A Python implementation of the NSGA-II algorithm (Kalyanmoy Deb, Samir Agrawal, Amrit Pratap, and T. Meyarivan. 2000. A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II, link)
The algorithm uses dynamic programming techniques to find all of the Pareto fronts in a given set of points. A naive approach where the algorithm for finding a Pareto front (which itself has a complexity of O(mN^2) where m is number of objectives and N is number of elements) is repeated after removing the elements belonging to the found front from the population would have a computational complexity of O(mN^3). The file pareto_front.ipynb uses this simple algorithm. With NGSA-II this complexity is reduced to O(mN^2) with the cost of increased memory complexity. This algorithm is implemented in pareto_fronts_dynamic.ipynb.
Given an example set of data points representing the mass-price tradeoff in bicycles where y axis is weight in kg, and x axis is the price of the bike:
the algorithm produces the list of Pareto fronts like this:
