The placement of production equipments plays a major role in designing a layout in cellular manufacturing. The better placement increases the productivity. This article introduces a new algorithm to design and optimize a fixed area cellular layout problem by using an artificial bee colony (ABC) technique which is based on the intelligent foraging behavior of a honeybee. The objective of this article is to determine the physical arrangement of work centers by minimizing the total traveling distance of the product. Volume of the product and distance between the work centers are the important factors that affect layout design. Some relative importance factors like priority of products, hazardous moves, and back-tracking moves are considered in this article. Layout moment ratio helps to compare the different proposed layouts. The higher layout moment ratio is the more desirable layout. Also this article compares the results of ABC technique with genetic algorithm (GA) and simulated annealing (SA) algorithm based on the total moment value, layout moment ratio, number of iterations, computation time, and back-tracking movements. Finally, it concluded that ABC is a better technique to solve fixed area cellular layout problems than the mentioned algorithms with high dimensionality.