A Genetic Algorithm for the Two Machine Flow Shop Problem

In scheduling, the two machine flow shop problem F2parSigma C_i is to find a schedule that minimizes the sum of finishing times of an arbitrary number of jobs that need to be executed on two machines, such that each job must complete processing on machine 1 before starting on machine 2. Finding such a schedule is NP-hard [6]. We propose a heuristic for approximating the solution for the F2parSigma C_i problem using a genetic algorithm. We calibrate the algorithm using optimal results obtained by a branch-and-bound technique. Genetic algorithms simulate the survival of the fittest among individuals over consecutive generations for solving a problem. Prior work has shown that genetic algorithms generally do not perform well for shop problems [21]. However, the fact that in the case of two machines the search space can be restricted to permutations makes the construction of effective genetic operators more feasible.