Genetic Algorithms for Cutting Stock Problems: With and Without Contiguity

A number of optimisation problems involve the optimal grouping of a finite set of items into a number of categories subject to one or more constraints. Such problems raise interesting issues in mapping solutions in genetic algorithms. These problems range from the knapsack problem to bin packing and cutting stock problems. This paper describes research involving cutting stock problems. Results show that the mapping that is used affects the solution in terms of both quality of the solution found and time taken to find solutions, and that different mappings are suitable for different variants of the problem.

[1]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[2]  David S. Johnson,et al.  Approximation Algorithms for Bin-Packing — An Updated Survey , 1984 .

[3]  Paul E. Sweeney,et al.  Cutting and Packing Problems: A Categorized, Application-Orientated Research Bibliography , 1992 .

[4]  David E. Goldberg,et al.  AllelesLociand the Traveling Salesman Problem , 1985, ICGA.

[5]  Nostrand Reinhold,et al.  the utility of using the genetic algorithm approach on the problem of Davis, L. (1991), Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York. , 1991 .

[6]  Harald Dyckhoff,et al.  A typology of cutting and packing problems , 1990 .

[7]  Constantine Goulimis.  Optimal solutions for the cutting stock problem , 1990 .

[8]  D. E. Goldberg,et al.  Genetic Algorithms in Search, Optimization & Machine Learning , 1989 .

[9]  Robert Hinterding,et al.  Mapping, order-independent genes and the knapsack problem , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[10]  R. Gomory,et al.  A Linear Programming Approach to the Cutting-Stock Problem , 1961 .

[11]  Robert Hinterding,et al.  A genetic algorithm for stock cutting: an exploration of mapping schemes1 , 1993 .

[12]  Patrick Prosser,et al.  A Hybrid Genetic Algorithm for Pallet Loading , 1988, ECAI.

[13]  Kate Juliff,et al.  A Multi-chromosome Genetic Algorithm for Pallet Loading , 1993, International Conference on Genetic Algorithms.

[14]  Colin Reeves,et al.  Hybrid genetic algorithms for bin-packing and related problems , 1996, Ann. Oper. Res..

[15]  Emanuel Falkenauer,et al.  Setting New Limits in Bin Packing with a Grouping GA Using Reduction , 1994 .

[16]  Ralph E. Gomory,et al.  A Linear Programming Approach to the Cutting Stock Problem---Part II , 1963 .

[17]  Alain Delchambre,et al.  A genetic algorithm for bin packing and line balancing , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[18]  Harvey J. Greenberg,et al.  New approaches for heuristic search: A bilateral linkage with artificial intelligence , 1989 .

[19]  David E. Goldberg,et al.  Alleles, loci and the traveling salesman problem , 1985 .

[20]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[21]  Boon J. Yuen.  Heuristics for sequencing cutting patterns , 1991 .

[22]  Derek Smith,et al.  Bin Packing with Adaptive Search , 1985, ICGA.