ncga : neighborhood cultivation genetic algorithm for multi-objective optimization problems
DESCRIPTION
NCGA : Neighborhood Cultivation Genetic Algorithm for Multi-Objective Optimization Problems. ○ Shinya Watanabe Tomoyuki Hiroyasu Mitsunori Miki. Intelligent Systems Design Laboratory , Doshisha University , Kyoto Japan. Multi-objective Optimization Problems. - PowerPoint PPT PresentationTRANSCRIPT
Doshisha Univ., Kyoto Japan
NCGA : Neighborhood Cultivation Genetic Algorithm
for Multi-Objective Optimization Problems
Intelligent Systems Design Laboratory,Doshisha University, Kyoto Japan
○ Shinya Watanabe
Tomoyuki Hiroyasu
Mitsunori Miki
Doshisha Univ., Kyoto Japan
Multi-objective Optimization Problems●Multi-objective Optimization Problems (MOPs)
In the optimization problems, when there are several objective functions, the problems are called multi-objective or multi-criterion problems.
f 1(x)
f 2(x
)
Design variables
Objective function
Constraints
Gi(x)<0 ( i = 1, 2, … , k)
F={f1(x), f2(x), … , fm(x)}
X={x1, x2, …. , xn} Feasible regionFeasible region
Pareto optimal solutions
Doshisha Univ., Kyoto Japan
• MOPs solved by Evolutionary algorithms
EMO
•VEGA :Schaffer (1985)
•MOGA :Fonseca (1993)
•DRMOGA :Hiroyasu, Miki, Watanabe (2000)
• SPEA2 :Zitzler (2001)
•NPGA2 :Erickson, Mayer, Horn (2001)
•NSGA-II :Deb, Goel (2001)
Typical method on EMO
• EMOEvolutionary Multi-criterion Optimization
Doshisha Univ., Kyoto Japan
• NCGA : Neighborhood Cultivation GA
• The neighborhood crossover.• Archive of excellent solutions.• A Method which cuts down reserved excellent
solutions.• Use of the reserved excellent solutions for
searching solutions.• Unification mechanism of the values of each
objective.
The features of NCGA
Neighborhood Cultivation GA (NCGA)
Doshisha Univ., Kyoto Japan
• A neighborhood crossover– In MOPs GA, the searching area is wide and the
searching area of each individual is different.
f2(x
)
f1(x)
If the distance between two selected parents is so large, the crossover may have no effect for local search.
Neighborhood Cultivation GA (NCGA)
Doshisha Univ., Kyoto Japan
• One of the objectives is changed at each generation.
• The sorting of a population includes a little probabilistic change.
f2(x
)
f1(x)
Neighborhood Cultivation GA (NCGA)• A neighborhood crossover
• Two parents in the crossover are chosen from the top of the sorted individuals.
In order not to make the same couple,
Doshisha Univ., Kyoto Japan
Neighborhood Cultivation GA (NCGA)
• NCGA has the neighborhood crossover mechanism.
• NCGA has only one selection in one generation.• Many methods have two types of selection
(the environment selection and the mating selection). But, NCGA has the environment selection only.
•The differences from the recent major algorithms like SPEA2 and NSGA-II.
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• Sampling of the Pareto frontier Lines of
Intersection (ILI) (Knowles and Corne 2000)
Comparison method
= 5/12=0.42= 7/12=0.58
Doshisha Univ., Kyoto Japan
• SPEA2• NSGA-II• NCGA• non-NCGA
(NCGA except neighborhood crossover )
Applied models and Parameters
GA OperatorApplied models• Crossover
– One point crossover
• Mutation– Bit flip
population size 100crossover rate 1.0mutation rate 0.01
Parameters
terminal condition 250
250
2000number of trials 30
Doshisha Univ., Kyoto Japan
• Discontinuous Function– Fdiscon (Deb’00)
Test Problems
100,,1,]1,0[
)10sin(11
)(101)(min
))2.0exp(10()(min
111 1
2
100
1
21
211
NNix
fg
f
N
xxf
xxxxf
i
N
i
i ii
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Pareto solutions of Fdiscon
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Comparison result of Fdiscon (ILI)
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• Continuous Function– KUR
100,,1,]5,5[
)sin(5||)(min
))2.0exp(10()(min38.0
2
100
1
21
21
nnix
xxxf
xxxf
i
ii
i ii
Test Problems
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Pareto solutions of KUR
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Comparison result of KUR (ILI)
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Objectives
Constraints
• Combination problem– KP 750-2
2,1)(750
1,
ixpxfj
jjii
750
1,
jijji cxw
1,0),,,( 75021 jxxxxx pi,j = profit of item j according to knapsack i
Test Problems
wi,j = weight of item j according to knapsack ici,= capacity of knapsack i
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Pareto solutions of KP750-2
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Comparison result of KP750-2 (ILI)
Doshisha Univ., Kyoto Japan
• We proposed a new model for Multi-objective GAs.– NCGA: Neighborhood Cultivation GA
Effective method for multi objective GA • The neighborhood crossover• Archive of excellent solutions.• A Method which cuts down reserved excellent solutions.• Use of the reserved excellent solutions for searching soluti
ons.• Unification mechanism of the values of each objective.
Conclusion
Doshisha Univ., Kyoto Japan
• NCGA was applied to some test functions and the results were compared to the other methods; such as SPEA2, NSGA-II and non-NCGA.
• In almost test functions, NCGA derives the good results.
• Comparing NCGA to NCGA without neighborhood crossover, NCGA is obviously superior to in all problems.
NCGA is an effective algorithm for multi-objective problems.
Conclusion
Doshisha Univ., Kyoto Japan
• Continuous Function– ZDT4
]5,5[]1,0[
)4cos(1091)(
)(1)()(min
)(min
1
10
2
2
12
11
i
iii
xx
xxxg
xg
xxgxf
xxf
Test Problems
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Pareto solutions of ZDT4
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Comparison result of ZDT4 (ILI)
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ILI of KP750-2
Doshisha Univ., Kyoto Japan
• About EMO– http://www.lania.mx/~ccoello/EMOO/EMOObib.ht
ml
• About 0/1 Knapsack problem– http://www.tik.ee.ethz.ch/~zitzler/
• NCGA source program– http://mikilab.doshisha.ac.jp/dia/research/mop_ga/
archive/
• My e-mail address– [email protected]
URL of reference
Doshisha Univ., Kyoto Japan
• The Ratio of Non-dominated Individuals (RNI) is derived from two types of Pareto solutions.
Performance Measure
(x)f 1
f 2(x
) Method B
(x)f 1
f 2(x
) Method A
(x)f 1
f 2(x
)
Method AMethod B
0.3330.666
Doshisha Univ., Kyoto Japan
• The following topics are the mechanisms that the recent GA approaches have.
EMO
• Archive of the excellent solutions• Cut down (sharing) method of the reserved
excellent solutions• An appropriate assign of fitness• Reflection to search solutions mechanism of the
reserved excellent solutions• Unification mechanism of values of each objective
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Performance Assessment
• The Ratio of Non-dominated Individuals :RNI– The Performance measure perform to compare
two type of Pareto solutions.– Two types of pareto solutions derived by
difference methods are compared.
• Cover Rate Index– Diversity of the Pareto optimum.
• Error – The distance between the real pareto front and
derived solutions.
• Various rate– Diversity of the pareto optimum individuals.
Measures
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Cluster System
Spec. of Cluster (16 nodes)Processor Pentium
(Coppermine)ⅢClock 600MHz# Processors 1 × 16Main memory 256Mbytes × 16Network Fast Ethernet (100Mbps)Communication TCP/IP, MPICH 1.2.1OS Linux 2.4Compiler gcc 2.95.4