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Multiobjective Calibration with PADDS: Testing Alternative Selection Metrics. Masoud Asadzadeh Bryan Tolson. Outline. Objectives PA-DDS algorithm Alternative selection metrics Experiment to choose proper selection metric MO Performance Evaluation with CNHV
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Multiobjective Calibration with PADDS: Testing Alternative Selection Metrics Masoud Asadzadeh Bryan Tolson
Outline • Objectives • PA-DDS algorithm • Alternative selection metrics • Experiment to choose proper selection metric • MO Performance Evaluation with CNHV • Validation of Selected Metric, MO Model Calibration • Conclusions and Future Work
Objectives • Evaluating PA-DDS performance: • Solving MOPs with more than 2 objectives • Using alternative selection metrics • Random (RND) • Crowding Distance (CD) • Hypervolume (HV) • Choosing proper selection metric • Validating selected metric, comparing modified PA-DDS against high quality MO algorithms: • AMALGAM vs. ɛ-NSGAIIvs. PA-DDS
Pareto Archive DDS Initialize starting solutions Perturb current ND solution Update ND solutions Create ND-solution set Pick a ND solution Pick the New solution New solution is ND? Y N Y STOP N Continue?
Alternative Selection Metrics • Random Selection (RND) • Crowding Distance (CD) • Deb et al. (2002) • Contribution to HyperVolume(HV) • Zitzler and Thiele 1999 • Used as selection metric in Emmerich et al. (2005) f2 f1
Experiment to Choose Selection Metric PA-DDS • Number of Trials: 50 • Budget: 1,000 and 10,000 • Performance Evaluation: CNHV RND CD HV 1 2 3 Mathematical Test Suites
Mathematical Test Problem, ZDT4Zitzler et al. (2000) • 10 decision variables • 2 objectives • 219 local fronts • Convex Pareto front
Mathematical Test Problem, WFG4Huband et al. (2006) • Scalable • 24 decision variables • 2 and 3 objectives • Highly Multi-modal • Concave front
MO Model Comparison • Comparative Normalized Hyper-Volume 1 Worst attained front Best attained front 1
CNHV vs. HV • Same as HV or NHV • CNHV always prefers dominating solution • CNHVA > CNHVB : B doesn’t weakly dominate A • CNHVmax = 1 & CNHVmin = 0 • Compares multiple trials of multiple algorithms • Measures performance across compared algorithms
Results: ZDT4 1 1 1 1
Validating the Selected Metric PA-DDS • Number of Trials: 10 • Budget: 10,000 • Performance Evaluation: CNHV RND CD HV 1 2 3 Mathematical Test Suites ε-NSGAII PA-DDS AMALGAM Model Calibration
Model Calibration, Town Brook • Sub-watershed in Cannonsville • 37 km2 • SWAT2000 • 26 Parameters • Nash Sutcliffe • Flow, Phosphorus delivery Tolson and Shoemaker 2007
Conclusions & Future Work • PA-DDS inherits simplicity and parsimonious characteristics of DDS • Generates good Pareto approximate front in the modeller's time frame • Reduces the need to fine tune the algorithm parameters • Solves both continuous and discrete problems • PA-DDS can solve MOPs with more than 2 objectives • HV based selection clearly improves PA-DDS performance • PA-DDS with HV selection is promising compared to two high quality benchmark algorithms, AMALGAM and ε-NSGAII • Evaluate PA-DDS performance in solving Multi Objective model calibrations with more than 2 objective functions • Implement a more efficient archiving strategy and dominance check (e.g. Fieldsend et al. 2003)
