A Parallel Genetic Algorithm Approach to the Knife Change Minimisation Problem

The knife change minimisation problem is a special case of the Generalised Travelling Salesman Problem arising in the paper industry as a sub-problem to the one-dimensional cutting stock problem. In the knife change minimisation problem a sequence of cutting patterns needs to be produced at a paper machine winder. Each of the patterns consists of a list of reels, the relative position of which can be varied. Thus each pattern gives rise to many permutations. Each knife re-positioning takes time and we therefore seek to minimise the total number of knife changes by determining the sequence of pattern production and which permutation will represent each pattern. A serial genetic algorithm with special crossovers and inversion as mutation was developed to solve the problem. The serial genetic algorithm produces optimal solutions for small problems and improved solutions for medium and large problems. The solutions obtained for instances of any size are of better quality than the solutions obtained in an industrial product, but require longer execution time. Could a distributed genetic algorithm produce better quality solutions for large problems than the serial genetic algorithm? A parallel genetic algorithm based on the serial genetic algorithm was implemented on the Fujitsu AP1000 to answer the question. The results indicate an improvement in the quality of the solutions.