based on a dynamic-size subpopulations for unit commitment problem

  • M. A. El-ShorbagyEmail author
  • A. A. Mousa
  • M. A. Farag
Application Article


A new intelligent computing based approach for solving multi-objective unit commitment problem (MOUCP) and its fuzzy model is presented in this paper. The proposed intelligent approach combines binary-real-coded genetic algorithm (BRCGA) and K-means clustering technique to find the optimal schedule of the generation units in MOUCP. BRCGA is used in order to tackle both the unit scheduling and load dispatch problems. While, K-means clustering technique is used to divide the population into a specific number of subpopulation with-dynamic-sizes. In this way, different genetic algorithm (GA) operators can apply to each sub-population, instead of using the same GA operators for all population. The proposed intelligent algorithm has been tested on standard systems of MOUCPs. The results showed the efficiency of the proposed approach to solve (MOUCP) and its fuzzy model.


Unit commitment problem Intelligent computing Genetic algorithm Dynamic subpopulation structure 

List of symbols


Real power generated from unit i during hour t (MW)


Unit’s status at hour t (\(u_{it} = 1\) when unit i is committed, \(u_{it} = 1\) when unit i is un-committed


Load demand at hour t (MW)


Total number of generating units

\(p_{i}^{{\rm max} }\)

Maximum generation limit of unit i (MW)

\(p_{i}^{{\rm min} }\)

Minimum generation limit of unit i (MW)

\(a_{i} ,b_{i} ,c_{i}\)

The fuel cost coefficients of unit i

\(C_{it} (p_{it} )\)

Fuel cost of unit i at hour t ($)


Startup cost of unit i at hour t ($)


Spinning reserve at hour t (MW)


Cold startup cost of unit i ($)


Hot startup cost of unit i ($)


Cold start hours of unit i (h)


Shut down cost of unit i at hour t ($)


The start-up atmospheric pollutant emissions of unit i at time period t

\(E_{it} (p_{it} )\)

The quantity of pollutants produced by unit i at time t

\(\alpha_{i} ,\beta_{i} ,\delta_{i}\)

The emission coefficients of unit i


The total scheduling period


Minimum down time of ith unit (h)


Minimum up time of ith unit (h)


The duration for which unit i has stayed continuously off up to hour t


The duration for which unit i has stayed continuously on up to hour t


Size of population


The initial status of the unit i



The authors are grateful to the anonymous reviewers for their valuable comments and helpful suggestions which greatly improved the paper’s quality.


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Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Department of Mathematics, College of Science and Humanities in Al-KharjPrince Sattam bin Abdulaziz UniversityAl-Kharj 11942Saudi Arabia
  2. 2.Department of Basic Engineering Science, Faculty of EngineeringMenoufia UniversityShebin El-KomEgypt
  3. 3.Department of Mathematics and Statistics, Faculty of SciencesTaif UniversityTaifSaudi Arabia

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