NSGA-II/SPEA2 Convergence and Diversity

[Jannie]

Hi I'm a new user of DEAP and MOEA problems and find DEAP is very useful to implement multi-objective optimizations. Thanks all the developers!

After successfully tested out NSGA-II and SEPA2 for a simple three-objective Knapsack problem, I would like to use some performance measures including Convergence rate and Diversity of the solutions to compare the performance of the two algorithms. 

I've found deap.benchmarks.tools.convergence(first_front, optimal_front) and deap.benchmarks.tools.diversity(first_front, first, last) on the benchmark page but not sure if these are the correct tools to address my problem and how to use them. For example, what should I put as "first_front"? What are the extreme points "first, last" I should use? As my problem is to selecting an optimal set of projects from a list of projects, I don't really know the true optimal pareto front of the problem.

It would be great if anyone can give me some ideas or an example to learn. Thanks!

Best,

Jannie

[François-Michel De Rainville]

The first front is the pareto front found the optimization. You cannot test for convergence if you don't know the optimal front. As for the first and last they are the extrema of the optimal pareto front. You could always estimate those. 

As for benchmarking for you problem without knowing the optimal pareto front, I would track the hypervolume of the pareto front. You can use the (undocumented) hypervolume function from the tool._hypervolume module with a arbitrary reference in d^N. Front is your the first pareto front given by sortNonDominated.

try:

# try importing the C version

from deap.tools._hypervolume import hv

except ImportError:

# fallback on python version

from deap.tools._hypervolume import pyhv as hv

# Must use wvalues * -1 since hypervolume use implicit minimization

# And minimization in deap use max on -obj

wobj = numpy.array([ind.fitness.wvalues for ind in front]) * -1

ref = EXTREMA_POINTS_OUTSIDE_YOUR_DOMAIN

hypervolume = hv.hypervolume(wobj, ref)

Cheers,

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[Jannie]

Hi François-Michel,

Thank you for the quick response. Based on your suggestions, I'm able to track the hypervolume and diversity during each generation. Many thanks!

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