Abstract

Evolutionary algorithms (EAs) have been applied to many optimization problems successfully in recent years. The genetic algorithm (GAs) and evolutionary programming (EP) are two different types of EAs. GAs use crossover as the primary search operator and mutation as a background operator, while EP uses mutation as the primary search operator and does not employ any crossover. This paper proposes a novel EP algorithm for cutting stock problems with and without contiguity. Two new mutation operators are proposed. Experimental studies have been carried out to examine the effectiveness of the EP algorithm. They show that EP can provide a simple yet more effective alternative to GAs in solving cutting stock problems with and without contiguity. The solutions found by EP are significantly better (in most cases) than or comparable to those found by GAs.

Scope and purpose

The one-dimensional cutting stock problem (CSP) is one of the classical combinatorial optimization problems. While most previous work only considered minimizing trim loss, this paper considers CSPs with two objectives. One is the minimization of trim loss (i.e., wastage). The other is the minimization of the number of stocks with wastage, or the number of partially finished items (pattern sequencing or contiguity problem). Although some traditional OR techniques (e.g., programming based approaches) can find the global optimum for small CSPs, they are impractical to find the exact global optimum for large problems due to combinatorial explosion. Heuristic techniques (such as various hill-climbing algorithms) need to be used for large CSPs. One of the heuristic algorithms which have been applied to CSPs recently with success is the genetic algorithm (GA). This paper proposes a much simpler evolutionary algorithm than the GA, based on evolutionary programming (EP). The EP algorithm has been shown to perform significantly better than the GA for most benchmark problems we used and to be comparable to the GA for other problems.

Author Keywords: Evolutionary algorithm; Cutting stock problems; Combinatorial optimization

Article Outline

1. Introduction

2. The cutting stock problem

2.1. CSP without contiguity

2.2. CSP with contiguity

2.3. Evolutionary approaches to CSPs

3. The evolutionary programming approach

3.1. Problem representation

3.2. Swap mutation

3.3. Fitness functions

3.4. The evolutionary programming algorithm

4. Experimental studies

5. Conclusion

Appendix A. The benchmark problems

Appendix B. The solution examples

References