Dear Luis, 

My first idea would be, as you suggested, to penalise the individual leading to a non-convergent reliability index, i.e. instead of NaN assigning 0 (if 0 is the worst possible reliability index). Alternately, you may want to test:

• (i) for a nearby individual (if your index is highly nonlinear, a neighbouring point might converge);
• (ii) for an approximate value of your index (maybe you can interpolate from previous solutions or calculate differently your index).

Hope it can help.

Pierre

Although still a very respectful and useful algorithm, the NSGA-II is a bit outdated. If you do not manage to solve the problem you could try the BORG algorithm which is known to ouperform NSGA-II (check out http://borgmoea.org/) and is freely available to academic and non-commercial users. 

Cheers,

Riccardo

you can try Elitist Multiobjective Genetic Algorithm in matlab (2013 version) which is better then controlled elitist genetic algorithm (a variant of NSGA-II )

g

ood luck 

Hybrid GA with PSO (Particle Swarm Optimization) has been proven to be a good tool for these cases. Basically instead of fitness, using similarity metric could be a good solution. In this case there will be more than one sub-cohort with possible (semi) optimum, and the one with the highest velocity & similarity index will be the best solution one can get under the circumstances. 

One of the main tools to harness the strength and to improve convergence of any GA, including MOEAs (e.g., NSGA-II) is to inject an heuristic perturbation operator with its characteristic components (e.g., in its crossover or mutation operator). The heuristic operator should inspire its logic from the problem at hand to improve one objective or the other or even, when more intelligently design it, to improve both objectives.

Dear Louis,

In my opinion, to design a good search algorithm needs to deal well with balance between exploration and exploitation. In the early stage of the search, diversity is important for exploring promising area of the search space. In the later stage, when the promising area has been located, a refined search is needed to quickly find the (near-) optimum.

So in your case, as you said, you could just punish the bad individual or eliminate them. In addition, you may try the following method at every generation of the evolution process: 

(1) Find the best individual in the population at the current generation.

(2) Randomly, and Slightly perturb it to generate some new individuals.

(3) Replace the worst individuals in the population with these new individuals.

Cheers, Xin

Thank you for your comments and suggestions.

 I think that it would eliminate the individuals when I can obtain reliability indexes for them.

Then population size can be different in each generation: larger in the initial generations and smaller in the last generations.

Hello I want to use the SGNA II algorithm in converge but I don't know how to go about it. I would like to have your help here is my email: [email protected]