a distance-based ranking eda for the permutation flowshop scheduling problem
DESCRIPTION
Josu Ceberio. A distance-based ranking EDA for the permutation flowshop scheduling problem. Previously…. EDAs for integer domains. EDAs for real value domains. Few efficient designs for permutation-based problems. POOR PERFORMANCE. EHBSA and NHBSA ( Tsutsui et al.). - PowerPoint PPT PresentationTRANSCRIPT
A distance-based ranking EDA for the
permutation flowshop scheduling problem
Josu Ceberio
Previously… EDAs for integer domains. EDAs for real value domains.
Few efficient designs for permutation-based problems.
POOR PERFORMANCE
EHBSA and NHBSA (Tsutsui et al.)
Distance-based ranking models The Mallows model is a distance-based
exponential model.
Two parametersConsensus ranking, Spread parameter,
Probability distribution
Distance-based ranking models Kendall’s tau distance
Decomposition of the distance
Factorization of the probability distribution
1 2 3 4 5 6
2 3 1 6 5 4
2 0 0 2 1
Distance-based ranking EDA Generalized Mallows EDA is proposed. A generalization of the Mallows model. spread parameters.
Probability distribution
The problem To check the performance we approach:
Permutation Flowshop Scheduling Problem.
Extensively studied.
The Mallows EDA demonstrated good performance.
Permutation Flowshop Scheduling Problem Given a set of n jobs and m machines and processing
times pij.
Find the sequence for scheduling jobs optimally. Optimization criterion: Total Flow Time (TFT).
Codification1 3 2 5 4
m1m2m3m4
j1 j3j2 j5j4
Example
Objective function
Generalized Mallows EDAPreliminary experimentsSpread parameters
Generalized Mallows EDAPreliminary experimentsGM model convergence
Generalized Mallows EDAApproximating spread parametersNewton-Raphson
An upper bound for the spread parameters is fixed!!
Generalized Mallows EDAApproximating spread parameters
Standart evolutionary shape
Restart mechanism shape
Generalized Mallows EDAPreliminary experimentsRestart mechanism
Improvement !
PFSPstate-of-the-art
LR(n/m)GA
VNSCrossoverVNS
Asynchronus Genetic Algorithm (AGA) – Xu et al. 2009
Local Search (Swap)
Local Search (Insert)
Shake
PFSP state-of-the-art
LR(n/m) Local Search (Swap)
Local Search (Insert)
Shake
Variable Neighborhood Search 4 (VNS4) – Costa et al. 2012
PFSP state-of-the-art
Fundamentalist approaches rarely achieve optimum solutions.
Hybridization is the path to follow.
High presence of VNS algorithms.
First approach to the PFSP GM-EDA does not succeed. An hybrid approach is considered:
Hybrid Generalized Mallows EDA (HGM-EDA)
Hybrid Generalized Mallows EDA
Generalized Mallows EDA
Local Search (Swap)
Local Search (Insert)
Orbit Shake
VNS
Experimentation Algorithms: AGA, VNS4, GM-EDA, VNS and
HGM-EDA.20 repetitions
Taillard’s PFSP benchmarks: 100 instances• 20 x 05• 20 x 10• 20 x 20• 50 x 05• 50 x 10• 50 x 20
• 100 x 05• 100 x 10• 100 x 20• 200 x 10• 200 x 20• 500 x 20
Experimentation Spread parameters upper bound.
Select the upper-theta that provides the best solutions for GM-EDA
Stopping criterion: maximum number of evaluations.Evaluations performed by AGA in n x m x 0.4s.
Experimentation Taillards benchmark
20 x 5 20 x 10 20 x 20
AGA 13932 20003 32911
VNS4 13932 20003 32911
GM-EDA 13934 20009 20003
VNS 13932 20003 32911
HGM-EDA 13932 20003 32911
Experimentation Taillards benchmark
50 x 5 50 x 10 50 x 20
AGA 66301 85916 121294
VNS466757 86479 121739
GM-EDA 66309 86948 122830
VNS 66309 85980 121386
HGM-EDA 66307 85958 121317
Experimentation Taillards benchmark
100 x 5 100 x 10 100 x 20
AGA 240102 288988 374974
VNS4242974 292425 378402
GM-EDA 241346 292472 379691
VNS 240162 289438 375410
HGM-EDA 240122 288902 374664
Experimentation Taillards benchmark
200 x 10 200 x 20 500 x 20
AGA 1039507 1243928 6754943
VNS41048520 1252165 6770472
GM-EDA 1046146 1252545 7225665
VNS 1041846 1246474 6863483
HGM-EDA 1036303 1237959 6861070
Experimentation Taillard’s benchmark - Summary
20x05 20x10 20x20 50x05 50x10 50x20 100x05 100x10 100x20 200x10 200x20 500x20
AGA ✔ ✔ ✔ ✔ ✔ ✔ ✔ ✔VNS4 ✔ ✔ ✔GM-EDA
VNS ✔ ✔ ✔HGM-EDA ✔ ✔ ✔ ✔ ✔ ✔ ✔
Experimentation Taillard’s benchmark – Results analysis
HGM-EDA outperforms state-of-the-art results in some cases.○ Which is the reason for the performance fall
given in instances of 500x20?
Biased instances?- A tabu search algorithm was used for to choose the
hardest instances.
We generate a random benchmark
Experimentation Random benchmark
New configurations between 200 and 500.
Total: 100 instances.
• 250 x 10• 250 x 20• 300 x 10• 300 x 20• 350 x 10
• 350 x 20• 400 x 10• 400 x 20• 450 x 10• 450 x 20
Experimentation Random benchmark - Summary
250x10 250x20 300x10 300x20 350x10 350x20 400x10 400x20 450x10 450x20
AGA ✔ ✔ ✔VNS4
GM-EDA
VNS
HGM-EDA ✔ ✔ ✔ ✔ ✔ ✔ ✔
Experimentation Random benchmark – Results analysis
Statistical Analysis confirms experimentation.○ Friedman test + Shaffer’s static.
HGM-EDA and AGA are definitely the best algorithms.
VNS4 results do not match with those reported.The performance falls onwards 400x20.
What’s wrong with largest instances?
Analysis – Hybrid approachImprovement ratio EDA vs. VNS
20x0
520
x10
20x2
050
x05
50x1
050
x20
100x
05
100x
10
100x
20
200x
10
200x
20
250x
10
250x
20
300x
10
300x
20
350x
10
350x
20
400x
10
400x
20
450x
10
450x
20
500x
2050%
55%
60%
65%
70%
75%
80%
85%
90%
95%
100%
EDA VNS
Instances
%
Analysis – Generalized Mallows EDAAGA vs. GM-EDA
20x5
20x1
020
x20
50x5
50x1
050
x20
100x
5
100x
10
100x
20
200x
10
200x
20
250x
10
250x
20
300x
10
300x
20
350x
10
350x
20
400x
10
400x
20
450x
10
450x
20
500x
201
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.1
Instances
RPD
(%)
Analysis – Generalized Mallows EDAThetas convergence
Analysis – Generalized Mallows EDAThetas convergence
Analysis – Generalized Mallows EDAThetas convergence
Analysis – Generalized Mallows EDAThetas convergence
Analysis – Generalized Mallows EDAThetas convergence
Analysis – Generalized Mallows EDAThetas convergence
Stops prematurely!!!
Analysis – HGM-EDA vs. AGAMore evaluations
Max eval. AGA HGM-EDA x1 6710650 6841042
x2 6708656 6816514
x3 6708162 6769335
x4 6708123 6778298
x5 6708029 6779509
x6 6708029 6775003
x7 6706879
x8 6706879
One instance of 500x20
Analysis – Generalized Mallows EDALR vs. GM-EDA
20x0
520
x10
20x2
050
x05
50x1
050
x20
100x
05
100x
10
100x
20
200x
10
200x
20
250x
10
250x
20
300x
10
300x
20
350x
10
350x
20
400x
10
400x
20
450x
10
450x
20
500x
200.8
0.85
0.9
0.95
1
1.05
1.1
1.15
Instances
%
Analysis – HGM-EDA vs. AGAMore evaluations
Max eval. AGA HGM-EDA x1 6710650 6841042
x2 6708656 6816514
x3 6708162 6769335
x4 6708123 6778298
x5 6708029 6779509
x6 6708029 6775003
x7 6706879
x8 6706879
One instance of 500x20
Analysis – HGM-EDA vs. AGAMore evaluations
Max eval. AGA HGM-EDA Guided HGM-EDAx1 6710650 6841042 6743775
x2 6708656 6816514 6721295
x3 6708162 6769335 6732300
x4 6708123 6778298 6707129
x5 6708029 6779509 6716032
x6 6708029 6775003 6712273
x7 6706879
x8 6706879
One instance of 500x20
Analysis – HGM-EDA vs. AGAMore evaluations One instance of 500x20
1 2 3 4 5 6 7 86600000
6650000
6700000
6750000
6800000
6850000
6900000
AGAHGM-EDA Guided HGM-EDA
Conclusions Hybrid Generalized Mallows EDA is a
efficient algorithm for solving the PFSP.Succeed in 152/220 instances.
The participation of the GM-EDA is essential.
Future Work - PFSP Test other parameters: evaluations,
population size, theta bounds, selection size…
Include information of the instance.
Guided InitializationShake the solution of the LR(n/m) to
build up the population?
Future Work – GM-EDA Set different upper bounds to the spread
parameters
Study other distances. Is suitable Kendall’s-tau distance? Other distances: Cayley, Ulam, Hamming Study the problem.
Other problems: TSP QAP LOP (work in progress)
Eskerrik asko
Josu CeberioEskerrik asko
Josu Ceberio
Distance-based ranking EDA Mallows EDA
Learning and Sampling
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