Optimizing Fish Passage Barrier Removal
Using Mixed Integer Linear Programming
[Preliminary Report]
Carla P. Gomes, Ashish Sabharwal
Cornell University
CROCS-09 Workshop at CP-09
Lisbon, Portugal
September 20, 2009
Overview: Stream Barriers and Fish Migration

Artificial stream barriers (e.g., dams, levees, dikes, … [see next slide])
hinder upstream and downstream movement of migratory fish

Result: dramatic impact on fish populations worldwide

Extensive guidelines have been created for undertaking projects to
 Build new in-stream structures
 Retrofit existing barriers to enhance fish passage

Issue: limited budget; must prioritize
 Some attempts but no clear guideline on which projects to focus on

Optimization question, informally: Given a budget, a stream topology, a
set of barriers, a set of restoration projects with costs and benefits,
which projects should one undertake to maximize the “net benefit”?
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
2
Stream Barriers
Hume Dam,
South Australia
Culvert
Saitama Floodgate,
Japan
North Fork Weir,
Alaska, U.S.
CROCS-09 Workshop
Levee
Ashish Sabharwal (joint work with Carla Gomes)
Texas City Dike,
Texas, U.S.
3
Impact of Fish Barriers

Well-studied issue in environmental science and conservation biology
 Drastic population decline of fish such as salmon
 Artificial barriers identified as a key reason

Barriers result in direct impacts to migratory fish:
 Increased mortality and predation
 Decreased egg production

Indirect impacts:
 Artificial selection of better swimming fish / species
 Increased in-breeding among resident fish
 Lowered nutrient inputs to upstream fish from carcasses
Good news: barriers retrofitting has also been identified as the most
cost-effective and beneficial way to mitigate the impact
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
4
Enhancing Fish Passage Through Barriers
Extensive guidelines available for
 Better design of barriers
 Retrofitting of barriers
so as to enhance fish passage through the barriers
E.g., for anadromous fish such as salmon,
fish ladders are commonly used to
assist with upstream migration for breeding
Fish ladder
at Ballard Locks, Seattle
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
5
Setup: Upstream Problem, Tree-Topology
Discrete decision vars: should we undertake project i at barrier j ?
Continuous auxiliary vars: accessibility immediately upstream of
barrier j to region with volume vj
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
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Setup: Upstream Problem, Tree-Topology
Optimization question:
Given
 budget b
 a stream topology
 set of barriers j  J
- immediately upstream region volume vj
 set of potential repair/restoration projects i  Aj for each barrier j
Decide which project to undertake at which barriers in order to
maximize the net “accessibility”
=
CROCS-09 Workshop
j vj  (fraction of fish that can access vj)
Ashish Sabharwal (joint work with Carla Gomes)
7
Traditional (and real-world) Approaches
Most approaches focus on simplicity and scalability
 Use domain experts to identify
ci,j
pi,j
:
:
cost of undertaking project i at barrier j
resulting “passability” of barrier j
 Note: domain experts = land use planners, environmental scientists,
conservation planners, wildlife service, etc.;
usually not applied mathematicians or computer scientists
 Scoring and Ranking Method: Consider each project in isolation
i. identify the one (or a few) with locally the most “bang for the buck”
ii. undertake this project, re-visit the problem with the residual budget
[e.g., Pess et al, 1998]
 akin to the greedy approach for fractional bin-packing
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
8
Traditional (and real-world) Approaches

Well-understood issue:
This ignores key spatial arrangement between the barriers
and can lead to highly sub-optimal solutions
 E.g. a high-cost high-benefit project at an upstream barrier is not very
fruitful if all barriers downstream are left with low passabilities

[O’Hanley-Tomberlin-2005]:
 First clear optimization model
• for the upstream problem with tree-like topology
 Examples to show that simple Scoring and Ranking in isolation can be
arbitrarily far from the optimal
 Created a high-degree Mixed Integer Program (Non-Linear MIP)
[ degree = number of barriers on a path from stream origin to ocean/sea ]
 Dynamic programming exact solution method
 Greedy approximation solution method
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
9
This Work: Goals
Extend O’Hanley-Tomberlin-2005 approach in the following ways:
A.
Linearize their upstream model for tree-like stream topology
B.
Use efficient MIP (Linear) solvers such as Cplex



C.
Extend to downstream migration accessibility


D.
More flexibility, e.g., could easily add incidental constraints or tweak the
optimization function
Better scalability than their exact dynamic programming approach
For large problems, closer approximation than their greedy heuristic
raises new modeling issues
simultaneous upstream + downstream migration
Relax tree-like topology restriction

Key issues identified
for practical utility
[Olivero et al, 2009;
The Nature Conservancy]
i.e., allow streams in the model to split and merge
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
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MIP (Linear) for Upstream, Tree-Topology
accessibility immediately
upstream of barrier j
Net accessibility to upstream regions
[ constraints to compute yj for each barrier j ]
≤ 1 project per barrier
total cost ≤ budget
decision variables
(discrete)
auxiliary variables
(continuous)
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
11
MIP (Linear) for Upstream, Tree-Topology
O’Hanley-Tomberlin-05 proposed Non-Linear constraints for computing
yj = net accessibility immediately upstream of barrier j
Actually, they computed
j = net increase in accessibility immediately upstream of barrier j
product over all barriers k
downstream of j
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original passability of
barrier k
new passability of
barrier k if project i
is undertaken
Ashish Sabharwal (joint work with Carla Gomes)
12
MIP (Linear) for Upstream, Tree-Topology
Our proposal: linear constraints for computing
yj = net accessibility immediately upstream of barrier j
 If repair/restoration project i is carried out at barrier j, then
accessibility immediately upstream of j is pi,j times the accessibility
immediately downstream of j

Works because yj and pi,j yparent(j) are both between 0 and 1
 their difference is bounded above by 1
 unconstrained when xi,j=0 but must be equal when xi,j=1
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
13
Lesson?
Experts in conservation biology and other core sustainability fields are
often unaware of the computational and algorithmic aspects of the
mathematical models they are trying to work with
(e.g., high non-linearity often doesn’t “bother” them)
Sustainability researchers
Computer Scientists
• Generally use predictions based
on model simulations or, at best,
simulated annealing style methods
• Generally like simple, “clean”,
abstract models that they can be
analyzed and optimized (or
approximated within control)
• Often work with highly complex
dynamical models
• See no “need” to create
computationally simple models
• Perhaps a bit too willing to give
up on many details
• Highly concerned with
computational difficulty
Need close collaboration to create
meaningful yet tractable models and solutions.
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
14
Extending to Downstream, Tree-Topology
E.g., catadromous fish migrate downstream for breeding and/or in the
winter season – need downstream accessibility as well!
Raises several design issues to begin with, e.g.
1. Multiple “parents” for any barrier
2. Different initial fish populations at various upstream starting points
(rather than a single fish mass in the ocean wanting to migrate upstream)
 can’t simply work with fractions of fish mass;
must take actual initial mass distribution into account
3. “Utility” of reaching a downstream region varies from region to region
E.g., being able to reach a region immediately downstream may be
much less beneficial than reaching a warm region very close to sea
Have created a linear MIP model to take these considerations into account
(messy but with similar ideas as before)
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
15
Extending to General Acyclic Topology
Streams may split and merge – not too often, but does happen
 Need to relax tree-like topology assumption
Raises more design issues, e.g.
 Multiple paths between two points
(rather than a unique “parent” where fish always arrive from)
 how should accessibility along different paths be combined?
max? min? average?
 should passability of the initial few barriers along each path matter?
Key is to to balance reality (obtained from domain experts)
with what’s computationally feasible
(still in progress)
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
16
Empirical Evaluation: Ongoing

Currently looking at “real” data used by O’Hanley-Tomberlin-05 from
Washington state, U.S.
 From real life but still simplified to a very small scale
(solved within seconds)
 The Nature Conservancy, e.g., would like much larger data sets
– hundreds of stream barriers, several potential projects at each
[Olivero et al, 2009]
 Computational scalability issues often not studied at all
 need to develop reasonable parameterized models to help evaluate
and tune solvers

Lesson:
 Gathering real data for sustainability problems is critical + time consuming
 Conservation planners and other sustainability researchers often spend
months and years of field work to collect data
 Naturally, not shared as easily as computer scientists are used to
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
17
Summary

Optimization for fish barrier removal is an important environmental
problem

Many guidelines on possibly restoration projects to undertake

Not much know about which projects to undertake

Natural role for constraint reasoning and optimization to enable the best
use of given resources in order to maximize migratory fish accessibility
CROCS-09 Workshop
Ashish Sabharwal (joint work with Carla Gomes)
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