Dispersive Flies Optimization

This is an implementation in Python (using numpy) of the swarm algorithm called Dispersive Flies Optimization.

The concept is based on the swarming behaviour of flies near food sources. It is a bare-bones swarm intelligence algorithm (i.e. it has very few tunable parameters), where:

1. The exploratory phase is based on randomly altering a fly's coordinates (rather like mutation in a genetic algorithm); and

2. The exploitative phase is based on a fly adjusting its coordinates based on those of its closest neighbour of highest fitness and the fly with the overall best fitness.

The use of the fly with the best fitness has been criticized by some, since this information would not be available to flies in real swarm intelligence; the authors of the article, however, have stated that it is unneccessary, and I will be doing experiments where it can be disabled to see how performance compares.

The article for the Dispersive Flies Optimization can be found here:

https://annals-csis.org/Volume_2/pliks/142.pdf

It is also described on Wikipedia:

https://en.wikipedia.org/wiki/Dispersive_flies_optimisation

Along with the implementation are two programs to employ the algorithm:

1. An implementation that chases a mouse cursor around a window in two dimensions; and

2. An implementation to find Steiner systems.

A S(t, k, v) Steiner system is a set of k-sets from a v-set such that every t-set appears in exactly one k-set. A simple example is S(2, 3, 7), the Steiner triple system of order 7, also denoted STS(7). Let {0, ..., 6} be the v-set. The STS(7) is thus, unique up to isomorphism, of the form:

{0, 1, 2}
{0, 3, 4}
{0, 5, 6}
{1, 3, 5}
{1, 4, 6}
{2, 3, 6}
{2, 4, 5}

This is also called the Fano plane and is the projective plane of order 2.

More on Steiner systems can be read at:

https://en.wikipedia.org/wiki/Steiner_system

The algorithm is able to find an STS of order 9 with relative ease:

(0, 1, 3)
(0, 2, 5)
(0, 4, 6)
(0, 7, 8)
(1, 2, 7)
(1, 4, 8)
(1, 5, 6)
(2, 3, 4)
(2, 6, 8)
(3, 5, 8)
(3, 6, 7)
(4, 5, 7)