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

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

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

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

Background: Reference point-based NSGA-II • Evolutionary Optimization Algorithm • Deb et al. (2006)

NSGA-II-Selection step

NSGA-II

NSGA-II

R-NSGA-II-Selection step

Diversity Control • R-NSGA-II on deterministic benchmark problem ZDT1

R-NSGA-II-Interactive

R-NSGA-II-Interactive

R-NSGA-II-Interactive

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

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

Resampling strategies • Selection Sampling • Accuracy Sampling x, y • Selection Sampling for single-objective problems: OCBA • R-NSGA-II uses scalar fitness criterion, but only secondary •  complex

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

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

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

Time-based Resampling • Transformation function • NumSamples ϵ {Min,..,Max} • Sampling need ϵ [0,1] • Mapping: Need  NumSamples

Time-based resampling • Linear allocation

Time-based resampling • Delayed allocation

Standard Error Dynamic Resampling • Based on variance information • Single-objective version by Di Pietro (2004) • Multi-objective: • Adds k samples at a time    i • Checks whether max threshold se i H

Distance-based Resampling • Infeasible case • Feasible case

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

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

Infeasible case Use until a solution is found that dominates R

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

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

Feasible case

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

Numerical experiments • Benchmark functions • ZDT1 • Additive noise

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

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

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

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

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

Results • R = (WiP, TH) = (8, 0.8)

Results • R = (WiP, TH) = (8, 0.8)

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

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

Questions? • Thank you!