A multi-objective chaotic ant swarm optimization for environmental/economic dispatch Jiejin Cai a , Xiaoqian Ma b , Qiong Li c, * , Lixiang Li d , Haipeng Peng d a School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan b Electric Power College, South China University of Technology, Guangzhou 510640, China c Research Center of Building Energy Efficiency, State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510640, China d Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China article info Article history: Received 19 September 2008 Received in revised form 14 June 2009 Accepted 28 January 2010 Keywords: Chaotic ant swarm optimization Environmental/economic dispatch Multi-objective optimization Ant colony algorithm Swarm intelligence abstract Since the environmental issues caused by the pollutant emissions from fossil-fueled power plants are concerned, it is necessary to develop the conventional economic dispatch (ED) into environmental/eco- nomic dispatch (EED) which considers both economic and environmental issues. This paper developed a multi-objective chaotic ant swarm optimization (MOCASO) method for solving the multi-objective EED problems of thermal generators in power systems. The proposed MOCASO method was applied to three test power systems. Simulation results demonstrated that the MOCASO method can obtain feasible and effective solutions and it is a promising alternative approach for solving the EED problems in prac- tical power systems. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Economic dispatch (ED) problem [1–3] is one of the mathematical optimization issues in power system operation and it attracts researchers’ attention all the way. With an increasing concern over the environmental pollution caused by thermal power plants, envi- ronmental/economic dispatch (EED) problem [4,5] has drawn much more attention for a good dispatch scheme from it would not only re- sult in great economical benefit, but also reduce the pollutants emis- sion. Different techniques have been reported in the literature pertaining to EED problem, including conventional approaches such as weighted minimax method [6], direct analytical solution method [7], linear programming [7–9] and 1-constraint method [10], and artificial intelligence technology such as genetic algorithm [11– 13], particle swarm optimization [14–17], fuzzy set theory [18] and evolutionary programming [19]. In principle, these approaches usually employed to deal with EED problems can be classified into two categories, namely, Lagrange multiplier methods and a multi- objective stochastic search technique. Many researchers have per- formed studies in this field. For instance, Brodesky and Hahn deal with the EED problem as a single objective problem by treating the emission as a constraint [20]. This method, however, meets a diffi- culty in getting the trade-off relations between cost and emission. Alternatively, minimizing the emission is handled as another objec- tive in addition to the cost. Farag et al. considered both these objec- tives through a linear programming based optimization procedures [8]. However, this approach need many mathematical simplification assumptions, and does not give any information regarding the trade- offs involved. In other research direction, Zahavi et al. converted the multi-objective EED problem to a single objective problem by linear combination of different objectives as a weighted sum [9], in which a set of non-inferior (or Pareto-optimal) solutions are obtained by varying the weights. Unfortunately, this method requires multiple runs as many times as the number of desired Pareto-optimal solu- tions and cannot be used in problems having a non-convex Pareto- optimal front. To avoid this difficulty, Yokoyama et al. presented the 1-constraint method to optimize the most preferred objective and consider the other objectives as constraints bounded by some allowable levels 1 [10]. However, the most obvious weaknesses of this approach are that it is time-consuming and tends to find weakly non-dominated solutions. The recent direction is to handle both objectives simultaneously as competing objectives. Srinivasan and Tettamanzi proposed an evolutionary algorithm based approach to evaluate the economic impacts of environmental dispatching and fuel switching [19]. However, some non-dominated solutions may be lost during the search process while some dominated solutions may be misclassified as non-dominated ones due to the selection process adopted. Huang et al. presented a fuzzy satisfaction-maxi- mizing decision approach to solve the bi-objective EED problem 0142-0615/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2010.01.006 * Corresponding author. Tel.: +86 20 8711 0164. E-mail address: joanli97@hotmail.com (Q. Li). Electrical Power and Energy Systems 32 (2010) 337–344 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes