Ant Colony Optimization Algorithm for 1D Cutting Stock Problem
Every day different companies in industry have to solve many optimization problems. One of them is cutting out of linear materials, like steel or aluminum profiles, steel or wood beams and so on. It is so called cutting stocks problem (CSP). It is well known NP-hard combinatorial optimization problem. The accurate and fast cutting out is very important element from the working process. The aim in CSP is to cut items from stocks of certain length, minimizing the total number of stocks (waste). The computational time increases exponentially when the number of items increase. Finding the optimal solution for large-sized problems for a reasonable time is impossible. Therefore, exact algorithms and traditional numerical methods can be apply of only on very small problems. Mostly appropriate methods for this kind of problems are methods based on stochastic search or so called metaheuristic methods. We propose a variant of Ant Colony Optimization (ACO) algorithm to solve linear cutting stocks problem.
Work presented here is partially supported by the Bulgarian National Scientific Fund under Grants DFNI I02/20 “Efficient Parallel Algorithms for Large Scale Computational Problems” and DN 02/10 “New Instruments for Data Mining and their Modeling”.
- 3.Fidanova, S.: Evolutionary algorithm for multiple Knapsack problem. In: International Conference Parallel Problems Solving from Nature, Real World Optimization Using Evolutionary Computing, Granada, Spain (2002). ISBN No 0-9543481-0-9Google Scholar
- 6.Jahromi, M.H., Tavakkoli-Moghaddam, R., Makui, A., Shamsi, A.: Solving an one-dimensional cutting stock problem by simulated annealing and Tabu search. J. Ind. Eng. Int. 8(1), paper 24 (2012)Google Scholar
- 9.Reiman, M., Laumanns, M.: A hybrid ACO algorithm for the capacitate minimum spanning tree problem. In: Proceedings of First International Workshop on Hybrid Metaheuristics, pp. 1–10, Valencia, Spain (2004)Google Scholar
- 11.Stutzle, T., Dorigo, M.: ACO algorithm for the traveling salesman problem. In: Miettinen, K., Makela, M., Neittaanmaki, P., Periaux, J. (eds.) Evolutionary Algorithms in Engineering and Computer Science, pp. 163–183. Wiley (1999)Google Scholar
- 12.Vink, M.: Solving combinatorial problems using evolutionary algorithms (1997). http://citeseer.nj.nec.com/vink97solving.html
- 13.Zhang, T., Wang, S., Tian, W., Zhang, Y.: ACO-VRPTWRV: a new algorithm for the vehicle routing problems with time windows and re-used vehicles based on ant colony optimization. In: Sixth International Conference on Intelligent Systems Design and Applications, pp. 390–395. IEEE Press (2006)Google Scholar