Blended near-optimal tools for flexible
water resources decision making
David E. Rosenberg
CEE 6410
Grant #1149297
Now
Learning Objectives
• Formulate near-optimal
problems,
• Generate, visualize, and explore
near-optimal alternatives,
• Apply the near-optimal tools to
a reservoir optimization
problem,
• Identify improvements to tools
Best or better?
2
Near-Optimal Defined
1. Find optimal
Max Z  f  x1 , x2 
s.t.
Ax  b
2. Alternatives a
specified tolerance (γ)
from optimal (Z*)
f  x1 , x2     Z
*
3
Near-Optimal Defined
1. Find optimal
Max Z  f  x1 , x2 
s.t.
Ax  b
2. Alternatives a
specified tolerance (γ)
from optimal (Z*)
f  x1 , x2     Z
*
4
New Blended Near-Optimal Tools
1. Alternative generation
– Stratify Monte Carlo Markov Chain sample
2. Visualize
– Parallel coordinate plot
3. Interact
– Plot controls to render, filter, generate new alts.
– Update model formulation
Help managers find near-optimal alternatives
they prefer to the optimal solution
5
Monte-Carlo Markov Chain Alt.
Generation
1. Random sample to
cover near-optimal
region
2. GIBBS method
 Maximum extents
 Cycle through
coordinates
3. Much more
efficient that
rejection sampling
2nd Alt.
1st Alt.
6
Parallel Coordinate Visualization
7
Interaction tools
8
Further Information
[email protected]
http://rosenberg.usu.edu
@WaterModeler
Code Repository & Documentation
• https://github.com/dzeke/Blended-Near-Optimal-Tools
Rosenberg (2015). “Blended near-optimal
alternative generation, visualization, and interaction
tools for water resources decision making.”Water
Resources Research. 10.1002/2013WR014667.
Phosphorus removal, Echo Reservoir, Utah
Best Management
Practices
1. Fence streams
2. Grass filter strips
3. Protect grazing land
4. Stabilize stream banks
5. Retire land
6. Cover crop
7. Manage agricultural nutrients
…and others
Problem Specifics and Formulation
Decide BMP implementation levels (biws) to
 Pending TMDL in 2006
 Reduce non-point source
load by 8,067 kg/year
 10 practices (i)
3 sources (s)
3 sub-watersheds (w)
 39 decisions!!
∑ p
Minimize costs Z 
iws
U i 
iws
Such that
i. Define phosphorus removed,
piws = Ei × biws ; ∀ i, s, w
ii. Phosphorus reduction targets achieved,
∑( piws × Cis ) ≥Pws ;∀w, s
i
iii. Available resources to implement BMPs,
∑∑ C
is
s
Dgi biws  ≤ Bgw ;∀g, w
i
iv. Remove no more than the existing load, and
∑ p
iws
(Alminagorta et. al, 2013)
v.
 Cis   Lws ;∀w, s
i
Non-negative variable values
12i, w, s
piws ≥ 0;∀ i, w, s ; biws ≥ 0;∀