Timeline for New considerations for efficient solutions in multiobjective optimization
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15 at 3:27 | comment | added | BADJARA Mohamed el Amine | Exactly; this is what I said in my second comment, in this case, we will find Pareto optimal solutions of rank 1 (or supported solutions: those on the edge or near to the edge) but these solutions are not necessary representative solutions, and there is other ways more simple to find them. | |
| Mar 15 at 3:07 | comment | added | prubin♦ | If you optimize each objective individually and then create a vector in objective space consisting of the optimal values, that is sometimes called the "utopia point". You can then create a weighted distance ($L_1$, $L_2$ or $L_\infty$ metric) and optimize that to get an efficient solution. Changes the weights (or maybe the metric) and repeat a few times. | |
| Mar 14 at 23:12 | comment | added | BADJARA Mohamed el Amine | Also, a center of gravity must be among the efficient solutions that bring to him the other efficient solutions, or may be create clusters among the efficient solutions then choose one solution from each cluster like a location problem, but i do not have a clear idea or a method that can do that. | |
| Mar 14 at 22:29 | comment | added | BADJARA Mohamed el Amine | One of my colleague propose to take the ideal point as center, then search for the solutions with the smallest distance to this point, the idea guide directly to the supported efficient solutions (or Pareto solutions of rank 1), but i search maybe another distance with another point or something like that which has a signinificant meaning in mathematics. | |
| Mar 14 at 22:07 | comment | added | prubin♦ | Any sort of "center" of the solutions will be Pareto-inefficient. | |
| Mar 14 at 21:15 | comment | added | BADJARA Mohamed el Amine | Thanks for your response, this is what we call the interactive methods like STEM method. But those methods have a big inconvenient, the decision maker can accept a solution where he may could wait to improve some objectives to get better. What i search is a principle or an idea that has a mathematics background which when we represent the subsolutions set then I can ignore the others. I could say like a gravity center of all the solutions, but not one but a few solutions that can be considered like that. | |
| Mar 14 at 20:41 | history | answered | prubin♦ | CC BY-SA 4.0 |