A Practical Approach to Subset Selection for Multi-objective Optimization via Simulation

We describe a practical two-stage algorithm, BootComp, for multi-objective optimization via simulation. Our algorithm finds a subset of good designs that a decision-maker can compare to identify the one that works best when considering all aspects of the system, including those that cannot be modeled. BootComp is designed to be straightforward to implement by a practitioner with basic statistical knowledge in a simulation package that does not support sequential ranking and selection. These requirements restrict us to a two-stage procedure that works with any distributions of the outputs and allows for the use of common random numbers. Comparisons with sequential ranking and selection methods suggest that it performs well, and we also demonstrate its use analyzing a real simulation aiming to determine the optimal ward configuration for a UK hospital.

Improved Penalty Function with Memory for Stochastically Constrained Optimization via Simulation

Penalty function with memory (PFM) in Park and Kim [2015] is proposed for discrete optimization via simulation problems with multiple stochastic constraints where performance measures of both an objective and constraints can be estimated only by stochastic simulation. The original PFM is shown to perform well, finding a true best feasible solution with a higher probability than other competitors even when constraints are tight or near-tight. However, PFM applies simple budget allocation rules (e.g., assigning an equal number of additional observations) to solutions sampled at each search iteration and uses a rather complicated penalty sequence with several user-specified parameters. In this article, we propose an improved version of PFM, namely IPFM, which can combine the PFM with any simulation budget allocation procedure that satisfies some conditions within a general DOvS framework. We present a version of a simulation budget allocation procedure useful for IPFM and introduce a new penalty sequence, namely PS 2 + , which is simpler than the original penalty sequence yet holds convergence properties within IPFM with better finite-sample performances. Asymptotic convergence properties of IPFM with PS 2 + are proved. Our numerical results show that the proposed method greatly improves both efficiency and accuracy compared to the original PFM.

Replicated Computational Results (RCR) Report for“A Practical Approach to Subset Selection for Multi-Objective Optimization via Simulation”

In “A Practical Approach to Subset Selection for Multi-Objective Optimization via Simulation,” Currie and Monks propose an algorithm for multi-objective simulation-based optimization. In contrast to sequential ranking and selection schemes, their algorithm follows a two-stage scheme. The approach is evaluated by comparing the results to those obtained using the existing OCBA-m algorithm for synthetic problems and for a hospital ward configuration problem. The authors provide the Python code used in the experiments in the form of Jupyter notebooks. The code successfully reproduced the results shown in the article.

Rapid Discrete Optimization via Simulation with Gaussian Markov Random Fields

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.

Condition-based Maintenance Policy Optimization Using Genetic Algorithms and Gaussian Markov Improvement Algorithm

Condition-based maintenance involves monitoring the degrading health of machines in a manufacturing system and scheduling maintenance to avoid costly unplanned failures. As compared with preventive maintenance, which maintains machines on a set schedule based on time or run time of a machine, condition-based maintenance attempts to minimize the number of times maintenance is performed on a machine while still attaining a prescribed level of availability. Condition-based methods save on maintenance costs and reduce unwanted downtime over its lifetime. Finding an analytically-optimal condition-based maintenance policy is difficult when the target system has non-uniform machines, stochastic maintenance time and capacity constraints on maintenance resources. In this work, we find an optimal condition-based maintenance policy for a serial manufacturing line using a genetic algorithm and the Gaussian Markov Improvement Algorithm, an optimization via simulation method for a stochastic problem with a discrete solution space. The effectiveness of these two algorithms will be compared. When a maintenance job (i.e., machine) is scheduled, it is placed in a queue that is serviced with either a first-infirst- out discipline or based on a priority. In the latter, we apply the concept of opportunistic window to identify a machine that has the largest potential to disrupt the production of the system and assign a high priority to the machine. A test case is presented to demonstrate this method and its improvement over traditional maintenance methods.