DYNAMIC RESAMPLING FOR GUIDED EVOLUTIONARY MULTI-OBJECTIVE - - PowerPoint PPT Presentation

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DYNAMIC RESAMPLING FOR GUIDED EVOLUTIONARY MULTI-OBJECTIVE - - PowerPoint PPT Presentation

Feb 21, 2024 96 likes •520 views

DYNAMIC RESAMPLING FOR GUIDED EVOLUTIONARY MULTI-OBJECTIVE OPTIMIZATION OF STOCHASTIC SYSTEMS Florian Siegmund, Amos H.C. Ng University of Skvde, Sweden Kalyanmoy Deb Indian Institute of Technology Kanpur, India Outline Background

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DYNAMIC RESAMPLING FOR GUIDED EVOLUTIONARY MULTI-OBJECTIVE OPTIMIZATION OF STOCHASTIC SYSTEMS

Florian Siegmund, Amos H.C. Ng University of Skövde, Sweden Kalyanmoy Deb Indian Institute of Technology Kanpur, India

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Outline

  • Background Guided Search
  • Algorithm independent resampling techniques
  • Distance-based Resampling
  • Numerical Experiments
  • Conclusions/Future Work
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Background Guided Multi-objective Search

  • Precondition: Limited simulation budget
  • High budget required to explore Pareto-front
  • High-dimensional objective spaces
  • Costly evaluation of stochastic models
  • Focus on interesting areas in objective space
  • R-NSGA-II: Reference point
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Background: Reference point-based NSGA-II

  • Evolutionary Optimization Algorithm
  • Deb et al. (2006)
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NSGA-II-Selection step

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NSGA-II

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NSGA-II

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R-NSGA-II-Selection step

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Diversity Control

  • R-NSGA-II on deterministic benchmark problem ZDT1
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R-NSGA-II-Interactive

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R-NSGA-II-Interactive

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R-NSGA-II-Interactive

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Stochastic Simulation  Resampling

  • Noisy problem:
  • Simulation model has varying output for same input if

evaluatated multiple times

  • True output values are unknown
  •  Performance degradation
  • Handle noisy problem: Use sample mean and sample

standard deviation

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Resampling

  • Common: Static Resampling
  • Limited Budget
  • Trade-off: Exploration vs. Exploitation
  • Sampling allocation strategy needed
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Resampling strategies

  • Selection Sampling
  • Accuracy Sampling
  • Selection Sampling for single-objective problems: OCBA
  • R-NSGA-II uses scalar fitness criterion, but only

secondary

  •  complex

x, y

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Resampling techniques

  • Selection Sampling for EMO: complex
  •  Approximations for similar effect
  • Strategy: Good knowledge of solutions close to R will

support the algorithm

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Criteria for resampling

  • General
  • Time
  • Dominance-relation
  • Variance
  • Constraint Violation
  • Reference point
  • Distance to reference point
  • Progress
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Basic resampling techniques

  • Time-based resampling
  • Dominance-based
  • Pareto-rank-based
  • Standard Error Dynamic Resampling
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Time-based Resampling

  • Transformation function
  • NumSamples

ϵ {Min,..,Max}

  • Sampling need ϵ [0,1]
  • Mapping:

Need  NumSamples

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  • Linear allocation

Time-based resampling

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  • Delayed allocation

Time-based resampling

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  • Based on variance information
  • Single-objective version by Di Pietro (2004)
  • Multi-objective:
  • Adds k samples at a time
  • Checks whether max threshold

Standard Error Dynamic Resampling

  H se

i i

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Distance-based Resampling

  • Infeasible case
  • Feasible case
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Infeasible case

  • R is not attainable by any solution
  • R is ”below” Pareto-front
  • Minimum distance

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Infeasible case

  • R is not attainable by any solution
  •  Max number of samples never assigned
  •  Adapt transformation function
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Infeasible case

Use until a solution is found that dominates R

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Feasible case

  • R is ”over” the Pareto-front
  • Solutions can be found that dominate R
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Feasible case

  • Problem: Better solutions have higher distance to R
  • Define Virtual Reference Point VR as the solution that is
  • 1. Non-dominated
  • 2. And closest to R
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Feasible case

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Numerical experiments

  • Benchmark functions
  • Production line scheduling
  • Performance Measurement:
  • Measure average distance to R
  • From the α% closest solutions of the population
  • After every generation
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Numerical experiments

  • Benchmark functions
  • ZDT1
  • Additive noise
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R-NSGA-II, Static Resampling

  • Benchmark function ZDT1, addtive noise σ=0.15
  • R-NSGA-II, 5000 evals, R = (0.5, 0)
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Distance-based Resampling

  • Benchmark function ZDT1, addtive noise σ=0.15
  • R-NSGA-II, 5000 evals, R = (0.5, 0)
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R-NSGA-II, Time-based Resampling

  • Benchmark function ZDT1, addtive noise σ=0.15
  • R-NSGA-II, R = (0.5, 0)
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STANDARD ERROR DYNAMIC RESAMPLING

  • Benchmark function ZDT1, addtive noise σ=0.15
  • R-NSGA-II, R = (0.5, 0), SEDR
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Numerical experiments

  • Production line model
  • Minimize Work in progress
  • Maximize Throughput
  • High noise problem, CV = 1.5
  • 1 to 30 samples per solution
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Results

  • R = (WiP, TH) = (8, 0.8)
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Results

  • R = (WiP, TH) = (8, 0.8)
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Conclusions

  • Distance-based resampling is effective for R-NSGA-II
  • It performs better than algorithm independent strategies
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Future work

  • Evaluate on different noisy industrial SBO problems
  • Computing cluster with 100 workstations
  • Cooperation with Volvo
  • Obtain real output values for performance measurement
  • Accuracy Sampling
  • Selection Sampling
  • Distance to R is scalar value
  • Apply existing ranking and selection method, like OCBA
  • Simplify algorithm, only one fitness criterion
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Questions?

  • Thank you!