Optilearning for job shop problems

We exploit the two distinguishing features of Boltzmann machines-plasticity of connections and concentration of equilibrium states around the minima of a loss function-for designing an optimization algorithm where the neural network learns to suitably locate its equilibrium state on the target of the optimization problem. The algorithm is structured in two loops: an inner loop catches the equilibrium state providing reliable optima of a relaxed issue of the optimization problem; the outer loop modifies the weights of the neural network in order to make these solutions meanly translate into very fine approximated solutions of the exact optimization problem. The two loops have asymptotical trajectories drawn by the optima of the exact problem. We tested the algorithm on a simple non-preemptive job shop problem using the Lawrence benchmark. A trade-off analysis between running time and approximation accuracy shows that in many cases the algorithm achieves an accuracy of the same order of the best simulated annealing, taking at most one order higher running time, and does not require any user intervention to assess the parameters of the optimization process.