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% Optimal Foraging Theory Revisited: Chapter 5. Conclusion
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% (c) Copyright 2007 by Theodore P. Pavlic
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\chapter{Conclusion}
\label{ch:conclusion}

With increasing demand for automation, engineering design methods must
be developed that encapsulate complex high-level decision making.
Automated controllers need to perform tasks that would traditionally be
carried out by \index{cognition}cognitive agents (\eg, human beings).
So, engineering is progressively more interested in constructing
\emph{behaviors} rather than just decision rules. Therefore, it makes
sense that behavioral ecology could be influential to the development of
design methods in \index{artificial intelligence}artificial
intelligence. This insight is the genesis of this thesis. We demonstrate
how the study of patterns of natural \index{cognition}cognitive behavior
can be used to guide the construction of engineered agents.  This novel
extension of behavioral ecology can lead to new realizations about the
natural world. As these fields have a rich history, their combination
provides for many future research directions. 

\section{Contributions to Engineering}
\index{contributions!engineering|(}
\index{applications|see{examples, applications}}
\index{automation|see{examples, applications}}
\index{robotics|see{examples, applications}}
\index{queueing|see{examples, applications, queueing}}
\index{vehicles|see{examples, applications, autonomous vehicle}}
\index{AGV|see{examples, applications, autonomous vehicle}}
\index{autonomous ground vehicles|see{examples, applications, autonomous
vehicle}}
\index{AAV|see{examples, applications, autonomous vehicle}}
\index{autonomous air vehicles|see{examples, applications, autonomous
vehicle}}
\index{UGV|see{examples, applications, autonomous vehicle}}
\index{unmanned ground vehicles|see{examples, applications, autonomous
vehicle}}
\index{UAV|see{examples, applications, autonomous vehicle}}
\index{unmanned air vehicles|see{examples, applications, autonomous
vehicle}}

\index{examples!applications|(indexdef}Results from behavioral ecology
can be extended to engineering design.  At an abstract level, a forager
with a behavior favored by natural selection due to its energy-time
balance is no different from a single agent with protocols that achieve
a favorable work-resource balance.  This agent model is applicable in a
wide range of engineering applications.
\index{examples!applications!military}\index{examples!applications!autonomous
vehicle}The analogy between foraging and task processing is obvious in
military applications where agents search for targets to process while
also minimizing fuel cost or risk. Also consider an
\index{examples!applications!temperature control|indexdef}automated
centralized temperature controller in a large building. The controller
has limited control authority and faces random temperature disturbances.
It must prioritize its efforts to achieve some desirable temperature
profile given its limited resources. Our design methods may be used to
design a strategy that efficiently manages the temperature profile of
the building\footnote{For example, temperature perturbations away from
the desired profile may be viewed as task encounters.}. In fact,
\citet{QAP06} have implemented an \ac{OFT}-based temperature controller
prototype. Other controllers that must prioritize resource investment to
achieve some favorable outcome may be viewed in a similar way. Our model
is particularly useful in applications with \aimention{Sim\'{e}on-Denis
Poisson}Poisson encounters, as in many
\index{examples!applications!queueing}queueing applications. This model
could also be modified for use in other stochastic
environments.\index{examples!applications|)indexdef}
\index{contributions!engineering|)}

\section{Contributions to Biology}
\index{contributions!biology|(}

This new engineering approach is not only inspired by classical \ac{OFT}
but also provides new insights to behavioral ecology. While qualitative
results can be useful in justifying observed behavior in nature, the
design of engineered behaviors requires a strong quantitative analysis
of a trusted model. Therefore, the two fields have different priorities,
and they complement each other. Biologically-inspired engineering design
leads to elegant agent behaviors and new insights into the elegance of
observed foraging behaviors in nature. In particular, the work in this
thesis contributes to biology in the following ways.
%
\begin{description}
        \item\emph{Improved Agent Model:} Our solitary agent model that
                we discuss encapsulates the existing foraging model used
                in classical \ac{OFT}. However, we explicitly model a
                relationship between processing time and processing cost
                and none of our analysis requires that any cost is nil.
                We also allow for the possibility of negative search
                costs and gains, which expands the applicability of the
                model (\eg, negative search costs may indicate
                additional value accumulated while not in a processing
                mode). 
        \item\emph{Combination of Rate Maximization and Risk
                Sensitivity:} Our approach of defining an agent lifetime
                in terms of a finite number of tasks yields new ways of
                approaching statistical optimization of the agent model.
                Because the agent has a finite lifetime, thresholds of
                lifetime success may be added to the analysis. Success
                thresholds cannot be used in classical \ac{OFT} rate
                maximization because an infinite lifetime is assumed,
                and so any threshold will have zero impact on behavior.
                Gain thresholds are considered in risk-sensitive
                classical \ac{OFT} approach, but the impact of
                environmental parameters cannot easily be explored
                because the model does not provide an easy way to study
                finite-lifetime behavior. Because our approach is
                defined by a finite lifetime assumption, we can add a
                gain threshold to rate maximization (\ie, we consider
                \emph{excess} rate maximization) and study the impact of
                environmental parameter changes on risk-sensitive
                behavior. The former combines risk sensitivity and time
                minimization. The latter shows not only how parameters
                like encounter rates and costs can modulate
                risk-sensitive behavior but also how minimization of
                uncertainty is related to time minimization. 
        \item\emph{Evolutionary Justification for Efficiency
                Maximization:} Efficiency maximization is usually
                considered to be unrealistic in biology because it does
                not provide the time minimization important to both risk
                sensitivity and rate maximization. However, by studying
                efficiency with respect to our agent model, we show how
                its maximization does provide time pressure (\ie,
                minimization of costs has a related effect on time).
                This makes it an optimization objective that does not
                conflict with the expected pressures of natural
                selection or survival in general.
        \item\emph{Generalized \ac{MVT}:} By studying the maximization
                of a generalized rational value function, we provide a
                simple method for finding behaviors that are optimal
                with respect to existing objectives and objectives yet
                to be determined. The optimal solutions to this generic
                value function show that the \ac{MVT} is a
                specialization of a general rule based on marginal
                advantage and marginal disadvantage.
\end{description}
%
These contributions are the result of a fresh perspective on well-known
theoretical research in behavioral ecology. This suggests that
collaboration between engineers and biologists has synergistic value.
\index{contributions!biology|)}

\section{Future Directions}
\index{future directions|(}

There are several future directions for extending this work. For one,
the agent model we have described may be expanded to include the impact
of recognition cost and behavior-dependent encounter rates.  Nonlinear
fuel costs might also be added to the model\footnote{As our
justifications for using efficiency maximization as an alternative for
rate maximization are based on linear costs, this modification is not
trivial.}. Additionally, analytical results that use variance would be
valuable when considering risk in random environments. The optimization
methods also leave room for improvement. As discussed, \ac{MPT} and
\ac{PMPT} have studied nearly identical problems in finance. Modern
portfolio choice and capital budgeting research is far more advanced
than the economic literature typically cited by behavioral ecologists.
Approaching behavioral analysis and design from this updated point of
view may be valuable. Finally, it is important to engineering that
biologically-inspired agent design be tested experimentally in order to
validate its utility.
\index{future directions|)}

\section{The Value of Collaboration}

Studying ways of combining behavioral ecology, finance, and engineering
has been enlightening and stimulating. Researchers in these fields
approach similar problems from different directions. Their collaboration
can lead to unanticipated insights of genuine value. Even if the results
of this particular work fail to be successfully applied to engineering,
it is likely that starting a discussion among members of this diverse
group of fields will eventually yield mutual benefits.