Differential Evolution for the Flow Shop Scheduling Problem

The classical problem of scheduling n jobs on m machines in a flow shop is to minimize the throughput time of all the jobs under the assumption that all jobs are processed on all machines at the same sequence. This scheduling problem leads to the permutation situation in which there are n-factorial possible sequences to be considered which, for large number of jobs leads to combinatorial explosion. The flow shop scheduling-problem is among the combinatorial optimization problems because for large number of jobs, the search for the best job-sequence can be very demanding in terms of computational time. A summary of different methods for scheduling flow shop problem is found in Dudek et al (1992). Optimization algorithm such as branch-and-bound, has been employed by some researchers (see, for instance, Ignall and Linus (1965), and Hariri (1981)). Due to the difficulties associated with the computational requirements of optimization algorithms for large-sized problems, many researchers have opted for heuristic methods, which though do not guarantee optimal solutions, do produce satisfactory and reliable solutions with a reasonably small amount of computational efforts.