Dear Arash Olia,

NSGA-II offers a range of  solutions while heuristic and meta-heuristic algorithms search only for a single solution. NSGA-II tries to find a good trade-off between some conflicting objectives. More precisely, we provide a set of solutions for user and the user can choose one of them according to some criteria (it is also possible to use some computer methods to do so). The performance of a multi-objective algorithm such as NSGA-II strongly depends on its diversification components. 

Dear Hojjat Rakhshani,

Thanks for the answer. May you please explain more about "diversification components" and how it can be achieved?

Thanks again, 

Hi,

For multi-objective optimization, there is no a single global solution, but rather a set of Pareto-optimal solutions (a solution is Pareto optimal if none of the objective functions can be improved without degrading some of the other objective values). NSGA-II is a stochastic evolutionary multi-objective algorithm, that, as Hojjat pointed, produces a complete set of Pareto-approximated solutions in one single run. The performance of multi-objective algorithms is measured using the solutions they output, this could be done using different metrics: 1) Generational Distance, 2) Hypervolume 3) Unary-epsilon 4) R2 5) Spacing, and several others.

Check the attached link to the MOEA framework, where several of these metrics are implemented in JAVA. The references below are for some readings about metrics and an application of NSGA-II with hyper-heuristics.

Deb, K., & Jain, S. (2002). Running performance metrics for evolutionary multi-objective optimization.

http://moeaframework.org/features.html

Article Building general hyper-heuristics for multi-objective cuttin...

Thanks Juan, Two questions;

Thanks

Hi,

1. Indeed you can use hypervolume to compare the performance of the same algorithm (NSGA-II) in differente runs.

2. I already attached a link to the MOEA framework which allows to compute several measures.

Best

You received excellent answers, and I can only add one detail: for many practical real-world problems, it is not possible to compute the exact hypervolume, so it can be hard to assess NSGA-II's performance.

However, in those cases, NSGA-II is usually one of the few methods that are able to return an acceptable result in a reasonable amount of time.

Thanks, my understanding is that there is no explicit for the multiobjectie optimization problems in NSGA algorithm. The goodness of fit is based on the non-domination ranks of solutions. Is that correct?

I used NSGA-II for a problem that was solved used dynamic programming and the performance was excellent.

Optimal Planning and Scheduling for Repetitive Construction Projects

https://www.researchgate.net/publication/228904075_Optimal_Planning_and_Scheduling_for_Repetitive_Construction_Projects?ev=prf_pub

Article Optimal Planning and Scheduling for Repetitive Construction Projects

Hi Khaled,

I reviewed your paper. Very helpful. My question is that you mentioned that:

To my best on knowledge, binary tournament selection is employed to select the pair of parents. That is, randomly to random solution selected, the one with better rank would be one of the parent and the second one selected exactly based on the same process.

May you please explain about the selection process of parents in your paper? Also, how you evaluated the fitness functions? you mean objective functions?

Thanks,

The performance of NGSA is terrible. However, the point is that when there is no additional information about the underlying function being optimised, and when there are multiple conflicting objectives, probably with additional non-linear constraints, NGSA works at all. For many practical applications the fact that it often does find a good tradeoff curve, happily skipping large numbers of local minimal, is awesome. If you have the luxury that you can use something better, great, but if you need a workhorse algorithm that at the end of the day does the job without having to fine-tune a dozen numerical knobs for each individual application, NGSA is your best bet.

Dear Arash

I used NSGA-II to solve a supply chain network problem. I attached our recent paper which has published in Neural Computing and Applications Journal. In this paper, we much more emphasised on computational analysis. We discussed the performance evaluation of NSGA-II by using several performance metrics and statistical analysis. I hope this paper give you some insights. In addition, for more details, you can refer to this valuable text books: Metaheuristics: from design to implementation, Talbi 2009

Article A tuned NSGA-II to optimize the total cost and service level...

Dear Arash,

Indeed, comparing performance of multi-objective optimization algorithms requires very detailed reports. In first link, you can see an example of such consideration. For a more general comparison, you can use the other papers which are the most cited in this regard.

http://www.sciencedirect.com/science/article/pii/S009813541300241X

http://e-collection.library.ethz.ch/eserv/eth:25454/eth-25454-01.pdfysis and Review

http://link.springer.com/chapter/10.1007%2F978-3-540-88908-3_14

http://www.macs.hw.ac.uk/~dwcorne/onmetrics.pdf

Dear Arash,

I think you are trying to handle multiple objectives, which are strongly conflicting each other. In the literature many optimization techniques are available for handling this situation, among these NSGA-II is one of the approach. Before going to choose a particular meta-heuristic, you must aware of your problem falls under which category like whether continuous or combinatorial etc. Then, to choose a relevant  meta-heuristic, that can efficiently handle your problem, generally before conclusion of paper they indicate which type of functions, it work better way. For example NSGA-II work efficiently for combinatorial problems whereas NSPSO work well for continuous functions. Just I mentioned these two, please go through the literature recently many improved techniques proposed that works better these like CRO (Chemical Reaction Optimization) for multiple objectives and many.