Physics Bucharest 2017

6/3/2017

The inverse problem

A simple optimization problem: “A manufacturer needs to make a cylindrical can that will hold 1.5 liters of liquid. Determine the dimensions of the can that will minimize the amount of material used and as such the COST of its construction.”

“The search for the best independent variable value which results in minimal cost”

start

r=18 A=2206

r=16 A=1799

r=13 A=1294

r=10 A=929

r=6 A=727

r=4 A=851

⇒ ℎ = 1500 ଶ The analytic result is 6.20350491

Minimise A  3000 r

 2  r 2

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The inverse problem

Independent variables

Optimization can involve:

Intensity profiles Beam weights, segment weights Beam angles (gantry angle, couch angle) Number of beams Energy (especially in charged particle therapy) Type of radiation (photons, electrons, ...)

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