7 problems

A five-dimensional reflexive polytope is a lattice polytope whose only interior lattice point is the origin and whose polar dual is also a lattice polytope. Such a polytope gives r…

Let $(P)$ denote the problem considered by the genetic algorithm, let $n$ be its rank, and let $s$ be its instance length. A mean instance means the average-run setting used in the…

Let $n=10$, and let $k$ be the mean length of all words occurring during the entire run of the genetic algorithm whose words are to be reduced. Rank-10 reduction-complexity conject…

Computational-time conjecture. Such applications would require an extraordinary amount of computational time for a genetic algorithm to eventually converge to a better optimal solu…

Let $f$ solve the time-continuous kinetic equation for the genetic algorithm, and consider the same objective-function assumptions and Boltzmann--Gibbs selection framework used for…

Let $(x_k^1,\dots,x_k^N)$ be the GA particle system, and let $(\overline{x}_k^1,\dots,\overline{x}_k^N)$ be $N$ independent copies of the mono-particle process. Coupling conjecture…

Let $f^N_{(k)}$ denote the empirical measure of a genetic-algorithm particle system with population size $N$ at iteration $k$, and let $f_{(k)}$ denote the corresponding kinetic ev…