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Optimisation in Signal and Image Processing by Patrick Siarry

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Chapter 6

Probabilistic Modeling of Policies and Application to Optimal Sensor Management

6.1. Continuum, a path toward oblivion

In the domain of operational research several practical questions often lead on to combinatorial issues. This chapter covers planning and exploring problems. Generally speaking, this chapter will deal with the path planning or placement of sensors. Specific tasks like the detection of intrusion or surveillance are possible applications. For such a task, large scale planning is often required and/or different levels of decision making are considered. For some applications, an uncertain area might be explored by mobile sensors. In such cases, the observations are involved in the whole planning process, and feedback on the sensors orientations is necessary. For such problems, the optimal planning of the complete mission is very difficult to solve and various simplification techniques are addressed by the literature.

Main difficulties in optimization arise when manipulating discrete data. Even for continuous non-convex optimization, the implication of discrete data is implicit and associated to local minima. The combinatorics implied by integer data not only impact the optimization but also have logical implications (e.g. calculability and logical complexity). Various approaches have been investigated in order to reduce the combinatorics. Systematic enumeration methods like Branch and Bound can be used in combination with the computation of branching bounds ...

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