I would go for Pareto dominance approach. However the result is strongly coupled with the optimization algorithm, number of objectives and the shape of Pareto front.
You can look into Costa, Nuno R; Lourenço, João; Pereira, Zulema L. 2011. "Multiresponse Optimization and Pareto Frontiers", Quality and Reliability Engineering International 28, 7: 701 - 712. doi: 10.1002/qre.1262 to find an easy-to-imlement and easy-to-use approach for multiresponse optimization of problems developed under the Response Surface Methodology framework.
For general theoretical optimization, we can say the second, since weighted sum method (even with variable weights) cannot reach (to be as rigorous as possible, it can reach but sub-optimaly) the pareto-optimal solutions of non convex part of the Pareto frontier. However, when applied on a special field the (pure) Pareto approach cannot deal with preferences between objectives witch is an intrinsic feature of actual problems. When the problem is intractable, the solution is then to use some kind of Pareto approach guided with the problem specific preferences.
You may also want to look at a MO-TLBO method (teaching-learning-based optimization).
Other (interesting/good/effective and easy-to-apply) alternative:
1-Messac, A., Gupta, S. M., and Akbulut, B., “Linear Physical Programming: A New
Approach to Multiple Objective Optimization,” Transactions on Operational Research,
Vol. 8, Oct. 1996, pp.39-59.
2- Messac, A., “Physical programming: Effective Optimization for Computational Design,” AIAA Journal, Vol. 34, No. 1, January 1996, pp. 149-158.
I think pareto dominance approach is better for most multi-objective optimization problems. The summed objective makes no sense in reality and the weight is hard to determine.
Liu said:
- summed objective makes no sense in reality - I'm not sure about it; depends on the methodology used to solve multiresponse problems and problem in itself!
- weight is hard to determine - Yes, it is true. However there are alternative approaches to overtake this issue in some situations.
References presented below, among others, discuss these issues:
Rönnqvist M (2012). OR challenges and experiences from solving industrial applications. International Transactions in Operational Research 19(2): 227-251. Costa, Nuno R; Lourenço, João; Pereira, Zulema L. 2011. "Multiresponse Optimization and Pareto Frontiers", Quality and Reliability Engineering International 28, 7: 701 - 712. doi: 10.1002/qre.1262
Marler R and Arora J (2010). The weighted sum method for multi-objective optimization: some insights. Structural and Multidisciplinary Optimization 41(8): 853-862.
Dear Liu, I agree with Nuno costa. The convergence characteristic of algorithm that use weighted sum method is superior than pareto dominance based approach.
please send me anyone have matlab demo code of weighted sum approch to generate approx pareto front.
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