Animations with Reveal.js and SVG.js

Created by Asvin Goel

Monty hall problem

Graphical solution procedure

Multiple corner point solutions

Simplex algorithm

Linear relaxation and rounding

Integer enumeration

Branch and bound

Solution: $(x,y) = (3.8,3)$ Branch $x \geq 4$ Branch $x \geq 4$ ⟶ $(x,y) = (4,2.9)$ Branch $x \geq 4$, $y \geq 3$ Branch $x \geq 4$, $y \geq 3$ ⟶ infeasible Discard branch: $x \geq 4$, $y \geq 3$ Branch $x \geq 4$, $y \leq 2$ Branch $x \geq 4$, $y \leq 2$ ⟶ $(x,y) = (4,2)$ $(x,y) = (4,2)$ is an integer solution Branch $x \leq 3$ Branch $x \leq 3$ ⟶ $(x,y) = (3,2.6)$ Branch $x \leq 3$, $y \geq 3$ Branch $x \leq 3$, $y \geq 3$ ⟶ infeasible Discard branch: $x \leq 3$, $y \geq 3$ Branch $x \leq 3$, $y \leq 2$ Branch $x \leq 3$, $y \leq 2$ ⟶ $(x,y) = (1.8,2)$ Branch $x \leq 3$, $y \leq 2$, $x \geq 2$ Branch $x \leq 3$, $y \leq 2$, $x \geq 2$⟶ $(x,y) = (2,2)$ $(x,y) = (2,2)$ is an integer solution Branch $x \leq 3$, $y \geq 3$, $x \leq 1$ Branch $x \leq 3$, $y \geq 3$, $x \leq 1$ ⟶ $(x,y) = (1,1.6)$ $(x,y) = (1,1.6)$ is worse than best integer solution All branches solved, $(x,y) = (2,2)$ is optimal

Big-M constraint

$y \leq 1 + M(1-z)$ with $z=1$

Big-M constraint

$y \leq 1 + M(1-z)$ with $z=0$ and sufficiently large $M$

The end

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