Repository with some of the evolutionary algorithms to solve problems, highly recommend used Google Collab. If you wan't to know more of this topics (Spanish language), please check this link: https://drive.google.com/file/d/1H2VfEJNmvxyQP3iDVBxPZsBzEpiWL7zR/view?usp=sharing
DP is a paradigm that solves problems by combining subproblems once then saving the result. This subproblems overlapping and the principal characteristics are: - Using to optimizing problems. - They can have many solutions. - Each solution we can found, one solution with a local optimal value (maximum, minimum). - We can reconstruct which values are part of the solution.
Problems to solve:
- Snapsack problem.
- Coin Change.
- Stairs.
Problems to solve:
- Matrix Chain Multiplication.
It refers to a series of steps to solve a problem then when combining it with genetics, simulate the evolution of species to formulate the steps to follow with the same objective to solve problems.
Problems to solve:
- Genetic Algorithm (GAS) to minimize Ackley's function in 2D.
- GAS to minimize Rastrigin's function in 3D.
Combinatorial optimizations are problems where the solution space is made up of subsets, subarrays, but finding a solution set is very complicated even for moderate-sized problems, so genetic algorithms help us to find a valid solution or a good approximation.
Problems to solve:
- GAS to Knapsack problems with a total weight (0,1) and 20 items random integer values in the interval [1,100].
- GAS to TSP problem for 7 cities.
A Fractal is a type of mathematical shape that are infinitely complex. In essence, a Fractal is a pattern that repeats forever, and every part of the Fractal, regardless of how zoomed in, or zoomed out you are, it looks very similar to the whole image.
Problems to solve:
- Draw a landspace with fractals. reference: http://www.fgalindosoria.com/ecuaciondelanaturaleza/
This idea starts from the observation of what a swarm is (a large group of individuals such as animals, people, etc.) that has movement, that is, they move together.
Problems to solve:
- PSO to minimize Ackley's function in 2D.
- PSO to minimize Rastrigin's function in 3D.
Once again Alan Turing makes a biological proposal called morphogens, of the last publications before dying where the cells of an organism in an early stage of its development are visualized as a collection of "cells" that have communication and influence from the closest neighbors.
Problems to solve:
- PS in 2D with nearest neighbor interactions in a grid.
- PS in 2D with collisions.
Self-organizing maps are a type of neural network with competitive learning since influence and intertia are combined to avoid minimizing error, resulting in a better understanding of the problem.
Problems to solve:
- SOM using at least 10 indicators about at least 40 countries from the database in the World Bank
The Game of Life
Problems to solve:
- S = infinite rectangular grid.
N = {closest neighbors} U {self}
Q = {0,1,2}
δ = (b1, b2, s1, s2, u1, u2, r1, r2)
- S = Infinite 1-D grid.
N = {First 2 layers of closest neighbors} U {self} (| N | = 5)
Q = {0,1}
δ = W110 and δ = W110R