Genetic Algorithms for Bin Packing Problem

1. Genetic Algorithms for Bin Packing Problem Hazem Ali, Borislav Nikolić, Kostiantyn Berezovskyi, Ricardo Garibay Martinez, Muhammad Ali Awan

2. Outline • Introduction • Non-Population Metaheuristics • Population Metaheuristics • Genetic Algorithims (GA) • Scientific Paper on GA ”A New Design of Genetic Algorithm for Bin Packing”

3. Introduction • On the last session we discussed: • Local search (LS) and Heuristics • Metaheuristics • Examples of metaheuristics: • VNS • GRASP, SA, TS Non-Population Population • Genetic Algorithms (GA) • What is the difference?

4. Non-Population Metaheuristics • Initial phase = single solution population of size 1 • New solutions -> perturbations • Less complexity and computational time

5. Population Metaheuristics • Initial phase = group of solutions population of size M • New solutions : • Recombining (Crossover) • Perturbations (Mutation) • More complex • Tradeoff Complexity and performance

6. Population Vs. Non-population Metaheuristics • Examples: • Particle Swarm Optimization (PSO) • Ant Colonies (AC) • Genetic Algorithms (GA)

7. Genetic Algorithms (GA) - Overview • Based on biological evolution (Survival for the FITTEST) • Developed by John Holland, University of Michigan (1970’s) • To understand the adaptive processes of natural systems • To design artificial systems software that retains the robustness of natural systems

8. Genetic Algorithms (GA) - Overview • “Genetic Algorithms are good at taking large, potentially huge search spaces and navigating them, looking for optimal combinations of things, solutions you might not otherwise find in a lifetime.” Salvatore Mangano - Computer Design, May 1995 • Efficient, effective techniques : • Optimization • Machine learning applications • Widely-used : • Business • Scientific • Engineering

9. Genetic Algorithms (GA) – Basic Components • Encoding technique • Initialization procedure • Evaluation function • Selection of parents • Genetic operators • Parameter settings

10. Genetic Algorithms (GA) – Basic Components • Encoding technique Gene Genotype

11. Genetic Algorithms (GA) – Basic Components • Initialization procedure Creation of Initial Population

12. Genetic Algorithms (GA) – Basic Components • Evaluation function 88% 31% 5% 41% 77% 67% 20% 10% 35% 46% 90% 12% 87% 81% 55% 11% 99% 74% 99% 55% 61% 89% Environment

13. Genetic Algorithms (GA) – Basic Components • Selection of parents 88% 31% 5% 41% 77% 67% 20% 10% 35% 46% 90% 12% 87% 81% 55% 11% 99% 74% 99% 55% 61% 89% Reproduction

14. Genetic Algorithms (GA) – Basic Components • Genetic operators Crossover Mutation

15. Genetic Algorithms (GA) – Basic Components • Parameter settings Practice and Art

16. Advantages of GA • Easy to understand • Modular & Flexible, separate from application • Supports multi-objective optimization • Good for “noisy” environments • Always an answer; gets better with time • Inherently parallel; easily distributed • Many ways to speed up and improve • Easy to exploit previous or alternate solutions

17. Scientific Paper on GA A New Design of Genetic Algorithm for Bin Packing By Hitoshi Iima Tetsuya Yakawa Kyoto Institute of Technology, Japan, Published on 2003

18. Scope • Presenting a new design of GA for solving 1D BPP • FF and MBS hueristics are used Previous Presentation • Effective and outperform TABU & VNS • Next slides explains: • GA for BPP • Results

19. GA for BPP • Encoding Phase: • Gene: 10 2 6 10 (1,3,10) 3 4 3 3 5 2 1 1 • Genotype: g1: (1,3,10) (2,3,5)(2,4,6)

20. GA for BPP • Initialization Procedure: • FF hueristic is used to generate the initial population (genotypes) • Selection of Parents: • Two parents selected randomly P2: (3,4,12,15) (6,7,11) (9,20) (1,5,8) (2,13,14) P1: ( 1,3,20 ) (2,9,11) (5,7,13,15) (4,6,14) (8,12)

21. GA for BPP • Genetic operators: • Crossover: P2: (3,4,12,15) (6,7,11) (9,20) (1,5,8) (2,13,14) P1: ( 1,3,20 ) (2,9,11) (5,7,13,15) (4,6,14) (8,12) Tc S1 Replacement: O1: (2,7,9,13) (4,6,20)(1,5,8) O1: (2,9,11) (4,6,14) (1,5,8) (2) (9) (11) (2,9) (2,11) (9,11) (2,9,11) (7,20) (7,13) (20,13) Ta: (11) (14) Tb: (3,12,15) Ta: (7) (20) (13) Tb: (3,12,15) T O1 O2 FF & MBS’ applied O1: (2,7,9,13) (4,6,20)(1,5,8,14) (3,11,12,15)

22. GA for BPP • Genetic operators: • Mutation: P2: (3,4,12,15) (6,7,11) (9,20) (1,5,8) (2,13,14) P1: ( 1,3,20 ) (2,9,11) (5,7,13,15) (4,6,14) (8,12) Tc S1 Replacement: O3: (2,9,11) (4,6,14) (2) (9) (11) (2,9) (2,11) (9,11) (2,9,11) (1,3) (1,5) (1,7) (1,8) . . . (1) (3) (5) (7) (8) (20) (12) (13) Tm O3 O4 Apply the same replacement procedure

23. GA for BPP • GA Outline: • Generate the initial population • Pick up two solutions x1and x2 • Generate two solutions x3 and x4 by crossover • Generate two solutions x5 and x6 by mutation • Select the best two solutions {x1,...,x6} • Discard x1, x2 from initial population • Add the two best solutions to the new generation • Repeat

24. Experiment and Results No. of optimal solutions Average relative deviation (rd) Average absolute deviation (ad)

25. Conclusion • New GA design that suits well BPP • Genetic operators designed in such a way that offsprings inheret parents characteristics • FF and MBS´used to enhance the obtained results • Better performance over VNS & TABU