Jean-Michel Gallone and Francois Charpillet
Scheduling techniques have been intensively studied by several research communities and have been applied to a wide range of applications in computer and manufacturing environments. Most of the scheduling problems are NPHard. Therefore, heuristics and approximation algorithms must be used for large problems when timing constraints have to be addressed. Obviously these methods are of interest when they provide near optimal solutions and when computational complexity can be controlled. This paper presents such a method based on Hopfield Neural Networks. With this approach, a scheduling problem is solved in an iterative way, finding a solution trough the minimization of an energy function. As the minimization process can fall into a local minimum we can not guarantee that the process will find an optimal solution. Worst, a solution can be missed in some cases. An interesting property of this approach is its capacity to trade-off the quality for computation time. Indeed, the convergence speed of the minimization process can be tuned by adapting several parameters that influence the quality of the results. We will demonstrate in this paper that an anytime probabilistic algorithm can be constructed by combining in sequence a set of minimization processes with decreasing convergence speed.