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% Optimal Foraging Theory Revisited: Chapter 1. Introduction
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% (c) Copyright 2007 by Theodore P. Pavlic
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\chapter{Introduction}
\label{ch:introduction}

Following the example of \citet{APW04}, \citet{APW06}, \citet{PP06}, and
\citet{QAP06}, we synthesize ideas from \citet{SK86} to apply
\index{classical OFT|see{optimal foraging theory}}\index{classical
optimal foraging theory|see{optimal foraging
theory}}\index{OFT|see{optimal foraging theory}}\acro[\index{optimal
foraging theory|indexdef}optimal foraging
theory~(OFT)]{OFT}{\index{optimal foraging theory"|indexglo}optimal
foraging theory} to engineering applications. In particular, we expand
the solitary agent framework from classical \ac{OFT} so that it applies
to more general cases. This framework describes a solitary agent (\eg,
an \index{examples!applications!autonomous vehicle}autonomous vehicle)
that faces tasks to process at random. On encounters with a task, the
designed agent behavior specifies whether or not the agent should
process the task and for how long processing should continue.  This is
inherently an optimal portfolio \citep{Markowitz52} problem as it
involves allocating resources (\eg, time and cost of processing) in a
way that optimizes some aspect of random future returns (\eg, value of
tasks relative to fuel cost). Therefore, we then derive optimization
results in this framework using methods borrowed from optimal portfolio
theory.  We hope that these extensions of \ac{OFT} will be useful in the
design of high-level control of \index{examples!applications!autonomous
vehicle}autonomous agents and will also provide new insights in
biological applications.

In \longref{ch:model}, we use insights from behavioral ecology to
develop a general stochastic model of a solitary agent with statistics
that may be used in analyzing or designing optimal behavior. In
particular, we generalize the stochastic model used by classical
\ac{OFT} and propose a new analysis approach. The statistics used in
classical \ac{OFT} are conditioned on the number of tasks
\emph{encountered} regardless of whether or not those tasks are
processed. In our approach, we focus on statistics conditioned on the
number of tasks \emph{processed}. Not only does this have greater
applicability to engineering, but it provides a new method for
finite-lifetime analysis.

In \longref{ch:optimization_objectives}, we study various ways that
statistics of our generalized agent may be combined for multiobjective
optimization. We first describe the approaches used in classical
\ac{OFT}. By generalizing these classical objectives, we suggest new
explanations for peculiar foraging behaviors observed in nature. We then
propose new optimization objectives for use in engineering; however, we
discuss how these objectives may also be applicable in behavioral
ecology.  Finally, we discuss how existing work in classical \ac{OFT}
may be duplicating existing work in economics. We suggest that a study
of the most recent optimal portfolio theory literature may provide
valuable insights to both behavioral analysis and design.

In \longref{ch:optimization_results}, we analyze a class of optimization
functions that share a particular structure. Many of the functions we
introduce in \longref{ch:optimization_objectives} for multiobjective
optimization have this structure, and so this analysis leads to optimal
solutions for them. We present some of those solutions at the end of the
chapter.

Concluding remarks are given in \longref{ch:conclusion}.
\longref{app:markov_renewal_sto_limits} provides some results from
renewal theory that are used in \longref{ch:model}. Lists of acronyms,
model terms, and mathematical symbols that we use are given at the end
of this document. Topic and people indices follow the bibliography.