approximation model guided selection for evolutionary .../file/ref_17.pdf · 11 ams framework o a....
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Approximation Model Guided Selection for Evolutionary Multiobjective Optimization
Aimin Zhou1, Qingfu Zhang2, and Guixu Zhang1
1Each China Normal University, Shanghai, China
2University of Essex, Colchester, UK
03/2013
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Outline
§ Background
§ Approximation Model Guided Selection
§ Experimental Results
§ Discussions & Conclusions
Approximation Model Guided Selection, EMO 2013
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Outline
§ Background
§ Approximation Model Guided Selection
§ Experimental Results
§ Discussions & Conclusions
Approximation Model Guided Selection, EMO 2013
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minF (x) = ( f1 (x), f2 (x),…, fm (x))s.t x ∈ D
Multiobjective Optimization Problem
Approximation Model Guided Selection, EMO 2013
o Definition
where
o Pareto domination
o Optimum • Pareto set (PS) • Pareto front (PF)
2f
1f
)(DF
Pareto front (PF)
Pareto set (PS)
F
D : decision (variable) space. fi : D→ R, objective functionF : D→ Rm, objective vector function
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o Find an approximation set, which is
• as diverse as possible • as close to the PF (PS)
as possible
Target of MOEA
Approximation Model Guided Selection, EMO 2013
Lower dimensional problems!
2f
1f
)(DF
Pareto front (PF)
Pareto set (P)
F
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o Reproduction • Generate new trial solutions
o Selection • Select fittest ones into the
next generation
A General MOEA Framework
Approximation Model Guided Selection, EMO 2013
Population
New Solutions
Reproduction Selection
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o Step 1: rank population • dominance rank • dominance count • dominance strength
o Step 2: estimate density • niche and fitness sharing • crowding distance • K-nearest neighbor • gridding
Dominance based Selection
Approximation Model Guided Selection, EMO 2013
Define a complete order over individuals!
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o Convert an MOP into an SOP • Obj. = performance metric
Indicator based Selection
Approximation Model Guided Selection, EMO 2013
Define a complete order over populations!
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Model Guided Selection
Approximation Model Guided Selection, EMO 2013
o Step 1: model the PF
o Step 2: choose reference points
o Step 3: select promising solutions
Much work needs to be done along this direction!
o H. J. F. Moen, et al., Many-objective Optimization Using Taxi-Cab Surface Evolutionary Algorithm, EMO, 2013.
o H. Jain, and K. Deb, An improved Adaptive Appraoch for Elitist Nondominated Sorting Genetic Algorithm for Many-Objective Optimization, EMO, 2013.
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Outline
§ Background
§ Approximation Model Guided Selection
§ Experimental Results
§ Discussions & Conclusions
Approximation Model Guided Selection, EMO 2013
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AMS Framework
o A. Zhou, Estimation of Distribution Algorithms for Continuous Multiobjective Optimization, Ph.D Thesis, University of Essex, 2009. (Chapter 5.3)
o A. Zhou, Q. Zhang, Y. Jin, and B. Sendhoff, Combination of EDA and DE for Continuous Biobjective Optimization, CEC 2008.
o Q. Zhang and H. Li, MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition, IEEE Trans. on Evolutionary Computation, 2007.
Approximation Model Guided Selection, EMO 2013
Model PF
Define sub-problem
Select
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Zero-order Approximation(AMS0)
o A single point to approximate the PF
o Model (ideal point)
o Distance to utopian PF (sub-problem)
Approximation Model Guided Selection, EMO 2013
Simple, but does not consider the shape of PF!
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First-order Approximation(AMS1)
o A simplex to approximate the PF
o Model (vertices of simplex)
o Distance to simplex
Approximation Model Guided Selection, EMO 2013
Simple, and consider the shape of PF in a sense!
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Outline
§ Background
§ Approximation Model Guided Selection
§ Experimental Results
§ Discussions & Conclusions
Approximation Model Guided Selection, EMO 2013
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Settings
o Offspring reproduction operator • A probability model based reproduction operator (RM-MEDA)
o Comparison strategy • NDS: non-dominated sorting scheme (NSGA-II)
o Test instances • 8 instances with different properties
o Performance metric • IGD: inverted general distance
Approximation Model Guided Selection, EMO 2013
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Convex PF
NDS
Approximation Model Guided Selection, EMO 2013
AMS0 AMS1
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Concave PF
NDS
Approximation Model Guided Selection, EMO 2013
AMS0 AMS1
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Tri-objective MOP
NDS
Approximation Model Guided Selection, EMO 2013
AMS0 AMS1
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Statistical Results
Approximation Model Guided Selection, EMO 2013
NDS:1 AMS0:4 AMS1:4
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Outline
§ Background
§ Approximation Model Guided Selection
§ Experimental Results
§ Discussions & Conclusions
Approximation Model Guided Selection, EMO 2013
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o AMS works better than NDS in most of the test instances
o AMS0 is more stable than AMS1
o AMS1 works better than AMS0 if a good simplex model can be found
Approximation Model Guided Selection, EMO 2013
order of model
stability of AMS
number of objectives
stability of AMS
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o How to build a high-quality model? • model should be cheap • model should be stable
o What’s the performance on complicated problems? • non-concave (non-convex) • with disconnected PF
o What’s the performance on many-objective problems? • interesting sub-problems (reference points, targets points)
Approximation Model Guided Selection, EMO 2013
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Thanks!
The source code is available from [email protected]
Approximation Model Guided Selection, EMO 2013