Animations with Quarto/Reveal.js and SVG.js

Based on the animate plugin by @rajgoel

Animated Heart

Monty Hall Problem

Linear Program

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 \(M\)