A stochastic method for discrete and continuous optimization in manufacturing systems

Algorithms for discrete and continuous optimization are a very important part of decision making systems in manufacturing. Most planning, scheduling and layout problems require these algorithms. In practice, research into efficient algorithms meets two principal obstacles. The first one is linked to the fact that quite often the criteria cannot be expressed in an analytic form, so it is not possible to use existing theoretical resolution methods. The second is due to the fact that most of the problems for which the criteria can be represented in analytic form are NP-hard problems. This situation can be simplified using simulation. But the use of simulation and optimization methods together often gives a local optimum. The proposed method in this paper is based on the use of a discrete modification of -transforms jointly with some heuristics for local optimization. The originality of this approach is in the possibility to avoid a local optimum, while using models of simulation for the computation of values of the criteria. An example of the utilization of the method is given: it concerns the optimization of the launching of the parts in production in systems of the job-shop type. The proposed method is compared with a heuristic known to be very good in the same number of simulations. The results of five tests with different model sizes show the efficiency of the proposed method.