A generalized permutation approach to job shop scheduling with genetic algorithms

In order to sequence the tasks of a job shop problem on a number of machines related to the technological machine order of jobs, a new representation technique-mathematically known as ‘permutation with repetition’ is presented. The main advantage of this single chromosome representation is-in analogy to the permutation scheme of the traveling salesman problem-that it cannot produce illegal operation sequences. As a consequence of the representation scheme a new crossover operator preserving the initial scheme structure of permutations with repetition will be sketched. Its behavior is similar to the well known Order-Crossover for simple permutation schemes. Actually the GOX operator for permutations with repetition arises from a Generalisation of OX. Computational experiments show, that GOX passes the information from a couple of parent solutions efficiently to offspring solutions. Together, the new representation and GOX support the cooperative aspect of genetic search for scheduling problems strongly.