genetic algorithms for bin packing problem hazem ali, borislav nikolić, kostiantyn berezovskyi,...
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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