Optimal Computing Budget Allocation for Ordinal Optimization in Solving Stochastic Job Shop Scheduling Problems

摘要

We focus on solving Stochastic Job Shop Scheduling Problem (SJSSP) with random processing time to minimize the expected sum of earliness and tardiness costs of all jobs. To further enhance the efficiency of the simulation optimization technique of embedding Evolutionary Strategy in Ordinal Optimization (ESOO) which is based on Monte Carlo simulation, we embed Optimal Computing Budget Allocation (OCBA) technique into the exploration stage of ESOO to optimize the performance evaluation process by controlling the allocation of simulation times. However, while pursuing a good set of schedules, “super individuals,” which can absorb most of the given computation while others hardly get any simulation budget, may emerge according to the allocating equation of OCBA. Consequently, the schedules cannot be evaluated exactly, and thus the probability of correct selection (PCS) tends to be low. Therefore, we modify OCBA to balance the computation allocation: (1) set a threshold of simulation times to detect “super individuals” and (2) follow an exclusion mechanism to marginalize them. Finally, the proposed approach is applied to an SJSSP comprising 8 jobs on 8 machines with random processing time in truncated normal, uniform, and exponential distributions, respectively. The results demonstrate that our method outperforms the ESOO method by achieving better solutions.