Carla P. Gomes, Ashish Sabharwal Cornell University CROCS-09 Workshop at CP-09 Lisbon, Portugal

1. 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

2. 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”? Ashish Sabharwal (joint work with Carla Gomes)

3. Stream Barriers Texas City Dike,Texas, U.S. Hume Dam,South Australia Saitama Floodgate,Japan Levee Culvert North Fork Weir,Alaska, U.S. Ashish Sabharwal (joint work with Carla Gomes)

4. 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 mostcost-effective and beneficial way to mitigate the impact Ashish Sabharwal (joint work with Carla Gomes)

5. 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 toassist with upstream migration for breeding Fish ladderat Ballard Locks, Seattle Ashish Sabharwal (joint work with Carla Gomes)

6. Setup: Upstream Problem, Tree-Topology Discrete decision vars: should we undertake project i at barrier j? Continuous auxiliary vars: accessibility immediately upstream of barrier jto region with volume vj Ashish Sabharwal (joint work with Carla Gomes)

7. 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” • = jvj  (fraction of fish that can accessvj) Ashish Sabharwal (joint work with Carla Gomes)

8. Traditional (and real-world) Approaches Most approaches focus on simplicity and scalability • Use domain experts to identifyci,j : cost of undertaking project i at barrier jpi,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 • identify the one (or a few) with locally the most “bang for the buck” • undertake this project, re-visit the problem with the residual budget  akin to the greedy approach for fractional bin-packing [e.g., Pess et al, 1998] Ashish Sabharwal (joint work with Carla Gomes)

9. Traditional (and real-world) Approaches • Well-understood issue:This ignores key spatial arrangement between the barriersand 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 Ashish Sabharwal (joint work with Carla Gomes)

10. This Work: Goals Extend O’Hanley-Tomberlin-2005 approach in the following ways: • Linearize their upstream model for tree-like stream topology • Use efficient MIP (Linear) solvers such as Cplex • 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 • Extend to downstream migration accessibility • raises new modeling issues • simultaneous upstream + downstream migration • Relax tree-like topology restriction • i.e., allow streams in the model to split and merge Key issues identifiedfor practical utility [Olivero et al, 2009;The Nature Conservancy] Ashish Sabharwal (joint work with Carla Gomes)

11. MIP (Linear) for Upstream, Tree-Topology Net accessibility to upstream regions accessibility immediatelyupstream of barrier j [ constraints to compute yj for each barrier j ] ≤ 1 project per barrier total cost ≤ budget decision variables(discrete) auxiliary variables(continuous) Ashish Sabharwal (joint work with Carla Gomes)

12. MIP (Linear) for Upstream, Tree-Topology O’Hanley-Tomberlin-05 proposed Non-Linear constraints for computingyj= net accessibility immediately upstream of barrier j Actually, they computed j= net increase in accessibility immediately upstream of barrier j new passability ofbarrier k if project iis undertaken original passability ofbarrier k product over all barriers kdownstream of j Ashish Sabharwal (joint work with Carla Gomes)

13. MIP (Linear) for Upstream, Tree-Topology Our proposal: linear constraints for computingyj= net accessibility immediately upstream of barrier j • If repair/restoration project i is carried out at barrier j, thenaccessibility immediately upstream of j is pi,j times the accessibilityimmediately downstream of j  • Works because yj and pi,jyparent(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 Ashish Sabharwal (joint work with Carla Gomes)

14. 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 • Generally use predictions based on model simulations or, at best, simulated annealing style methods • Often work with highly complex dynamical models • See no “need” to create computationally simple models • Computer Scientists • Generally like simple, “clean”, abstract models that they can be analyzed and optimized (or approximated within control) • Perhaps a bit too willing to give up on many details • Highly concerned with computational difficulty Need close collaboration to createmeaningful yet tractable models and solutions. Ashish Sabharwal (joint work with Carla Gomes)

15. 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. • Multiple “parents” for any barrier • 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 • “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) Ashish Sabharwal (joint work with Carla Gomes)

16. 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) Ashish Sabharwal (joint work with Carla Gomes)

17. 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 Ashish Sabharwal (joint work with Carla Gomes)

18. 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 Ashish Sabharwal (joint work with Carla Gomes)