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The Rapid Gaussian Markov Improvement Algorithm (rGMIA) solves discrete optimization via simulation problems by using a Gaussian Markov random field and complete expected improvement as the sampling and stopping criterion. rGMIA has been created as a sequential sampling procedure run on a single processor. In this paper, we extend rGMIA to a parallel computing environment when q+1 solutions can be simulated in parallel. To this end, we introduce the q-point complete expected improvement criterion to determine a batch of q+1 solutions to simulate. This new criterion is implemented in a new object-oriented rGMIA package. 

The Rapid Gaussian Markov Improvement Algorithm (rGMIA) solves discrete optimization via simulation problems by using a Gaussian Markov random field and complete expected improvement as the sampling and stopping criterion. rGMIA has been created as a sequential sampling procedure run on a single processor. In this paper, we extend rGMIA to a parallel computing environment when q+1 solutions can be simulated in parallel. To this end, we introduce the q-point complete expected improvement criterion to determine a batch of q+1 solutions to simulate. This new criterion is implemented in a new object-oriented rGMIA package. 

Abstract When maintenance resources in a manufacturing system are limited, a challenge arises in determining how to allocate these resources among multiple competing maintenance jobs. This work formulates an online prioritization problem to tackle this challenge using a Markov decision process (MDP) to model the system behavior and Monte Carlo tree search (MCTS) to seek optimal maintenance actions in various states of the system. Further, case-based reasoning (CBR) is adopted to retain and reuse search experience gathered from MCTS to reduce the computational effort needed over time and to improve decision-making efficiency. The proposed method results in increased system throughput when compared to existing methods of maintenance prioritization while also reducing the computation time needed to identify optimal maintenance actions as more information is gathered. This is especially beneficial in manufacturing settings where maintenance decisions must be made quickly to minimize the negative performance impact of machine downtime. 

Inference-based optimization via simulation, which substitutes Gaussian process (GP) learning for the structural properties exploited in mathematical programming, is a powerful paradigm that has been shown to be remarkably effective in problems of modest feasible-region size and decision-variable dimension. The limitation to “modest” problems is a result of the computational overhead and numerical challenges encountered in computing the GP conditional (posterior) distribution on each iteration. In this paper, we substantially expand the size of discrete-decision-variable optimization-via-simulation problems that can be attacked in this way by exploiting a particular GP—discrete Gaussian Markov random fields—and carefully tailored computational methods. The result is the rapid Gaussian Markov Improvement Algorithm (rGMIA), an algorithm that delivers both a global convergence guarantee and finite-sample optimality-gap inference for significantly larger problems. Between infrequent evaluations of the global conditional distribution, rGMIA applies the full power of GP learning to rapidly search smaller sets of promising feasible solutions that need not be spatially close. We carefully document the computational savings via complexity analysis and an extensive empirical study. Summary of Contribution: The broad topic of the paper is optimization via simulation, which means optimizing some performance measure of a system that may only be estimated by executing a stochastic, discrete-event simulation. Stochastic simulation is a core topic and method of operations research. The focus of this paper is on significantly speeding-up the computations underlying an existing method that is based on Gaussian process learning, where the underlying Gaussian process is a discrete Gaussian Markov Random Field. This speed-up is accomplished by employing smart computational linear algebra, state-of-the-art algorithms, and a careful divide-and-conquer evaluation strategy. Problems of significantly greater size than any other existing algorithm with similar guarantees can solve are solved as illustrations. 

Often in manufacturing systems, scenarios arise where the demand for maintenance exceeds the capacity of maintenance resources. This results in the problem of allocating the limited resources among machines competing for them. This maintenance scheduling problem can be formulated as a Markov decision process (MDP) with the goal of finding the optimal dynamic maintenance action given the current system state. However, as the system becomes more complex, solving an MDP suffers from the curse of dimensionality. To overcome this issue, we propose a two-stage approach that first optimizes a static condition-based maintenance (CBM) policy using a genetic algorithm (GA) and then improves the policy online via Monte Carlo tree search (MCTS). The static policy significantly reduces the state space of the online problem by allowing us to ignore machines that are not sufficiently degraded. Furthermore, we formulate MCTS to seek a maintenance schedule that maximizes the long-term production volume of the system to reconcile the conflict between maintenance and production objectives. We demonstrate that the resulting online policy is an improvement over the static CBM policy found by GA.