Mathematical Optimization = finding the best solution base on a given ojective function
Objective function = maximize or minimize
https://ampl.com/resources/the-ampl-book/chapter-downloads/
https://media.readthedocs.org/pdf/scipbook/latest/scipbook.pdf
Linear optimization (a1x1+a2x2+…+anxn) : most basic
– Integeroptimization: more complicate (NP-class)
Ex. find maximum number of chicken and rabbit, while theare are 5 heads and 16 feet.
Non-linear optimization : difficult to solve
-Quadric optimization (x^2+xy) polinomial up to 2 : able to solve by using SCIP (especially if convex function)
To solve
1. define mathematical fomular
- variables :
- x1
- x2
- objective function :
- maximize 25×1+30×2
- contraints :
- 0<=x1<=6000
- 0<=x2<=4000
- x1/200+x2/140<=40
2. write AMPL code from mathematical formular
var XB;
var XC;
maximize Profit: 25 * XB + 30 * XC;
subject to Time: (1/200) * XB + (1/140) * XC <= 40;
subject to B_limit: 0 <= XB <= 6000;
subject to C_limit: 0 <= XC <= 4000;