\chapter{Glossary and Definitions}

Definitions of some of the key terms appearing in the thesis.

\begin{itemize}

\item {\bf Fitness Function}: Fitness function is a mathematical
equation that describes the relative value of each member of a family
of objects with respect to some criterion. The fitness function is
maximized or minimized (depending upon the criterion) to find the best
object in the family.

\item {\bf Landscape Analysis}: Landscape analysis is a mathematical
process used to search for the best solution to a multi-variable
optimization problem. It utilizes a fitness function. Within the
search space (i.e., a plot of all the possible solutions), the fitness 
of a particular solution can be shown graphically as its height. The
resulting ``landscape'' will have peaks in the regions of the search
space that contain better solutions; further analysis of the peak
regions can be used to refine the results and achieve even more
precise solutions.

\item {\bf Fitness landscape}: A fitness landscape is a particular
kind of representation of a large space of ``configurations''. For
example, this space could be ``The space of all possible routes
through 100 given cities'' or ``The space of all possible genotypes of
a given length''. A fitness landscape requires both a {\it fitness
function} assigning a value (usually in real numbers) to each {\it
configuration}, and a {\it neighborhood relation} amongst the
configurations.

\item {\bf Multi-Objective Optimization}: Is the task of maximizing or
minimizing a number of criteria simultaneously. Multi-objective
optimization is more difficult than most kinds of optimization
problems because the trade-offs between the multiple objectives may
be unknown. 

\item {\bf Simulated Annealing}: A mathematical technique for general
optimization problems. The same comes from the physical process of
annealing, during which a material is first heated and then slowly
cooled. During annealing, the component atoms of a material are
allowed to settle into a lower energy state so that a more stable
arrangement of atoms is maintained throughout the cooling process. SA
has been applied with success to a wide variety of optimization tasks.

\item {\bf Optimization problem}: A search problem in which we wish to 
know, in some given domain, the minimal (or maximal) value of a given
function. E.g. find $min_{\sigma \in \Sigma} f(\sigma)$, where $f:
\Sigma \rightarrow {\cal R}$.

\item {\bf Spin Glass}: Spin glasses are simplified models from
physics describing dilute magnetic alloys. They define an energy
function (or equivalently a fitness function) over tiny magnetic
dipoles called spins. Spins may point either up (+1) or down (-1). 
For every configuration of spins (e.g., +1-1+1+1-1 for a configuration
of 5 spins), the energy function assigns that configuration's energy
by summing up the interactions between spins. many aspects of spin 
glasses are utilized by physicists and they comprise a well-understood 
family of fitness landscapes.

\item {\bf Entropy}: A mathematical measure of the amount of disorder
in a system.

\item {\bf Phase transition}: Loosely a qualitative change in
behavior resulting from the smooth variation of a parameter. For
example as we reduce the temperature, water undergoes a phase
transition when it freezes: change from water into ice.

\end{itemize}




