A hybrid approach based on genetic algorithms to solve the problem of cutting structural beams in a metalwork company

This work presents a hybrid approach based on the use of genetic algorithms to solve efficiently the problem of cutting structural beams arising in a local metalwork company. The problem belongs to the class of one-dimensional multiple stock sizes cutting stock problem, namely 1-dimensional multiple stock sizes cutting stock problem. The proposed approach handles overproduction and underproduction of beams and embodies the reusability of remnants in the optimization process. Along with genetic algorithms, the approach incorporates other novel refinement algorithms that are based on different search and clustering strategies.Moreover, a new encoding with a variable number of genes is developed for cutting patterns in order to make possible the application of genetic operators. The approach is experimentally tested on a set of instances similar to those of the local metalwork company. In particular, comparative results show that the proposed approach substantially improves the performance of previous heuristics.Gracia Calandin, CP.; Andrés Romano, C.; Gracia Calandin, LI. (2013). A hybrid approach based on genetic algorithms to solve the problem of cutting structural beams in a metalwork company. Journal of Heuristics. 19(2):253-273. doi:10.1007/s10732-011-9187-xS253273192Aktin, T., Özdemir, R.G.: An integrated approach to the one dimensional cutting stock problem in coronary stent manufacturing. Eur. J. Oper. Res. 196, 737–743 (2009)Alves, C., Valério de Carvalho, J.M.: A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem. Comput. Oper. Res. 35, 1315–1328 (2008)Anand, S., McCord, C., Sharma, R., et al.: An integrated machine vision based system for solving the nonconvex cutting stock problem using genetic algorithms. J. Manuf. Syst. 18, 396–415 (1999)Belov, G., Scheithauer, G.: A cutting plane algorithm for the one-dimensional cutting stock problem with multiple stock lengths. Eur. J. Oper. Res. 141, 274–294 (2002)Christofides, N., Hadjiconstantinou, E.: An exact algorithm for orthogonal 2-D cutting problems using guillotine cuts. Eur. J. Oper. Res. 83, 21–38 (1995)Elizondo, R., Parada, V., Pradenas, L., Artigues, C.: An evolutionary and constructive approach to a crew scheduling problem in underground passenger transport. J. Heuristics 16, 575–591 (2010)Fan, L., Mumford, C.L.: A metaheuristic approach to the urban transit routing problem. J. Heuristics 16, 353–372 (2010)Gau, T., Wäscher, G.: CUTGEN1: a problem generator for the standard one-dimensional cutting stock problem. Eur. J. Oper. Res. 84, 572–579 (1995)Gilmore, P.C., Gomory, R.E.: A linear programming approach to the cutting stock problem. Oper. Res. 9, 849–859 (1961)Gilmore, P.C., Gomory, R.E.: A linear programming approach to the cutting stock problem. Part II. Oper. Res. 11, 863–888 (1963)Ghiani, G., Laganà, G., Laporte, G., Mari, F.: Ant colony optimization for the arc routing problem with intermediate facilities under capacity and length restrictions. J. Heuristics 16, 211–233 (2010)Gonçalves, J.F., Resende, G.C.: Biased random-key genetic algorithms for combinatorial optimization. J. Heuristics (2011). doi: 10.1007/s10732-010-9143-1Gradisar, M., Kljajic, M., Resinovic, G., et al.: A sequential heuristic procedure for one-dimensional cutting. Eur. J. Oper. Res. 114, 557–568 (1999)Haessler, R.W.: One-dimensional cutting stock problems and solution procedures. Math. Comput. Model. 16, 1–8 (1992)Haessler, R.W., Sweeney, P.E.: Cutting stock problems and solution procedures. Eur. J. Oper. Res. 54(2), 141–150 (1991)Haessler, R.W.: Solving the two-stage cutting stock problem. Omega 7, 145–151 (1979)Hinterding, R., Khan, L.: Genetic algorithms for cutting stock problems: with and without contiguity. In: Yao, X. (ed.) Progress in Evolutionary Computation. LNAI, vol. 956, pp. 166–186. Springer, Berlin (1995)Holthaus, O.: Decomposition approaches for solving the integer one-dimensional cutting stock problem with different types of standard lengths. Eur. J. Oper. Res. 141, 295–312 (2002)Kantorovich, L.V.: Mathematical methods of organizing and planning production. Manag. Sci. 6, 366–422 (1939) (Translation to English 1960)Liang, K., Yao, X., Newton, C., et al.: A new evolutionary approach to cutting stock problems with and without contiguity. Comput. Oper. Res. 29, 1641–1659 (2002)Poldi, K., Arenales, M.: Heuristics for the one-dimensional cutting stock problem with limited multiple stock lengths. Comput. Oper. Res. 36, 2074–2081 (2009)Suliman, S.M.A.: Pattern generating procedure for the cutting stock problem. Int. J. Prod. Econ. 74, 293–301 (2001)Talbi, E.-G.: A taxonomy of hybrid metaheuristics. J. Heuristics 8, 541–564 (2002)Vahrenkamp, R.: Random search in the one-dimensional cutting stock problem. Eur. J. Oper. Res. 95, 191–200 (1996)Vanderbeck, F.: Exact algorithm for minimizing the number of set ups in the one dimensional cutting stock problems. Oper. Res. 48, 915–926 (2000)Wagner, B.J.: A genetic algorithm solution for one-dimensional bundled stock cutting. Eur. J. Oper. Res. 117, 368–381 (1999)Wäscher, G., Haußner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183, 1109–1130 (2007

Ant colony optimisation and local search for bin-packing and cutting stock problems

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization problems. Exact solution methods can only be used for very small instances, so for real-world problems, we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimization (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO

An Improved Hierarchical Genetic Algorithm for Sheet Cutting Scheduling with Process Constraints

For the first time, an improved hierarchical genetic algorithm for sheet cutting problem which involves n cutting patterns for m non-identical parallel machines with process constraints has been proposed in the integrated cutting stock model. The objective of the cutting scheduling problem is minimizing the weighted completed time. A mathematical model for this problem is presented, an improved hierarchical genetic algorithm (ant colony—hierarchical genetic algorithm) is developed for better solution, and a hierarchical coding method is used based on the characteristics of the problem. Furthermore, to speed up convergence rates and resolve local convergence issues, a kind of adaptive crossover probability and mutation probability is used in this algorithm. The computational result and comparison prove that the presented approach is quite effective for the considered problem

Comparing several heuristics for a packing problem

Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items, into a minimum size rectangular bin, without overlapping. The restriction is that the items cannot be rotated. The current paper is comparing a greedy algorithm with a hybrid genetic algorithm in order to see which technique is better for the given problem. The algorithms are tested on different sizes data.Comment: 5 figures, 2 tables; accepted: International Journal of Advanced Intelligence Paradigm