As we known, to solve a multi-objective optimization problem, there are two choices: (1) Aggregating the objectives into a single objective by weighting and summing them up, and then the obtained single objective problem is solved by GA, PSO, etc. (2) Developing the multi-objective EAs to generate a Pareto solutions.
Now, I have two objectives with different scales and different meanings.
And my question is: Does it meaningful if I use choice(1)? Are there any conditions that the objectives must meet when using (1)? Does it meaningful by comparing (1) with (2) experimentally?
I ask you all for valuable comments. [References] are appreciated.
Thank you in advance.
Hi Zhongyi,
(1) If you are able to define a proper scalariziation function to aggregate these two objective values, I think the scalarization function is a reasonable choice.
(2) However, if you find that you need to try many different scalarization functions or many different sets of weights, it might be better to find out the Pareto set and then select your favorite solution. You can also find the Pareto set based on scalarization functions. For example, check Prof. Q. Zhang's MOEA/D.
http://dces.essex.ac.uk/staff/zhang/webofmoead.htm
Please note that the choice of the scalarization function could affect the solution quality. The paper from Prof. Ishibuchi may give some information:
http://link.springer.com/content/pdf/10.1007%2F978-3-642-01020-0_35.pdf
(3) Assume that we are minimizing two objectives, I think that a typical result of these two kinds of methods would like this: ('x' from scalarization method and 'o' from Pareto method)
| o
| o
| o
| o
| * o
|______________o______
It would not be easy to compare them. For a certain aggregated objective, the scalarization method would be better; however, the Pareto method provides more information on the distribution of the solutions and more choices. It depends on what you really want.
Hope it's useful to you. :)
https://www.researchgate.net/publication/297245624_Particle_Swarm_Optimization_Algorithm_and_its_Codes_in_MATLAB
Research Particle Swarm Optimization: Algorithm and its Codes in MATLAB
https://www.researchgate.net/publication/296636431_Codes_in_MATLAB_for_Particle_Swarm_Optimization
Code Codes in MATLAB for Particle Swarm Optimization
- Badges
- Science topic
- Similar topics
- Linguistics
- Philology
- Classical Philology
- Manuscripts