1. 1 Forming Hyper-heuristics with GAs when Solving 2D-Regular Cutting Stock Problems Kuo-Hsien Chuang 2009/03/24

2. 2 Introduction Cutting Stock Problem 圖片來源： http://www.mediatinker.com/blog/archives/009842.html

3. 3 Introduction Problem: –Given a set of 2D retangular pieces –Generate cutting pattern from sheets of stock material Objective: –Minimize the trim loss –Minimize the number of objects used

4. 4 Introduction In general, some methods work well for particular instances, but not for all of them. A hyper-heuristic is used to define a high- level heuristics that controls low-level heuristics.

5. 5 The Set of Heuristics Used In this investigation two kinds of heuristics were considered for: –selecting the figures and objects –placing the figures into the objects.

6. 6 Selection Heuristics Selection by area, height or width –Decreasing order. –Increasing order. –Average. These heuristics are combined with the First-Fit algorithm for choosing the object, so all objects remain open.

7. 7 Placement Heuristics They are based on a sliding technique. –Bottom-Left (BL) [Jak66] –Improved-Bottom Left (BLLT) [LT99] –Bottom-Left Fill (BLF) [Cha83] –Bottom-Left Last (BLD) [HT01]

8. 8 Rotation Heuristics This investigation also considered rotation heuristics (by 90 degrees) which can be described as follows: –No Rotation –Rotate pieces by 90 degrees –Rotate pieces to align them vertically –Rotate pieces to align them horizontally (

9. 9 Combining Heuristics with the GA The representation of a chromosome

10. 10 Evaluation

11. 11 Experiment Tournament One/Two point crossover Gaussian mutation

12. 12 Experiment