Solving Cutting Stock Problems by Evolutionary Programming

Evolutionary algorithms (EAs) have been applied to many optimisation problems successfully in recent years. The genetic algorithm (GA) and evolutionary programming (EP) are two of the major branches of EAs. GAs use crossover as the main search operator and mutation as a background operator in search. EP typically uses mutation only. This paper investigates a novel EP algorithm for cutting stock problems. It adopts a mutation operator based on the concept of distance between a parent and its offspring. Without using crossover, the algorithm is less time consuming and more efficient in comparison with a GA-based approach. Experimental studies have been carried out to examine the effectiveness of the EP algorithm. They illustrate that EP can provide a simple yet more efficient alternative to GAs in solving some combinatorial optimisation problems.

[1]  R. Hinterding.  Self-adaptation using multi-chromosomes , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[2]  George Bilchev.  Evolutionary Metaphors for the Bin Packing Problem , 1996, Evolutionary Programming.

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

[4]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[5]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

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

[7]  David B. Fogel,et al.  Exploring Self-Adaptive Methods to Improve the Efficiency of Generating Approximate Solutions to Travelling Salesman Problems Using Evolutionary Programming , 1997, Evolutionary Programming.

[8]  Xin Yao,et al.  Simulated annealing with extended neighbourhood , 1991, Int. J. Comput. Math..

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

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

[11]  David B. Fogel,et al.  System Identification Through Simulated Evolution: A Machine Learning Approach to Modeling , 1991 .

[12]  David B. Fogel,et al.  An Evolutionary Programming Approach to Self-Adaptation on Finite State Machines , 1995, Evolutionary Programming.

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

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

[15]  Robert G. Reynolds,et al.  Evolutionary Programming VI , 1997, Lecture Notes in Computer Science.

[16]  Robert Hinterding,et al.  Genetic Algorithms for Cutting Stock Problems: With and Without Contiguity , 1993, Evo Workshops.

[17]  David B. Fogel,et al.  A Comparison of Evolutionary Programming and Genetic Algorithms on Selected Constrained Optimization Problems , 1995, Simul..

[18]  Xin Yao,et al.  Fast Evolutionary Programming , 1996, Evolutionary Programming.

[19]  D. Fogel.  Applying evolutionary programming to selected traveling salesman problems , 1993 .

[20]  D. B. Fogel,et al.  Applying evolutionary programming to selected control problems , 1994 .

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

[22]  David B. Fogel,et al.  A Comparison of Self-Adaptation Methods for Finite State Machines in Dynamic Environments , 1996, Evolutionary Programming.