Hello, I have another questions for the experts who are all giving much great advice on multi-objective optimization.
I have another problem, a bi-objective one so that I am planning on using the much used NSGA-II to solve it.
I am trying to decide the parameters(population, iteration, mutation, crossover rate) and was wondering if people could direct me as where best to start or maybe the most recommended default setting.
For example, I have seen a lot of paper with population 20~100, generations 500, mutation=0.1 or less, and crossover=0.9 .
I am thinking of starting with these (with population 100). Do you think that its okay?
Also, could anyone suggest any papers as to why these figures are so often used?
Also, I am thinking of working my way through a sensitivity analysis where I change the parameters a bit as recommended by other answers.
How do I know how much to much the parameters by and how well the algorithm is performing?
If it helps, my optimization problem is
Objective functions f(x,y,z)
Minimize 0.210/x + 0.067/y+ 0.001/z+ 0.443/x*y+ 0.0006/x*z+ 0.010/y*z+ 0.160/x*y*z
and
Minimize 33*x+ 1*x*y+1*x*y*z
Variable Bounds:
x= 15~268
y= 2~15
z= 2~15
Constraint:
x,y,z are all integers
Thank you all in advance for all your help.
This is my experience.
I often test the next parameters and 30 independent runs:
- population size: 50, 100, 200
- number of generations: 100, 200, 500
- mutation probability: 0.1, 0.2, 0.5, and sometimes 0.8, 1.0
- crossover rate: 0.9, 0.8, 0.6
In population size, number of generations, and mutation probability I always starts with the lower values. In crossover rate start in a decreasing way. The population size and the number of generation have an impact in the execution time of the algorithm. Also, something I like to do is to check in which generation the best fitness value is achieved.
Well, I hope this helps you.
With my experience, more the population size, more the number of generations should be to get proper convergence to optimised value. Mutation and cross over rates are just to induce differences, however convergence of the best fitness value will occur more or less at the same value, provided your data is good.
Dear Cassie Suh
You can find the appropriate parameter values for your evolutionary algorithms (EA) through of tuning methods such as Taguchi experimental design methods.
attached some references to articles that can help you solve your problem.
Eiben, A. E., & Smit, S. K. (2011). Evolutionary algorithm parameters and methods to tune them. In Autonomous search (pp. 15-36). Springer Berlin Heidelberg.
link: http://link.springer.com/chapter/10.1007%2F978-3-642-21434-9_2#page-1
Apply Method
*Sadeghi, J., & Niaki, S. T. A. (2015). Two parameter tuned multi-objective evolutionary algorithms for a bi-objective vendor managed inventory model with trapezoidal fuzzy demand. Applied Soft Computing, 30, 567-576.
link: http://www.sciencedirect.com/science/article/pii/S1568494615001040
*Sun, J. U. (2007). A Taguchi approach to parameter setting in a genetic algorithm for general job shop scheduling problem. IEMS, 6(2), 119-124.
Dear Cassie Suh,
The value of parameters can be selected according to existing experiences or you should conduct you own experiment. If you do so, factorial experimental design methods are helpful due to their time efficiency (as an example you can use Taguchi method as mentioned by Jesus Armando Beltran). You can also see the following links.
https://en.wikipedia.org/wiki/Factorial_experiment
https://en.wikipedia.org/wiki/Design_of_experiments
https://en.wikipedia.org/wiki/Taguchi_methods
My experience: generation is 500 ~ 100. Population is 200, Pc = 0.6, Pm = 0.01
Using exhaustive (brute-force) search is the best approach here because your search space is extremely small. In fact, a population size of 100 and 500 generation leads to MORE function evaluations than your entire search space. That doesn't make any sense. NGSA-II is a 'last-resort' algorithm that works wonderful when everything else fails, but because of its stochastic nature there are no guarantees. With exhaustive search on the other hand you are 100% sure you get the correct Pareto front, and in your case this can be done in far less than a second on a smartphone. Good luck.
As far as I know, the variables are strongly related with the size of the problem. As Bas Van der Geer said, for small problams is even better to use exhaustive search through the whole set of solutions. I'm still researching the NSGA-II algorithm, but with Genetic Algorithm I use a population N at least bigger than the number of variables and a mutation rate of about 1/N. The experiments we did with crossover showed that a rate of 80% is good enough.
For NSGA-II I'm starting with a population of NDV times NO, where NDV is the number of decision variables and NO is the number of objetives. Unfortunately, I have no results yet of its performance.
Best regards.
In case if someone is using a multi-objective genetic algorithm, one may understand these parameters by practice this tutorial:https://ariadacapo.net/blog/2019-12-18-genetic-optimization-with-dakota-2-3-a-sandbox-for-experimentation/
I did an extensive sensitivity test to benchmark my GA. My suggestion is 80% crossover, 10% elite size, and 10% mutation probability. There is a trade-off between the number of generations (5000) and population size (250). Although these parameters are problem-specific, you can try them.