In this article, we present a detailed overview of the literature on the design of computer
experiments. We classify the existing literature broadly into two categories, viz. static and …

There are many interesting optimization problems associated with the packing and covering
of objects in a closed volume or bounded surface. Typical examples arise in classical …

In one sense, the problem of finding the densest packing of congruent circles in a square is
easy to understand. But on closer inspection, this problem reveals itself to be an interesting …

In this paper the problem of packing n equal circles into the unit square will be considered.
Starting from a general rectangular branch-and-bound algorithm, many tools, which exploit …

Given a fixed set of identical or different-sized circular items, the problem we deal with
consists on finding the smallest object within which the items can be packed. Circular …

The problem of maximizing the radius of n equal circles that can be packed into a given
square is a well-known geometrical problem. An equivalent problem is to find the largest …

The densest packings of n equal circles in a square have been determined earlier for n≤ 20
and for n= 25, 36. Several of these packings have been proved with the aid of a computer …

The problem of finding the maximum diameter of n equal mutually disjoint circles inside a
unit square is addressed in this paper. Exact solutions exist for only n= 1,…, 9, 10, 16, 25, 36 …

Densest packings of eleven congruent circles in a circle Page 1 Geometriae Dedicata 50: 15-25,
1994. 15 © 1994 KluwerAcademic Publishers. Printed in the Netherlands. Densest Packings …

Dense packings of n congruent circles in a circle were given by Kravitz in 1967 for n= 2,...,
16. In 1969 Pirl found the optimal packings for n≤ 10, he also conjectured the dense …