Finding feasible systems with subjective probability constraints with a military application
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Kim, Taehoon
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Abstract
We consider the problem of determining feasible systems among a finite set of simulated alternatives with respect to probability constraints, where observations from stochastic simulations are Bernoulli distributed. Most statistically valid procedures for feasibility determination consider constraints on the means of normally distributed observations. When observations are Bernoulli distributed, one can still use the existing procedures by treating batch means of Bernoulli observations as basic observations. However, achieving approximate normality may require a large batch size, which can lead to the unnecessary waste of observations in reaching a decision. This thesis proposes procedures that utilize Bernoulli-distributed observations to determine feasibility. We allow for subjective constraints, meaning that thresholds can be tightened if too many systems are feasible or relaxed if no feasible system exists, and adding thresholds sequentially over multiple passes. We demonstrate that our procedures outperform an existing feasibility determination procedure for subjective constraints, originally developed for normal observations. We also show that the proposed procedure can be used to find a system with the largest or smallest probability.
Next, we consider the problem of finding feasible combinations of army aviation assets, specifically attack helicopters and unmanned aerial vehicles, to counter enemy armored units in the presence of constraints on the expected total cost and the mission failure probability. Both performance measures need to be estimated by stochastic simulation of a battlefield. Moreover, the decision maker may be interested in how the feasible combinations change as the threshold values are tightened or loosened, which can help identify the bi-objective optimal solution. We formulate this problem as feasibility determination with subjective constraints and combine two feasibility determination procedures originally designed for mean and probability, respectively. A case study is performed for an imaginary battlefield scenario in the area near the Korean border with an agent-based simulation.
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2024-04-29
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