Search planning under incomplete information using stochastic optimization and regression
Miranda, Sofia I.
Royset, Johannes O.
Borges, Carlos F.
Rockafellar, R. Tyrrell.
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This thesis deals with a type of stochastic optimization problem where the decision maker does not have complete information concerning the objective function. Specifically, we consider a discrete time-and-space search optimization problem where we seek to find a moving target in an area of operations. There are two sources of uncertainty: the target location and the sensor performance. We formulate the objective function for this problem in terms of a risk measure of a parameterized random variable and consider three cases involving various degrees of knowledge about the sensor performance. In all cases, we consider both the expectation and superquantile risk measures. While the expectation results in an objective function representing the probability of missing the target, the superquantile gives rise to more conservative search plans that perform reasonably well even under exceptional circumstances. In the case of incomplete in-formation about the distribution of the sensor performance, we approximate the random variable using a nonstandard regression that minimizes the error induced in some sense. We examine the cases in a series of numerical examples.
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