Job Shop Scheduling by Simulated Annealing

TLDR

Simulated annealing, a generalization of iterative improvement for combinatorial optimization, underlies the algorithm. The paper presents an approximation algorithm to minimize makespan in job shop scheduling. It employs simulated annealing, accepting cost‑increasing transitions with nonzero probability to escape local minima, as an approximation method for job shop makespan minimization. The algorithm asymptotically converges to a globally minimal solution and experimentally achieves shorter makespans than two recent tailored approaches, albeit with significantly longer runtimes.

Abstract

We describe an approximation algorithm for the problem of finding the minimum makespan in a job shop. The algorithm is based on simulated annealing, a generalization of the well known iterative improvement approach to combinatorial optimization problems. The generalization involves the acceptance of cost-increasing transitions with a nonzero probability to avoid getting stuck in local minima. We prove that our algorithm asymptotically converges in probability to a globally minimal solution, despite the fact that the Markov chains generated by the algorithm are generally not irreducible. Computational experiments show that our algorithm can find shorter makespans than two recent approximation approaches that are more tailored to the job shop scheduling problem. This is, however, at the cost of large running times.