  Narrow escape and narrow capture problems which describe the average times
required to stop the motion of a randomly travelling particle within a domain
have applications in various areas of science. While for general domains, it is
known how the escape time decreases with the increase of the trap sizes, for
some specific 2D and 3D domains, higher-order asymptotic formulas have been
established, providing the dependence of the escape time on the sizes and
locations of the traps. Such results allow the use of global optimization to
seek trap arrangements that minimize average escape times. In a recent paper
\cite{iyaniwura2021optimization}, an explicit size- and trap location-dependent
expansion of the average mean first passage time (MFPT) in a 2D elliptic domain
was derived. The goal of this work is to systematically seek global minima of
MFPT for $1\leq N\leq 50$ traps in elliptic domains using global optimization
techniques, and compare the corresponding putative optimal trap arrangements
for different values of the domain eccentricity. Further, an asymptotic formula
the for the average MFPT in elliptic domains with $N$ circular traps of
arbitrary sizes is derived, and sample optimal configurations involving
non-equal traps are computed.

Statistical Mechanics