A Generalized Permutation Approach toJob Shop Scheduling with Genetic Algorithms ?

In order to sequence the tasks of a job shop problem (JSP) 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 (TSP) { that it cannot produce illegal sets of operation sequences (infeasible symbolic solutions). 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 eeciently to oospring solutions. Together, the new representation and GOX support the cooperative aspect of the genetic search for scheduling problems strongly.