genetic algorithms for bin packing problem

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


• Encoding technique

Gene

Genotype


• Initialization procedure

Creation of Initial Population


• 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%


• 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 operators

CrossoverMutation


• 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

genetic algorithms for bin packing problem

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