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Calculating Point on Pareto Front with Minimum Distance from Utopia Point

  • 11 October 2019
  • 4 replies
  • 156 views

Dear all,
I want to find the point on the pareto front (obtained with the epsilon constraint method) that has the minimum distance from the utopia point.
How can I do this in aimms?
Thanks
Best
Grazia
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Best answer by mohansx 30 July 2021, 23:04

@graleo would a goal programming approach work for you ? Use the utopia point as the target for each objective and minimize the deviation from this point which will give you a solution that is feasible and is closest to the utopia point. 

 

An example is here: Goal Programming — AIMMS How-To

 

@sjatty what difficulties are you having with implementing epsilon constraint method ? It is fairly straight forwad. If you have two objectives, y1 and y2, you introduce an additional constraint that limits the value of y2, say y2 <= epsilon2 and then use y1 as the objective function in the math program that you are solving. Or vice versa, solve for minimizing y2 and introduce an epsilon constraint for y1. 

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4 replies

Dear all,
I have the extreme points of the pareto front, (x1,y1) and (x2,y2) and the utopia point.
I would like to calculate the point on the pareto with the minimum distance by the utopia.

Then I think that I should create a cycle as
for x1<=epsilon_o<=x2 and y1<=Total_Costs_o<=y2
do
min_=( (utopia_x-epsilon_o)^2 + (Total_Costs_o-utopia_y)^2)^0.5

what do you think?
Is it correct? It seems that an error is preset. Which is parameter and variable?
Best
GL
Badge

Hello GL, 

I seem to be having issues implementing epsilon constraint method in AIMMS, have you been able to resolve your issues around getting the pareto curve? If yes, what worked for you to generate the pareto solutions? 

 

Best, 
sjatty

Userlevel 5
Badge +2

@graleo would a goal programming approach work for you ? Use the utopia point as the target for each objective and minimize the deviation from this point which will give you a solution that is feasible and is closest to the utopia point. 

 

An example is here: Goal Programming — AIMMS How-To

 

@sjatty what difficulties are you having with implementing epsilon constraint method ? It is fairly straight forwad. If you have two objectives, y1 and y2, you introduce an additional constraint that limits the value of y2, say y2 <= epsilon2 and then use y1 as the objective function in the math program that you are solving. Or vice versa, solve for minimizing y2 and introduce an epsilon constraint for y1. 

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@mohansx Thank you for your feedback. I realize that the issue with my code is prior to solving the epsilon constraint method. I have opened another thread for that and would appreciate any help you can provide

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