I have used epsilon constraint method as well ass the sum weighted method to find Pareto point for bi-objective model;in this case I have found same results ,same number of Pareto points,
can we claim which our bi-objective model is not non-convex if the results raised from epsilon constraint method and the sum weight method are same?
I should think that it depends on the original data; it could, for example, be that you have found the same solution in both cases, but it is not a global one.
Dear Iman,
Please see answer of similar question posed through ResearchGate Jul.26, 2015 here is folowing link :
-Model : weighted sum multi objective.Can I use one of the objective in ...
https://www.researchgate.net/.../Model_weighted_sum_multi_obje...
Also i suggest to you a links and attached files in topics.
-Patent EP2575965A2 - Multi-objective radiation therapy optimization ...
https://www.google.ch/patents/EP2575965A2?cl=en
-Patent WO2011153639A2 - Multi-objective radiation therapy ... - Google
www.google.com/patents/WO2011153639A2?cl=en
Best regards
Dear Iman,
Could you be a bit more precise? Are you wanting to give evidence that the feasible region is convex, that the objectives are convex, or both?
Dear Adam,
yes,I tend to proof that my model,including region and objectives are convex.
Then, I think that, in general, just looking at the efficient solutions is not sufficient. Suppose you have just two continuous variables, x and y, and that your feasible region is defined by the following two quadratic constraints:
x^2 + y^2 = 1.
This feasible region is non-convex, but if your objectives are max x and max y, then the weighted sum and epsilon-constraint methods will give the same efficient frontier, namely, the region:
(x,y): 0
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