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I Help me solve this chemical engineering NLP optimization problem, All you have to do is write me what to paste in Gams. QUESTIONProblem 4
I Help me solve this chemical engineering NLP optimization problem, All you have to do is write me what to paste in Gams. QUESTIONProblem points
Three columns of equal height and different diameter are available, with values of
and respectively. Determine the minimum available space
perimeter in the plant for their placement. Below I have provioded the expected explanation that you have to develop into gams codeApproach Erom Class Example
Diagram
Problem Setup
Objective: Arrange three cylindrical columns with diameters of
and respectively, within a rectangle to minimize the
perimeter of that rectangle.
Two possible objective functions: Minimize AB and the other using
Minimize AB Both approaches will use the same set of variables
and constraints but will differ slightly in the objective function to illustrate
the different emphasis each approach brings.
General Setup for Both Approaches
Decision Variables
: coordinate of the center of the ith cylinder nd :coordinate of the
center of the th cylinder. Hence X :;;
Rectangle Dimensions A: Length of the rectangle &B: Width of the
rectangle.Constraints
Nonoverlapping Constraints
The distance between the centers of any two cylinders must be greater
than or equal to the sum of their radii:
For Cylinder and
For Cylinder and
For Cylinder and
Cylinder Position
For each cylinder to be fully inside the box, we have the following constraints:
For cylinder
;;
For cylinder
and ;
For cylinder :
;Approach Erom Class Example
Diagram
Problem Setup
Objective: Arrange three cylindrical columns with diameters of
and respectively, within a rectangle to minimize the
perimeter of that rectangle.
Two possible objective functions: Minimize AB and the other using
Minimize AB Both approaches will use the same set of variables
and constraints but will differ slightly in the objective function to illustrate
the different emphasis each approach brings.
General Setup for Both Approaches
Decision Variables
: coordinate of the center of the ith cylinder nd :coordinate of the
center of the th cylinder. Hence X :;;
Rectangle Dimensions A: Length of the rectangle &B: Width of the
rectangle.
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