Stochastic and distributed anytime task scheduling

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 NP-hard. Therefore, heuristics and approximation algorithms must be used for large problems. Obviously these methods are of interest when they provide near optimal solutions and when computational complexity can be controlled. For this purpose, we have developed a method based on the Hopfield neural network model. This approach permits us to solve in an iterative way a scheduling problem, finding a solution through the minimization of an energy function. 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. By tuning these parameters, we can build a library of a set of run-time executions (contracts) of the Hopfield minimization process with different characteristics (quality, efficiency). We present two applications exploiting the advantage of having available anytime contract algorithms. The first application illustrates how to build a solution of a one machine scheduling problem within a delay that follows a stochastic distribution. The second application deals with unrelated parallel machine scheduling of non preemptive tasks.