Chuljin Park

Handling stochastic constraints in discrete optimization via simulation

We consider a discrete optimization via simulation problem with stochastic constraints on secondary performance measures where both objective and secondary performance measures need to be estimated by simulation. To solve the problem, we present a method called penalty function with memory (PFM), which determines a penalty value for a solution based on history of feasibility check on the solution. PFM converts a DOvS problem with stochastic constraints into a series of new optimization problems without stochastic constraints so that an existing DOvS algorithm can be applied to solve the new problem.

Penalty Function with Memory for Discrete Optimization via Simulation with Stochastic Constraints

We consider a discrete optimization via simulation (DOvS) problem with stochastic constraints on secondary performance measures in which both objective and secondary performance measures need to be estimated by stochastic simulation. To solve the problem, we develop a new method called the Penalty Function with Memory (PFM). It is similar to an existing penalty-type method—which consists of a penalty parameter and a measure of violation of constraints—in a sense that it converts a DOvS problem with constraints into a series of unconstrained problems. However, PFM uses a different penalty parameter, called a penalty sequence, determined by the past history of feasibility checks on a solution. Specifically, assuming a minimization problem, a penalty sequence diverges to infinity for any infeasible solution but converges to zero for any feasible solution under certain conditions. As a result, a DOvS algorithm combined with PFM performs well even when an optimal feasible solution is a boundary solution with one or more active constraints. We prove convergence properties and discuss parameter selection for the implementation of PFM. Experimental results on a number of numerical examples show that a DOvS algorithm combined with PFM works well.

Designing an optimal water quality monitoring network for river systems using constrained discrete optimization via simulation

The problem of designing a water quality monitoring network for river systems is to find the optimal location of a finite number of monitoring devices that minimizes the expected detection time of a contaminant spill event while guaranteeing good detection reliability. When uncertainties in spill and rain events are considered, both the expected detection time and detection reliability need to be estimated by stochastic simulation. This problem is formulated as a stochastic discrete optimization via simulation (OvS) problem on the expected detection time with a stochastic constraint on detection reliability; and it is solved with an OvS algorithm combined with a recently proposed method called penalty function with memory (PFM). The performance of the algorithm is tested on the Altamaha River and compared with that of a genetic algorithm due to Telci, Nam, Guan and Aral (2009).

Designing optimal water quality monitoring network for river systems and application to a hypothetical river

The problem of designing a water quality monitoring network for river systems is to find the optimal location of a finite number of monitoring devices that minimizes the expected detection time of a contaminant spill event with good detection reliability. We formulate this problem as an optimization problem with a stochastic constraint on a secondary performance measure where the primary performance measure is the expected detection time and the secondary performance measure is detection reliability. We propose a new objective function that integrates the stochastic constraint into the original objective function in a way that existing Optimization via Simulation (OvS) algorithms originally developed for an optimization problem without any stochastic constraint can be applicable to our problem. The performance of an OvS algorithm, namely the nested partitions method, with the new objective is tested on a hypothetical river.

Impact of sensor measurement error on sensor positioning in water quality monitoring networks

This paper studies the impact of sensor measurement error on designing a water quality monitoring network for a river system, and shows that robust sensor locations can be obtained when an optimization algorithm is combined with a statistical process control (SPC) method. Specifically, we develop a possible probabilistic model of sensor measurement error and the measurement error model is embedded into a simulation model of a river system. An optimization algorithm is used to find the optimal sensor locations that minimize the expected time until a spill detection in the presence of a constraint on the probability of detecting a spill. The experimental results show that the optimal sensor locations are highly sensitive to the variability of measurement error and false alarm rates are often unacceptably high. An SPC method is useful in finding thresholds that guarantee a false alarm rate no more than a pre-specified target level, and an optimization algorithm combined with the thresholds finds a robust sensor network.

Selective disassembly sequencing with random operation times in parallel disassembly environment

Selective disassembly sequencing is the problem of determining the sequence of disassembly operations to extract one or more target components of a product. This study considers the problem with random operation times in the parallel disassembly environment in which one or more components can be removed at the same time by a single disassembly operation. After representing all possible disassembly sequences using the extended process graph, a stochastic integer programming model is developed for the objective of minimising the sum of disassembly and penalty costs, where the disassembly costs consist of sequence-dependent set-up and operation costs and the penalty cost is the expectation of the costs incurred when the total disassembly time exceeds a threshold value. A sample average approximation-based solution algorithm is proposed that incorporates an optimal algorithm to solve the sample average approximating problem under a given set of scenarios for disassembly operation times. The algorithm is illustrated with a hand-light case and a large-sized random instance, and the results are reported.

Self-adjusting the tolerance level in a fully sequential feasibility check procedure

Abstract We consider the problem of determining the feasibility of systems when the performance measures in stochastic constraints need to be evaluated via simulation. We develop a new procedure, namely the adaptive feasibility check procedure. Specifically, the procedure uses an existing feasibility check procedure iteratively as its subroutine with a decreasing sequence of tolerance levels. Our procedure is designed to return the set of strictly feasible systems with at least a prespecified probability. The validity and efficiency of the procedure are investigated through both analytical and experimental results. The procedure is also tested using numerical examples.

The bivariate measure of risk and error (BMORE) plot

We develop a graphical method, namely the bivariate measure of risk and error (BMORE) plot, to visualize bivariate output data from the stochastic simulation. The BMORE plot consists of a sample mean, median, minimum/maximum values for each measure, an outlier, and the boundary of a certain percentile of the simulation data on a two-dimensional space. In addition, it depicts confidence regions of both the true mean and the percentile to show how accurate the two estimates are. From the BMORE plot, scholars, practitioners, and software engineers in simulation fields can understand the variability and potential risk of the simulation data intuitively, design simulation experiments effectively, and reduce a great deal of time and effort to analyze the simulation results.