In the case, of many objective models, the epsilon constraint method has been seen as an efficient approach. This method is considered an exact approach and existing literature has discussed much about it. So I have two following questions:
1. How to implement this method (share the link in case of any source code available).
2. What are the other similar/different exact methods available for dealing with many objective problems.
#OperationResearch #Closed-loopSupplyChain #Optimization
Hello,
For the epsilon constraint method, the basic idea is to keep one objective to optimize and transform the others into constraints (less or equal to a certain epsilon value in the case of minimization). Epsilon values can vary among the feasible domain of each objective.
For each version of your problem (depending on the kept objective function), you obtain single objective problems to optimize, and through the variation of epsilon values you can plot your pareto front.
The other very well know exact method is the weighted sum, in which you use an aggregated function of the weighted objectives.
Dear Yasmine
This is approximately the way in which the SIMUS method works
Vivek
The SIMUS method is the answer to your question
If you need more information and even the SIMUS software, (free) pls write me
Dear professor Nolberto Munier Thank you for your time. Yes, it would be great if you give an idea about the SIMUS method.
Thank you in advance.
Thank you so much Yasmine Alaouchiche for giving this wonderful explanation to my question. I am working on this method currently.
Dear Vivek
SIMUS starts from the initial decision making and considers that objectives and criteria are the same thing, because both have identical algebraic properties. Then a criterion can be used as an objective
In SIMUS the software selects the first criterion, removes it from the initial matrix, and uses it as the objective function, which is subject to all the remaining criteria. Using the Simplex algorithm it finds the optimal solution.
It then replaces the extracted criterion and selects the second criterion as an objective function. This process is repeated until all the criteria have been used as objective functions
After that, it adds up the scores obtained by each alternative, and this sum is multiplied by a weight that depends on the number of times the alternative satisfies all criteria. Thus, the best alternative is chosen
Nolberto Munier Thank you professor For this idea. Sure I will try this, it looks new and interesting too.
You can follow this research:
I am welcome any cooperation.
Article Multi-objective models for biomass supply chain planning wit...
You are welcome Vivek Kumar Chouhan
For an application, I have used epsilon constraint to solve a bi-objective optimization problem in manufacturing systems in this paper: https://ieeexplore.ieee.org/abstract/document/9667349
I also compare it to the weighted sum and the genetic algorithm NSGA-2, it could help you find out how and what to put it in practice for your problem.
Thank you so much Yasmine Alaouchiche . I will go through this article.
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