I have two objectives, one is product purity and the other one is total annual cost. I would like to optimize distillation column using 'fmincon' function of Matlab. In this regard if i club these two objectives into a single objective. Is it correct to do so.
You can make the objective function a combination of product purity and cost if that is really what you want. You could also add individual constraints on both purity and cost to see which one is constraining or to drive an objective function to achieve the best combination of the two constraints. More details about your problem would probably be helpful.
You can use (Product Purity = P and Cost=C):
Objetive = X1*P + X2*C
Where X1 and X2 are weights (fit dimensions of the problem) between 0 and 1.
I would think that greater the purity of the product, more expensive the process is. Therefore, I recommend carrying out a sensitivity analysis to obtain a pareto front, this is achieved by varying X1 and X2, in such a way that X1 + X2 = 1.
For example in the first iteration:
X1 = 0; X2 = 1, then optimizes the process economically (minimize the cost).
X1= 0.1; X2= 1-X1,
.
.
.
Last iteration:
X1 = 1; X2 = 0, then you maximize the purity of the product.
Once finished, all points will be optimal (non-dominated) and you can use a decision making tool in order to select the optimal point that most favors.
Another option is to impose a purity as a constraint (>99%) and optimize the cost of the process.
Dear Andres Felipe Abril Duran, your suggestion is helpful to me. I would like to know the last point :
' Another option is to impose a purity as a constraint (>99%) and optimize the cost of the process '
Can u guide me how to use this constraint while using fmincon in matlab.
Thanks dear
Quality has a financial value. You can combine it with total cost if you can put relative values on the two components.
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