Design and Validation of a Hybrid Interactive Reference Point Method for Multi-Objective Optimization

Introduction Interactive Multi-Objective Optimization Hybrid Interactive Reference Point Method Tools Conclusion Design and Validation of a Hybri...
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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Design and Validation of a Hybrid Interactive Reference Point Method for Multi-Objective Optimization Madan Sathe1 , G¨unter Rudolph2 , Kalyanmoy Deb3 1 University of Basel (Switzerland), Department of Computer Science Dortmund University of Technology (Germany), Department of Computer Science Indian Institute of Technology Kanpur (India), Department of Mechanical Engineering 2

3

June 05, 2008

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Some Background . . .

Work is based on • my Diploma Thesis at Dortmund University of Technology • including a 3 months visit at IIT Kanpur, India.

Madan Sathe: Interactive Evolutionary Algorithms for Multi-Objective Optimization. VDM Verlag Dr. M¨uller, May 2008. (ISBN-13: 978-3639015287)

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Motivation

• Approximation of Pareto front requires much computation time. • The more objectives the more computation time. • At the end of the optimization process a decision maker has to

determine a single solution. • ⇒ Include user in optimization process! • Interactive tools are very rare in the field of EMOs.

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Outline

• Introduction • Interactive Multi-Objective Optimization • Hybrid Interactive Reference Point Method • Tools • Conclusions

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Interactive Multi-Objective Optimization Basic Idea • Include a user who has an internal preference function. • Self-exploration of the search space. • Feedback to current solutions. • Focus on regions of interest. • Goal: Satisfying the decision maker (DM). • since 1960: Huge amount of classical interactive algorithms

(Idea: Transformation of MOOPs to SOOPs). • since 1993: Combination of classical methods with the field

Evolutionary Computation.

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Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Interactive Reference Point Method: Algorithm

General Outline 1. Present information about the problem to the DM. 2. Ask the DM to specify a reference point. 3. Minimize a scalarizing function and obtain a Pareto optimal solution. Present the solution to the DM. 4. Calculate a number of k other solutions by minimizing a scalarizing function with perturbed reference points. 5. Present alternatives to the DM. 6. If the user is not satisfied, specify a new reference point.

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Example: Scalarizing Function M

sf (x, z¯Ref , w) = max {wi (fi (x) − z¯Refi )} + ρ ∑ {wi (fi (x) − z¯Refi )} with i=1...M

i=1

ρ >0

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

User-Based Classification

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

User-Based Classification (cont.)

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Why Hybridization? I-EMOs • . . . calculate many solutions during one run. • User can choose some rough reference points. • User obtains a better insight into the promising region. • Focus on interesting trade-offs in the neighborhoods. • . . . cover several regions of interest. • User can choose different preference information. • . . . deal with non-smooth functions. • Parallel (1 + 1)-EAs guide the user by focusing on the reference

points.

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Interactive Evolutionary Methods - Classification Hybrid Interactive Reference Point Hybrid Approach Reference Point IBEA / I-PBEA R-NSGA II BiasedCrowding

g-dominance

Malakooti et al.

Rangarajan et al.

Modified MOEA I-MOM

RD-NSGA II Reference Direction

Interactive Evolutionary Methods

WWW-NIMBUS Tools I-MODE

Fernandez et al. Jin Parmee et al. Fuzzy Logic Sakawa et al. Kiyota et al.

Utility Function

Neuronal Networks Steuer et al. Wang et al. Hapke et al. Ulungu et al. Simulated Annealing / Tabu Search Alves et al.

Singh et al. Hsu et al. Phelps et al. Quan et al. Comparison Tao et al. Branke et al. Babbar et al.

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Related Work Differences to Related Work • Individual-based (1 + 1)-EA using scalarizing function. • Decision maker • . . . has to configure only few solutions (e.g. 5). • . . . analyzes the domain of the problem by justifying the parameters (weights, reference point). • . . . can easily change the search direction and step size at each step. • . . . has a complete overview of the current state and the information attained. • . . . can assess solutions in the neighborhood at each step. • . . . obtains new calculated solutions very quickly.

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Hybrid Interactive Reference Point Method: Basic Idea (1 + 1) - EA

(1 + 1) - EA + Scalarizing

Choose x0 ∈ S at random, i = 0. while i < maxGenerations yi =mutpol (xi ); if f (yi ) < f (xi ) then xi+1 = yi else xi+1 = xi ; i++;

Choose x0 ∈ S at random, i = 0. while i < maxGenerations yi =mutpol (xi ); if sf (yi , z¯i , w) < sf (xi , z¯i , w) then xi+1 = yi else xi+1 = xi ; i++;

where

M

sf (x, z¯Ref , w) = max {wi (fi (x) − z¯Refi )} + ρ ∑ {wi (fi (x) − z¯Refi )} i=1...M

(ρ =

i=1

10−6 )

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Hybrid Interactive Reference Point Method

Hybrid Interactive Reference Point Algorithm 1. Create n randomized and feasible starting points zi . 2. DM determines n reference points z¯i with i ∈ {1, . . . , n}. 3. While DM not satisfied with solution. • Optimize with the (1 + 1) - EA + Scalarizing.

4. Possible local improvement with “Pareto descent method”1 . 5. Calculate user-defined neighborhood.

1 Harada

et al. (2006) 14 / 20

Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Configuration - Display

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Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Interactive Reference Point - Display

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Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Demonstrator - Display

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Introduction

Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Summary • Classification of existing interactive classical methods via a

user-based approach. • Classification of existing evolutionary methods. • New Hybrid Interactive Reference Point Method. • New tool to support the DM finding regions of interest.

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Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

Outlook • Checking the Pareto optimality. • Tests and comparison with other interactive methods. • Many-objective optimization problems (colors). • Consideration of the decision space. • Multiple DMs.

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Interactive Multi-Objective Optimization

Hybrid Interactive Reference Point Method

Tools

Conclusion

The End Any questions?

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