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

Genetic Algorithms for Bin Packing Problem

Hazem Ali, Borislav Nikolić, Kostiantyn Berezovskyi, Ricardo Garibay Martinez,

Muhammad Ali Awan

Outline

• Introduction

– Non-Population Metaheuristics

– Population Metaheuristics

• Genetic Algorithims (GA)

• Scientific Paper on GA ”A New Design of Genetic Algorithm for Bin Packing”

Introduction

• On the last session we discussed: Local search (LS) and Heuristics Metaheuristics Examples of metaheuristics:• VNS• GRASP, SA, TS Non-Population

• Genetic Algorithms (GA)

• What is the difference?

Population

Non-Population Metaheuristics

• Initial phase = single solution population of size 1

• New solutions -> perturbations

• Less complexity and computational time

Population Metaheuristics

• Initial phase = group of solutions population of size M

• New solutions : – Recombining (Crossover)– Perturbations (Mutation)

• More complex

• Tradeoff Complexity and performance

Population Vs. Non-population Metaheuristics

Pobulation Metaheuristics Non-Pobulation Metaheuristics

Population of size M Population of size 1

Recombining and Perturbations Only perturbations

Complex Less complex

• Examples: Particle Swarm Optimization (PSO) Ant Colonies (AC) Genetic Algorithms (GA)

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

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

Genetic Algorithms (GA) – Basic Components

• Encoding technique

• Initialization procedure

• Evaluation function

• Selection of parents

• Genetic operators

• Parameter settings

Genetic Algorithms (GA) – Basic Components

• Encoding technique

Gene

Genotype

Genetic Algorithms (GA) – Basic Components

• Initialization procedure

Creation of Initial Population

Genetic Algorithms (GA) – Basic Components

• Evaluation function

Environment

90%

61%

77%

81%

20% 10%

87%

35%

74%

55%

5%46%

67% 41%31% 88%

11%99%

55%

12%

99%

89%

Genetic Algorithms (GA) – Basic Components

• Selection of parents

Reproduction

90%

61%

77%

81%

20% 10%

87%

35%

74%

55%

5%46%

67% 41%31% 88%

11%99%

55%

12%

99%

89%

Genetic Algorithms (GA) – Basic Components

• Genetic operators

CrossoverMutation

Genetic Algorithms (GA) – Basic Components

• Parameter settings

Practice and Art

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

Scientific Paper on GA

A New Design of Genetic Algorithm for Bin Packing

ByHitoshi Iima Tetsuya Yakawa

Kyoto Institute of Technology, Japan,Published on 2003

Scope

• Presenting a new design of GA for solving 1D BPP

• FF and MBS hueristics are used

• Effective and outperform TABU & VNS

• Next slides explains:– GA for BPP– Results

Previous Presentation

GA for BPP

• Encoding Phase:

13

10 (1,3,10)

24

6

5

32

13

10

g1: (1,3,10) (2,3,5) (2,4,6)

– Gene:

– Genotype:

GA for BPP

• Initialization Procedure:– FF hueristic is used to generate the initial

population (genotypes)

P1: ( 1,3,20 ) (2,9,11) (5,7,13,15) (4,6,14) (8,12) P2: (3,4,12,15) (6,7,11) (9,20) (1,5,8) (2,13,14)

• Selection of Parents: – Two parents selected randomly

GA for BPP

• Genetic operators:• Crossover:

P1: ( 1,3,20 ) (2,9,11) (5,7,13,15) (4,6,14) (8,12) P2: (3,4,12,15) (6,7,11) (9,20) (1,5,8) (2,13,14)

O1 O2

O1: (2,9,11) (4,6,14) (1,5,8)

Ta: (7) (20) (13)Tb: (3,12,15)

(7,20) (7,13)

(20,13)

Tc(2) (9)

(11)(2,9)

(2,11)(9,11)

(2,9,11)

S1O1: (2,7,9,13) (4,6,20)(1,5,8)

Ta: (11) (14)Tb: (3,12,15)

T

O1: (2,7,9,13) (4,6,20)(1,5,8,14) (3,11,12,15)

FF & MBS’ applied

Replacement:

GA for BPP

• Genetic operators:• Mutation:

P1: ( 1,3,20 ) (2,9,11) (5,7,13,15) (4,6,14) (8,12) P2: (3,4,12,15) (6,7,11) (9,20) (1,5,8) (2,13,14)

O3 O4

O3: (2,9,11) (4,6,14)

(1) (3) (5) (7) (8) (20) (12) (13)

(1,3) (1,5)(1,7)(1,8)

.

.

.

Tc(2) (9)

(11)(2,9)

(2,11)(9,11)

(2,9,11)

S1

Tm

Apply the same replacement procedure

Replacement:

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

Experiment and ResultsData Set GA VNS BISON

1 690 694 697

2 475 474 473

3 3 2 3

No. of optimal solutions

Data Set GA VNS BISON

1 0.04 0.07 0.04

2 0.01 0.14 0.01

3 0.70 0.80 0.70

Average absolute deviation (ad)

Data Set GA VNS BISON

1 0.04 0.05 0.04

2 0.02 0.36 0.02

3 1.24 1.44 1.26

Average relative deviation (rd)

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