Genetic Algorithms (GA)

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23 Οκτ 2013 (πριν από 3 χρόνια και 7 μήνες)

85 εμφανίσεις

Genetic Algorithms for Bin
Packing Problem

Hazem Ali, Borislav Nikoli
ć,

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


Genetic Algorithms (GA
)


What is the difference?

Non
-
Population Metaheuristics


Initial phase = single solution



New solutions
-
> perturbations


Less complexity and computational time


Population Metaheuristics


Initial phase = group of solutions



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


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


Genetic Algorithms (GA)


Basic
Components


Initialization procedure

Genetic Algorithms (GA)


Basic
Components


Evaluation function

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

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


Genetic Algorithms (GA)


Basic
Components


Parameter settings
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


By

Hitoshi 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

GA for BPP


Encoding Phase:

1

3

10

(1,3,10)

2

4

6

5

3

2

1

3

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)

S1

O1: (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
x
1
and
x
2


Generate two solutions
x
3

and
x
4

by crossover


Generate two solutions
x
5

and
x
6

by mutation


Select the best two solutions {
x
1
,...,x
6
}


Discard
x
1
, x
2

from initial population


Add the two best solutions to the new generation


Repeat

Experiment and Results

Data 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