Let us have some data $x_i\in\mathbb{R}^2$ for $i=1,\dots,n$. Let $m=1000$. Let a small number is given, e.g. $m=5$.

The goals is to cover $n$ data by $m$ squares of the same size. The size shall be as small as possible.

In the other words $$ \arg\min_{p\in P} a $$ where $$ p = c_{1,1},c_{1,2},\dots,c_{m,1},c_{m,2},a $$ are centers of squares and their size. Moreover $$ P=\{p:\forall i=1,\dots,n \; \exists j=1,\dots,m:x_i\in C_j\} $$ where $C_j$ is square given by center $c_{j,1},c_{j,2}$ and size $a$. In the other words, each data point must be covered at least by one square.

My attempt: To use differential evolution to optimize over $P$.

Let us have some data $x_i\in\mathbb{R}^2$ for $i=1,\dots,n$. Let $m=1000$. Let a small number is given, e.g. $m=5$.

The goals is to cover $n$ data by $m$ squares of the same size. The size shall be as small as possible.

In the other words $$ \arg\min_{p\in P} a $$ where $$ p = \left(c_{1,1},c_{1,2},\dots,c_{m,1},c_{m,2},a\right)\in\mathbb{R}^{2m+1} $$ are centers of squares and their size. Moreover $$ P=\{p:\forall i=1,\dots,n \; \exists j=1,\dots,m:x_i\in C_j\} $$ where $C_j$ is square given by center $c_{j,1},c_{j,2}$ and size $a$. In the other words, each data point must be covered at least by one square.

My attempt: To use differential evolution to optimize over $P$.

EDIT: Squares cannot be rotated, they are aligned with axes.