Advanced Mate Selection in Evolutionary Algorithms

Missouri University of Science and Technology

Mate Selection

• Classic Mate Selection– Tournament– Roulette wheel– Panmictic

• Limitations– No genotypic restrictions on mating– More fit individuals mate more often– Fixed parameters during an EA run– Time consuming process of tuning mate

selection parameters for each problem


Mate Selection

• Mate selection with restrictions– Niching– Assortative Mating– Outbreeding

• Mate selection learning mechanisms– Reinforcement learning– LOOMS and ELOOMS


Niching

0110

01111110

1111

1001

10000001

1110 1111 1000 0001

1111 1000


Assortative Mating

0110

0111

1110

1111

1001

1000

0001

1111 0001

0111 1111 1000 1001


Variable Dissortative Mating Genetic Algorithm (VDMGA)• Negative assortative mating• Hamming distance threshold

restriction– Adaptive– Restriction tends to loosen over time– Assumes dissimilarity between genotypes

improves performance• Outperforms basic assortative mating

techniques


Outbreeding


Reinforcement Learning in CGAs• Cellular Genetic Algorithms (CGAs)

– Individuals organized on a topological grid– More likely to mate with nearby neighbors

• Reinforcement learning based on offspring quality– Good offspring – moves individuals closer

together on the grid– Bad offspring – moves individuals further

apart on the grid


LOOMS and ELOOMS

• Learning Offspring Optimizing Mate Selection (LOOMS)– Every individual examined all other

individuals in the population for best mate– Significant overhead

• Estimated LOOMS (ELOOMS)– Reduced overhead by looking for a good

enough mate– Features looked for in mates converged to

intermediate values

Estimated Learning Offspring Optimizing

Mate Selection(ELOOMS)

Traditional Mate Selection

25 3 8 2 4 5

MATES

5 8

5 4

• t – tournament selection• t is user-specified

ELOOMS

NOYES YES MATESYES

NOYES

YES

Mate Acceptance Chance (MAC)

(1 )

1

(1 ) ( 1)( , )

i

Lb

i ii

b dMAC j k

L

j How much do I like ?

k

b1 b2 b3 … bL

d1 d2 d3 … dL

Desired Features

j

d1 d2 d3 … dL

# times past mates’ bi = 1 was used to produce fit offspring

# times past mates’ bi was used to produce offspring

b1 b2 b3 … bL

• Build a model of desired potential mate• Update the model for each encountered mate• Similar to Estimation of Distribution Algorithms

ELOOMS vs. TGA

L=500With Mutation

L=1000With Mutation

Easy Problem

ELOOMS vs. TGA

Without Mutation With Mutation

Deceptive ProblemL=100

Why ELOOMS works on Deceptive Problem• More likely to preserve optimal

structure• 1111 0000 will equally like:

– 1111 1000– 1111 1100– 1111 1110

• But will dislike individuals not of the form:– 1111 xxxx

Why ELOOMS does not work as well on Easy Problem• High fitness – short distance to optimal• Mating with high fitness individuals –

closer to optimal offspring• Fitness – good measure of good mate• ELOOMS – approximate measure of

good mate

Learning Individual Mating Preferences

(LIMP)


LIMP

• Individuals learn what features to look for in a mate – desired features

• Learning is based on the results of prior reproductions

• D-LIMP – each individual tracks their own desired features

• C-LIMP – desired features are tracked on a population level


LIMP – Mate Selection

• λ individuals look for a mate• Each individual conducts a tournament

to find a mate• Comparison of desired features to

potential mates’ genes• Most suitable potential mate selected


Mate Selection – D-LIMP

0110

1000

0111

0101

1101

1010

0001 sk

.7 | .6 | .7 | .2dj

j

sk =

.30.65


.45

Mate Selection – C-LIMP

0110

1000

0111

0101

1101

1010

0001 sk

j

sk

.8 | .9 | .2 | .7

.3 | .4 | .8 | .8

dP0

dP1sj

=

.60


Learning Desirable Mate Qualities• Desired features update after

recombination• Track each parent’s gene contribution

to offspring• Outcome of the reproduction is

examined– If the child is more fit than a parent, that

parent considers its mate suitable– If the child is less fit than a parent, that

parent considers its mate unsuitable


Learning D-LIMP

0101 1010

0110

.2 | .9 | .3 | .8.7 | .6 | .7 | .2

.7 | .6 | .3 | .8

j k

mF(j)=20 F(k)=15

F(m)=18

.7 | .6 | .6 | .3 0 | 1 | .3 | .8.7 | .6 | .7 | .2 .2 | .9 | .3 | .8


.8 | .9 | .2 | .7

.3 | .4 | .8 | .8

dP0

dP1

.8 | .9 | .1 | .7

.3 | .4 | .8 | .9

dP0

dP1 .1 | .4 | .8 | .9

.8 | 1 | .1 | .7 dP0

dP1

.8 | .9 | .2 | .7

.3 | .4 | .8 | .8

dP0

dP1

.8 | .9 | .1 | .7

.3 | .4 | .8 | .9

dP0

dP1

Learning C-LIMP

0101 1010

0110

j k

mF(j)=20 F(k)=15

F(m)=18


Test Problems

• DTRAP– DTRAP1– DTRAP2

• NK Landscapes• MAXSAT• Performance Comparisons

– Mean Best Fitness (MBF)– Number of Evaluations until Convergence


Tested Algorithms

• C-LIMP• D-LIMP• Variable Dissortative Mating Genetic

Algorithm (VDMGA)• Traditional Genetic Algoritm (TGA)• Survival Selection Methods

– Tournament– Restricted Tournament Replacement (RTR)


DTRAP1 Results

Tournament RTR


DTRAP2 vs. DTRAP1 Results

TGA

VDMGA

C-LIMP

D-LIMP

0 20 40 60 80 100

DTRAP2DTRAP1

TGA

VDMGA

C-LIMP

D-LIMP

0 20 40 60 80 100

DTRAP2DTRAP1

Tournament RTR


NK Landscape Results

Tournament RTR


MAXSAT Results

Tournament RTR


DTRAP1 Convergence

Tournament RTR


NK Landscape Convergence

Tournament RTR


MAXSAT Convergence

Tournament RTR

Advanced Mate Selection in Evolutionary Algorithms

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