🌳Forest implements a simple Forest Evolution Algorithm (FEA). The idea behind Forest is based on the seed dispersal mechanism employed by trees to colonise nearby and far away land areas. Seed dispersal is the movement or transport of seeds away from the parent tree. This implementation is a variant of the Invasive Weed Algorithm (see ref. ➀).

This module is not implemented with speed in mind but, instead, it is a straightforward implementation of the underlying algorithm. If you have any suggestions for speed/feature improvements, please let me know!

In the biology of dispersal, a dispersal vector is an agent transporting seeds (or whatever dispersal units). Dispersal vectors may include biotic factors, such as animals, or abiotic factors, such as the wind or the ocean. Seeding - i.e. seed dispersal - can either be local - i.e. within a dispersal spread around the mother tree (exploitation phase) - or global, in which case, a dispersal vector transports a seed over a long distance away from the location of the mother tree in order to colonise new lands - i.e. exploration phase.

In nature, if a tree does not reproduce, its species becomes extinct. Thus, this leads to the requirement of a competitive exclusion in order to eliminate (not always) those trees that do not reproduce - i.e. potentially "bad" solutions. This is done to limit the maximum number of trees in the forest. Initially, fast reproduction of trees take place and all of them are given a chance to be part of the growing forest. The fitter trees reproduce more than the undesirable ones, however. An elimination mechanism is then activated when the population exceeds a sustainable number of trees within the forest land - i.e. search space.

The FEA model of Forest consists of four phases that are accomplished sequentially, namely

➊ An Initialisation Phase where the initial population is generated to cover the entire search space as much as possible by uniformly randomising individuals within the search space constrained by the prescribed lower and upper bounds.

➋ A Selection Phase (competitive exclusion) where trees with lower metric values might be eliminated from the forest. To do so, the trees are ranked and those with lower fitness values are removed to sustain a sustainable population of trees.

➌ A Reproduction Phase during which the trees will produce seeds based on their relative fitness. Seedlings - i.e. young plants - are created by randomly mutating the DNA of the mother trees. A linear increase in the number of seeds produced by the trees of the forest is considered from a maximum number of seeds for the tree with the lowest value to a minimum number of seeds for the tree with the highest fitness value - i.e. minimisation problem.

➍ A Dispersal Phase where seeds are randomly distributed over the dimensional search space by random numbers drawn from either a normal distribution or a uniform distribution. For each seed, a coin toss decides whether a local or global seeding takes place to ensure constant exploration of the search space.

If you use this module in your projects (whatever those are for!), I would like to hear from you, I am curious! Of course, you do not have to, but you can drop me a line at: romain (dot) wuilbercq (at) gmail.com

Suggestion:

Wuilbercq, R., Forest Optimisation Python Library, 2017.

➀ A. R. Mehrabian, C. Lucas, "A novel numerical optimization algorithm inspired from weed colonization," Ecological Informatics, vol. 1, pp. 355-366, 2006

Copyright (C) 2017 Romain Wuilbercq

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