THE ORDERED CUTTING STOCK PROBLEM 1D - USING GENETIC ALGORITHMS

The Standard Cutting Stock Problem is characterized by cutting stock rolls of width W (called objects) into smaller rolls of width Wi (where W>Wi), aiming at satisfying the demand di for each one of these m items.

Each combination of items in an object is called the cutting pattern, and each change in the cutting pattern has a setup cost to prepare the cutting machine.

practical example:
Suppose you need to cut smaller rolls (wi) of the following lengths
[1000,2000,3000,4000,5000,6000,7000,8000,9000,1000,
1000,2000,3000,4000,5000,6000,7000,8000,9000,1000]

After running the Genetic Algorithm the cutting pattern: