Environmental/economic power dispatch problem using multi-objective differential evolution algorithm

This paper presents a multi-objective differential evolution (MODE) algorithm for environmental/economic power dispatch (EED) problem. The EED problem is formulated as a nonlinear constrained multi-objective problem with competing and non-commensurable objectives of fuel cost, emission and system loss. The proposed MODE approach adopts an external elitist archive to retain non-dominated solutions found during the evolutionary process. In order to preserve the diversity of Pareto optimality, a crowding entropy diversity measure tactic is proposed. The crowding entropy strategy is able to measure the crowding degree of the solutions more accurately. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed approach have been carried out on the IEEE 30- and 118-bus test system. The results demonstrate the capability of the proposed MODE approach to generate well-distributed Pareto optimal non-dominated solutions of multi-objective EED problem. The comparison with reported results of other MOEAs reveals the superiority of the proposed MODE approach and confirms its potential for solving other power systems multi-objective optimization problems.

[1]  N. S. Babu,et al.  Analytical solution for combined economic and emissions dispatch , 2008 .

[2]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[3]  René Thomsen,et al.  A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[4]  L. Coelho,et al.  Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect , 2006, IEEE Transactions on Power Systems.

[5]  J. T. Wood,et al.  Potential impacts of clean air regulations on system operations , 1995 .

[6]  B. Babu,et al.  Differential evolution for multi-objective optimization , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[7]  Arthur C. Sanderson,et al.  Multi-objective differential evolution and its application to enterprise planning , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[8]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[9]  Zhigang Zeng,et al.  The Sixth International Symposium on Neural Networks, ISNN 2009, Wuhan, China, May 26-29, 2009, Proceedings, Part IV , 2009, ISNN.

[10]  M. Muslu.  Economic dispatch with environmental considerations: tradeoff curves and emission reduction rates , 2004 .

[11]  Hong-Tzer Yang,et al.  Bi-objective power dispatch using fuzzy satisfaction-maximizing decision approach , 1997 .

[12]  Lingfeng Wang,et al.  Reserve-constrained multiarea environmental/economic dispatch based on particle swarm optimization with local search , 2009, Eng. Appl. Artif. Intell..

[13]  Halis Altun,et al.  A new genetic algorithm with arithmetic crossover to economic and environmental economic dispatch , 2005 .

[14]  S. A. Al-Baiyat,et al.  Economic load dispatch multiobjective optimization procedures using linear programming techniques , 1995 .

[15]  D. B. Das,et al.  New multi-objective stochastic search technique for economic load dispatch , 1998 .

[16]  Ferial El-Hawary,et al.  A summary of environmental/economic dispatch algorithms , 1994 .

[17]  Ferial El-Hawary,et al.  Optimal environmental dispatching of electric power systems via an improved Hopfield neural network model , 1995 .

[18]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[19]  Dimitris K. Tasoulis,et al.  Vector evaluated differential evolution for multiobjective optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[20]  J.R. Cedeno-Maldonado,et al.  Differential evolution based economic environmental power dispatch , 2005, Proceedings of the 37th Annual North American Power Symposium, 2005..

[21]  Dipti Srinivasan,et al.  An evolutionary algorithm for evaluation of emission compliance options in view of the Clean Air Act Amendments , 1997 .

[22]  Cao Yijia,et al.  Multiple objective particle swarm optimization technique for economic load dispatch , 2005 .

[23]  Z. Dong,et al.  A Modified Differential Evolution Algorithm With Fitness Sharing for Power System Planning , 2008, IEEE Transactions on Power Systems.

[24]  T. Yalcinoz,et al.  A multiobjective optimization method to environmental economic dispatch , 2007 .

[25]  N. Sinha,et al.  Optimal Combined Non-convex Economic and Emission Load Dispatch Using NSDE , 2007, International Conference on Computational Intelligence and Multimedia Applications (ICCIMA 2007).

[26]  J. Yuryevich,et al.  Evolutionary-programming-based algorithm for environmentally-constrained economic dispatch , 1998 .

[27]  A. A. El-Keib,et al.  Economic dispatch in view of the Clean Air Act of 1990 , 1994 .

[28]  N. Madavan.  Multiobjective optimization using a Pareto differential evolution approach , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[29]  D. P. Kothari,et al.  Combined Economic and Emission Dispatch Using Improved Backpropagation Neural Network , 2000 .

[30]  H. Abbass,et al.  PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[31]  Yanbin Yuan,et al.  A hybrid differential evolution method for dynamic economic dispatch with valve-point effects , 2009, Expert Syst. Appl..

[32]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[33]  Li Xuebin.  RETRACTED: Study of multi-objective optimization and multi-attribute decision-making for economic and environmental power dispatch , 2009 .

[34]  Yaonan Wang,et al.  Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure , 2010, Soft Comput..

[35]  M. A. Abido.  Environmental/economic power dispatch using multiobjective evolutionary algorithms , 2003 .

[36]  Mohammad Ali Abido,et al.  Multiobjective evolutionary algorithms for electric power dispatch problem , 2006, IEEE Transactions on Evolutionary Computation.

[37]  Carlos A. Coello Coello,et al.  Evolutionary multi-objective optimization: a historical view of the field , 2006, IEEE Comput. Intell. Mag..

[38]  Narayana Prasad Padhy,et al.  Comparison and application of evolutionary programming techniques to combined economic emission dispatch with line flow constraints , 2003 .

[39]  M. A. Abido,et al.  Multiobjective particle swarm optimization for environmental/economic dispatch problem , 2009 .

[40]  H. Iba,et al.  Differential evolution for economic load dispatch problems , 2008 .

[41]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

[42]  P. Balasubramanie,et al.  Wavelet Feature Based Neural Classifier System for Object Classification with Complex Background , 2007, International Conference on Computational Intelligence and Multimedia Applications (ICCIMA 2007).

[43]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[44]  Lingfeng Wang,et al.  Environmental/economic power dispatch using a fuzzified multi-objective particle swarm optimization algorithm , 2007 .

[45]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[46]  Chih-Wen Liu,et al.  Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm , 2007 .

[47]  J. S. Dhillon,et al.  Economic-emission load dispatch using binary successive approximation-based evolutionary search , 2009 .

[48]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[49]  M. A. Abido,et al.  A niched Pareto genetic algorithm for multiobjective environmental/economic dispatch , 2003 .