In the present study an extension of particle swarm optimization (PSO) algorithm which is in conformity with actual nature is introduced for solving combinatorial optimization problems. Development of this algorithm is essentially based on balanced fuzzy sets theory. The classical fuzzy sets theory cannot distinguish differences between positive and negative information of membership functions, while in the new method both kinds of information "positive and negative" about membership function are equally important. The balanced fuzzy particle swarm optimization algorithm is used for fundamental optimization problem entitled traveling salesman problem (TSP). For convergence inspecting of new algorithm, method was used for TSP problems. Convergence curves were represented fast convergence in restricted and low iterations for balanced fuzzy particle swarm optimization algorithm (BF-PSO) comparison with fuzzy particle swarm optimization algorithm (F-PSO). © 2011 Elsevier Inc.
Robati, A., Barani, G. A., Nezam Abadi Pour, H., Fadaee, M. J., & Rahimi Pour Anaraki, J. (2012). Balanced fuzzy particle swarm optimization. Applied Mathematical Modelling, 36(5), 2169–2177. https://doi.org/10.1016/j.apm.2011.08.006