Opposition-based learning (OBL) and cooperative co-evolution (CC) have demonstrated promising performance when dealing with large-scale global optimization (LSGO) problems. In this work, we propose a novel framework for hybridizing these two techniques, and investigate the performance of simple implementations of this new framework using the most recent LSGO benchmarking test suite. The obtained results verify the effectiveness of our proposed OBL-CC framework. Moreover, some advanced statistical analyses reveal that the proposed hybridization significantly outperforms its component methods in terms of the quality of finally obtained solutions.

1. A Novel Hybridization of
Opposition-Based Learning and
Cooperative Co-evolutionary for
Large-Scale Optimization
Borhan Kazimipour
Mohammad Nabi Omidvar
Xiaodong Li
A.K. Qin

2. Outlines
1. Introduction
2. Background
3. Proposed Framework
4. Experiments
5. Future Work
6. Questions
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3. Outlines
1. Introduction
2. Background
3. Proposed Framework
4. Experiments
5. Future Work
6. Questions
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4. Research Question
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How to use both opposition concept and
divide and conquer approach to tackle the
curse of dimensionality in optimization?
Large Scale
Optimization
Divide and
Conquer
Opposite
Population

5. Contributions
• In this work…
– We propose a general framework to use opposition-based techniques in
cooperative co-evolutionary
– We implement a very simple, yet effective, example of the proposed framework
– We empirically show the effectiveness of the proposed framework even in the
simplest form
– We provide several advanced statistics to support our findings
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6. Outlines
1. Introduction
2. Background
3. Proposed Framework
4. Experiments
5. Future Work
6. Questions
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7. Large Scale Optimization
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•

8. Dealing with Dimensionality
Simplify Problems
• Cooperative Co-evolutionary
1. Divide the high dimensional
problem into smaller sub-problems
2. Solve each sub-problem almost
separately
3. Merge the sub-solutions to find the
solution of the original problem
Improve Solutions
• Opposition-based Learning
1. Calculate the opposite of the
potential solutions
2. Merge both original and
oppositional populations of
solutions
3. Select the best subset of the
merged population and evolve it.
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9. Cooperative Co-evolutionary (CC)
• Grouping or Decomposition
– Grouping is the process of dividing big given problem to small sub-problems (a.k.a.
groups or subcomponents)
– Interacting (non-separable) variables are better to be grouped in the same group
– Non-interacting (separable) variables are better to be grouped in different groups
– In black-box problems, we may have no information about the interactions between
variables
• Decomposition Methods
– Random Grouping
– Delta Grouping
– Variable Interaction Learning
– Differential Grouping
Note: Decomposition methods in CC framework are entirely independent of the optimizer
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10. Cooperative Co-evolutionary (CC)
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11. Opposition-Based Learning (OBL)
• Core Theorems
1. A candidate solution and its opposite have the equal probability of being closer
to the global optimum.
2. The probability of the opposite of a candidate solution being closer to the global
optimum is higher than the probability of a second random guess being closer to
the global.
• Opposition Techniques
– Opposition-Base Learning (OBL)
– Quasi-Opposition-Base Learning (QOBL)
– Quasi-Reflection Opposition-Base Learning (QROBL)
– Generalized Opposition-Base Learning (GOBL)
– Current Optimum Opposition-Base Learning (COOBL)
Note: All OBL techniques are entirely independent of the optimizer
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12. Opposition-Based Learning (OBL)
• Computing Opposite Points
• Graphical Examples
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13. Outlines
1. Introduction
2. Background
3. Proposed Framework
4. Experiments
5. Future Work
6. Questions
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14. Proposed Framework
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15. Proposed Framework
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16. Proposed Framework
• Generality of the proposed framework:
– Any kind of grouping technique (e.g., static, random, delta, differential,
ideal, etc.) can be employed
– Any kind of optimizer (e.g., DE, PSO, GA, ABC, etc.)
– Any kind of opposition operator (e.g., OBL, QOBL, QROBL, GOBL, etc. )
can be used.
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17. Outlines
1. Introduction
2. Background
3. Proposed Framework
4. Experiments
5. Future Work
6. Questions
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18. Experiments Setup
• Benchmark
– CEC 2013 LSGO Benchmarks
– 15 functions
– 1000 dimensions
– Categories
1. fully separable functions (f1 - f3),
2. partially separable functions with a separable subcomponent (f4 - f7),
3. partially separable functions with no separable subcomponents (f8 - f11),
4. overlapping functions (f12 - f14),
5. fully non-separable function (f15).
• Statistical Tests
– Iman and Davenport (a.k.a. Friedman rank) test is used for ranking
– Li post-hoc procedure is used as significance test
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19. Experiments Setup
• Implementations
– Hybridisation of OBL and CC (with random grouping) called OBL-CC
– Hybridisation of QOBL and CC (with random grouping) called QOBL-CC
– DECC is used as the control method (as suggested in CEC 2013 LSGO benchmark
report)
– Self-adaptive DE with Neighbourhood Selection (SaNSDE) used as optimizer (as
suggested in CEC 2013 LSGO benchmark report)
• Parameter Values
– Four Jumping Rate (the probability of applying OBL/QOBL operators) schemes are
used
– Fixed (0.3)
– Fixed (0.6)
– Monotonically increasing (0~0.6)
– Monotonically decreasing (0.6~0)
– Max FE = 3,000,000
– 51 independent runs
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20. Experiments Results
Simple Statistics
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21. Experiments Results
Win-Draw-Loss Table
• Control Method: DECC
• Statistics:
– Two algorithms are considered to be significantly different if the p-value of Wilcoxon rank-sum
test is less than 0.05, and statistically similar otherwise
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22. Experiments Results
Win-Draw-Loss Findings
• Except for OBLCC(0.6) and OBL-CC(0.6~0), the hybridization generally improves the
performance of DECC.
• QOBL-CC(0.6~0) with 9 wins shows the best performance
• OBL-CC(0.3) with 1 loss is the most reliable hybridization (i.e., has the least risk of
failure)
• The family of QOBL-CC is more effective in dealing with problems with some degrees
of non-separability (G2-G5)
• The family of QOBL-CC is less recommended to be used in dealing with fully separable
problems (G1).
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23. Experiments Results
nWins Table
nWins Score = # wins - # losses in an N X N comparison (Wilcoxon rank-sum )
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24. Experiments Results
nWins Findings
• All hybrid methods obtain better nWins scores than DECC (success of
hybridization)
• DECC is never the single best method among the others.
• The last row of Table III confirms that DECC is the weakest algorithm
amongst the others.
• QOBL-CC family is the best one, overally.
• QOBL-CC methods show weak performance in dealing with fully separable
functions (G1).
• For G2-G5, the best performer is always from QOBL-CC family
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25. Experiments Results
Friedman Ranking
• Friedman Test
– Is one of the state-of-the-art algorithms
for 1XN and NXN comparisons
– To avoid family-wise error rate (FWER)
– To have a strong conclusion
• Compatibility
– Findings from Friedman ranking confirm
all previous findings (win-draw-loss and
nWins).
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26. Experiments Results
Friedman Ranking Findings
• In f1, DECC shares the first position with
OBL-CC
• In f5 and f10 all algorithms performs
statistically similar.
• In all cases, except f1 and f5, hybridization
provide significant improvement.
• QOBL-CC is not as effective as the other
hybrid methods in dealing with fully
separable problems (G1)
• On partially separable and non-separable
functions (G2-G5), QOBL-CCs are always
the best performers.
• DECC is in general the worst algorithm.
• QOBL-CC(0~0.6) is the top performer.
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27. Experiments Results
Li Post-hoc
• Li Post-hoc
– Is used to compare all methods against
the control method (DECC).
– Helps to investigate if a method is
statistically significantly better than
another.
– Yes: Best method(s) is significantly
better than DECC
– No: Best method(s) in NOT significantly
better than DECC (statistically similar)
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28. Outlines
1. Introduction
2. Background
3. Proposed Framework
4. Experiments
5. Future Work
6. Questions
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29. Future Work
• Extension
– Comparing different opposition strategies, decomposition techniques and core
optimizers.
• Sensitivity Analysis
– Studying influencing parameters (e.g., Jr value)
• Comparison
– Comparing the performance of the framework with the state-of-the-art methods in
LSO
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30. Outlines
1. Introduction
2. Background
3. Proposed Framework
4. Experiments
5. Future Work
6. Questions
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31. Thank you
☺☺☺☺
Any question or comment?
31CEC 2014, Beijing, China Hybridization of OBL and CC for LSO