# BRKGA ADAPTED TO MULTIOBJECTIVE UNIT COMMITMENT - Solving Pareto Frontier for UC Multiobjective Problem using BRKGA SPEA2 NPGA and NSGA II Techniques

### Luís A. C. Roque, Dalila B. M. M. Fontes, Fernando A. C. C. Fontes

#### Abstract

The environmental concerns are having a significant impact on the operation of power systems. The traditional Unit Commitment problem, which to minimizes the fuel cost is inadequate when environmental emissions are also considered in the operation of power plants. This paper presents a Biased Random Key Genetic Algorithm (BRKGA) approach combined with non-dominated sorting procedure to find solutions for the unit commitment multiobjective optimization problem. In the first stage, the BRKGA solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0,1]. In the subsequent stage, a non-dominated sorting procedure similar to NSGA II is employed to approximate the set of Pareto solution through an evolutionary optimization process. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as, in the crossover strategy. Test results with the existent benchmark systems of 10 units and 24 hours scheduling horizon are presented. The comparison of the obtained results with those of other Unit Commitment (UC) multiobjective optimization methods reveal the effectiveness of the proposed method.

#### References

- Abido, M. A. (2003a). Environmental/economic power dispatch using multiobjective evolutionary algorithms. IEEE Trans. Power Syst., 7818:781529-1537.
- Abido, M. A. (2003b). A niched pareto genetic algorithm for multiobjective environmental/economic dispatch. Electr. Power Energy Syst., 7825:97-105.
- Abido, M. A. (2003c). A novel multiobjective evolutionary algorithm for environmental/economic power dispatch. Electr. Power Syst. Res., 7865:7871-81.
- Abido, M. A. (2006). Multiobjective evolutionary algorithms for electric power dispatch problem. IEEE Transactions on Evolutionary Computation, 7810:315- 329.
- Basu, M. (2008). Dynamic economic emission dispatch using non-dominated sorting genetic algorithm-ii. Electric Power Energy System, 30:140-149.
- Deb, K. and Agrawal, R. B. (1995). Simulated binary crossover for continuous search space. Complex Systems, 9:115-148.
- Deb, K., Pratab, A., Agarwal, S., and Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans. Evol. Comput., 6:182-197.
- Gonc¸alves, J. F. and Resende, M. G. C. (2010). Biased random-key genetic algorithms for combinatorial optimization. Journal of Heuristics, 17:487-525.
- Granelli, G. P., Montagna, M., Pasini, G. L., and Marannino, P. (1992). Emission constrained dynamic dispatch. 'Electr. Power Syst. Res., 7824:7856-62.
- Horn, J., Nafpliotis, N., and Goldberg, D. E. (1994). A niched pareto genetic algorithm for multiobjective optimization. In 1st IEEE Conf. Evol. Comput., IEEE World Congr. Comput. Intell., volume 1, pages 67-72.
- Hsiao, Y. T., Chiang, H. D., Liu, C. C., and Chen, Y. L. (1994). A computer package for optimal multiobjective var planning in large scale power systems. IEEE Trans. Power Syst., 789:78668-676.
- Roque, L., Fontes, D. B. M. M., and Fontes, F. A. C. C. (2011). A biased random key genetic algorithm approach for unit commitment problem. Lecture Notes in Computer Science, 6630:327-339.
- Sawaragi, Y., Nakayama, H., and Tanino, T. (1985). Theory of multiobjective optimization. Orlando: Academic Press.
- Srinivas, N. and Deb, K. (1994). Multiobjective function optimization using nondominated sorting genetic algorithms. Evol. Comput., 2:221-248.
- Wang, S., Shahidehpour, M., Kirschen, D. S., Mokhtari, S., and Irissari, G. (1995). Short-term generation scheduling with transmission and environmental constraints using an augmented lagrangian relaxation. IEEE Trans Power Systems, 7810:1294-300.
- (2003). Economical and environmental electric power dispatch optimisation. In 'EUROGEN-2003 ConferYamashita, D., Niimura, T., Yokoyama, R., and Marmiroli, M. (2010). Pareto-optimal solutions for trade-off analysis of c02 vs. cost based on dp unit commitment. In 2010 International Conference on Power System TechYamin, H. Y., El-Dwairi, Q., and Shaihidehpour, S. M.
- (2007). A new approach for genco profit based unit commitment in day-ahead competitive electricity markets considering reserve uncertainty. Int J Elec Power Energy Systems, 29:609-16.
- Zitzler, E., Laumanns, M., and Thiele, L. (2001). Spea2: Improving the strength pareto evolutionary algorithm.
- TIK-Rep. 103.
- Zitzler, E. and Thiele, L. (1998). An evolutionary algorithm for multiobjective optimization: The strength pareto approach. TIK-Rep., 43.
- Zitzler, E. and Thiele, L. (1999).
- Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Trans. Evol. Comput., 3:257-271.

#### Paper Citation

#### in Harvard Style

A. C. Roque L., B. M. M. Fontes D. and A. C. C. Fontes F. (2012). **BRKGA ADAPTED TO MULTIOBJECTIVE UNIT COMMITMENT - Solving Pareto Frontier for UC Multiobjective Problem using BRKGA SPEA2 NPGA and NSGA II Techniques** . In *Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-8425-97-3, pages 64-72. DOI: 10.5220/0003759500640072

#### in Bibtex Style

@conference{icores12,

author={Luís A. C. Roque and Dalila B. M. M. Fontes and Fernando A. C. C. Fontes},

title={BRKGA ADAPTED TO MULTIOBJECTIVE UNIT COMMITMENT - Solving Pareto Frontier for UC Multiobjective Problem using BRKGA SPEA2 NPGA and NSGA II Techniques},

booktitle={Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2012},

pages={64-72},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003759500640072},

isbn={978-989-8425-97-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - BRKGA ADAPTED TO MULTIOBJECTIVE UNIT COMMITMENT - Solving Pareto Frontier for UC Multiobjective Problem using BRKGA SPEA2 NPGA and NSGA II Techniques

SN - 978-989-8425-97-3

AU - A. C. Roque L.

AU - B. M. M. Fontes D.

AU - A. C. C. Fontes F.

PY - 2012

SP - 64

EP - 72

DO - 10.5220/0003759500640072