In this study a hybrid approach based on Particle Swarm Optimization (PSO) and Competitive Neural Network (CNN) is proposed to solve cell formation problems with alternative routings. Particles in PSO are decoded as representation of routings which will be followed by each part. By using the route information of the particles a cell formation problem without alternative routings corresponding to each particle is obtained. This reduced problem is solved by a Competitive Neural Network approach and its grouping efficacy result is assigned to particle as a fitness value.  Furthermore, in order to demonstrate efficiency of the PSO-CNN hybrid approach, proposed method is compared with purely PSO and Simulated Annealing – CNN hybrid as other two methods developed for solving same problem. Performance of the PSO-CNN approach is shown on the test problems with comparisons.