Kollat 2007 AGU ehBOA.pdf - Pennsylvania State University

Enhancing the Solution of Large Monitoring
Network Design Problems
Using a New Epsilon-Dominance
Hierarchical Bayesian Optimization
Algorithm
Joshua B. Kollat and Patrick M. Reed
Civil and Environmental Engineering
The Pennsylvania State University
juk124@psu.edu
Paper Number: H11K-08
AGU Fall Meeting – December 2007 Slide 1

Citation:
Presentation Information
Kollat, J.B., P.M. Reed. Enhancing the Solution of Large Monitoring Network Design Problems
Using a New Epsilon Dominance Hierarchical Bayesian Optimization Algorithm. Paper
#H11K-08. Proceedings of the AGU Fall Meeting, San Francisco, CA, (2007).
For additional information, refer to:
Kollat, J.B., P.M. Reed, J.R. Kasprzyk. A New Epsilon-Dominance Hierarchical Bayesian
Optimization Algorithm for Large Multi-Objective Monitoring Network Design Problems.
Advances in Water Resources. 31 (5) (2008) 828-845.
Note:
This presentation has been slightly modified from its original version in order to better suite the
static nature of PDF format.
AGU Fall Meeting – December 2007 Slide 2

Intro to Multi-Objective Optimization
� Two Objective
Example:
– Non-dominated
– Pareto Set
� Tradeoffs or Conflicts:
– Improvements in
performance in one
objective result in a
degradation of
performance in
another objective
AGU Fall Meeting – December 2007 Slide 3

Multi-Objective Evolutionary
� Mimic Darwinian natural
selection to optimize designs
– Selection
– Crossover
– Mutation
� Evolve entire tradeoff surfaces
in a single run
� Effective at optimizing:
– highly-nonlinear
– discrete
– non-convex
landscapes without
differentiation
Algorithms (MOEAs)
AGU Fall Meeting – December 2007 Slide 4

Motivation – Problem Size Scaling
AGU Fall Meeting – December 2007 Slide 5

Motivation – Objective Scaling
AGU Fall Meeting – December 2007 Slide 6

Motivation – Computational Scaling
AGU Fall Meeting – December 2007 Slide 7

Motivation – Computational Scaling
AGU Fall Meeting – December 2007 Slide 8

Motivation – Potential for Structure
� Potential for complex
spatial and/or
temporal interdependencies
� Hierarchical difficulty
– Correlations within
groups and across
groups
� Traditional MOEAs
– Assume decisions are independent
� Hierarchical Bayesian Optimization Algorithm
– Models dependency structure of decisions using Bayesian networks
– Uses chunking to model hierarchy
AGU Fall Meeting – December 2007 Slide 9

�-NSGAII
to �-hBOA
AGU Fall Meeting – December 2007 Slide 10

LTM Test Cases:
� Two Test Cases – PCE
Contamination Plume
– Small: 25 wells – 33-million
designs
– Large: 58 points – 2.88x10 17
designs
� Quantile Kriging
AGU Fall Meeting – December 2007 Slide 11

LTM Test Cases:
� Two Test Cases – PCE
Contamination Plume
– Small: 25 wells – 33-million
designs
– Large: 58 points – 2.88x10 17
designs
� Quantile Kriging
� Objectives:
– Sampling Cost
Cost = 16
AGU Fall Meeting – December 2007 Slide 12

LTM Test Cases:
� Two Test Cases – PCE
Contamination Plume
– Small: 25 wells – 33-million
designs
– Large: 58 points – 2.88x10 17
designs
� Quantile Kriging
� Objectives:
– Sampling Cost
– Concentration Error
Cost = 16
Concentration
Concentration
Error
AGU Fall Meeting – December 2007 Slide 13

LTM Test Cases:
� Two Test Cases – PCE
Contamination Plume
– Small: 25 wells – 33-million
designs
– Large: 58 points – 2.88x10 17
designs
� Quantile Kriging
� Objectives:
– Sampling Cost
– Concentration Error
– Concentration Uncertainty
– Mass Error
Cost = 16
Concentration
Concentration
Concentration
Uncertainty
Error
AGU Fall Meeting – December 2007 Slide 14

LTM Test Case Pareto Sets
� 25 Well Test Case
– True Pareto Set
– 2,472 Solutions
AGU Fall Meeting – December 2007 Slide 15

LTM Test Case Pareto Sets
� 25 Well Test Case
– True Pareto Set
– 2,472 Solutions
� 58 Point Test Case
– Generated by
combining solutions
from all algorithm
runs
– Represents best
known Pareto
approximation
– 22,333 Solutions
AGU Fall Meeting – December 2007 Slide 16

Results: �-Performance and Convergence Dynamics
AGU Fall Meeting – December 2007 Slide 17

Results: �-Performance and Convergence Dynamics
AGU Fall Meeting – December 2007 Slide 18

Results: Pie Chart
AGU Fall Meeting – December 2007 Slide 19

Results: �-NSGAII, �-hBOA-Base, �-hBOA-Static
AGU Fall Meeting – December 2007 Slide 20

Results: �-NSGAII, �-hBOA-Base, �-hBOA-Static
AGU Fall Meeting – December 2007 Slide 21

Results: �-NSGAII, �-hBOA-Base, �-hBOA-Static
AGU Fall Meeting – December 2007 Slide 22

Results: �-NSGAII, �-hBOA-Base, �-hBOA-Static
AGU Fall Meeting – December 2007 Slide 23

Results: �-NSGAII, �-hBOA-Base, �-hBOA-Static
AGU Fall Meeting – December 2007 Slide 24

Conclusions
� The �-hBOA was statistically superior to the �-NSGAII
� The �-hBOA’s superiority on the 25 well test case indicates
inter-related decisions and hierarchical problem difficulty
� Choosing static versus dynamic population sizing for the �hBOA
depends on computational resources and the user’s
goals
– Dynamic: rapid approximations and optimal population size
– Static: high quality end result, high reliability
� Still much work to be done…
– Test cases represent lower bound complexity
– Extension to space-time optimization
– Parallelization
AGU Fall Meeting – December 2007 Slide 25

Thank You
AGU Fall Meeting – December 2007 Slide 26