1. Heuristic Search and Information Visualization Methods for School Redistricting University of Maryland Baltimore County Marie desJardins, Blazej Bulka, Ryan Carr, Andrew Hunt, Priyang Rathod, and Penny Rheingans This work was partially supported by NSF # IIS-0414976. Thanks to David Drown and the Howard County Public School System for data and valuable inputs.

2. July 18, 2006 2 Overview  The Problem: School Redistricting  Searching for Good Plans  Results  Future Work and Conclusions

3. July 18, 2006 3 The Problem: School Redistricting

4. July 18, 2006 4 School Redistricting  Assign neighborhoods (or planning polygons) within a school district to schools while considering multiple factors, such as busing costs, test score distribution, and school utilization  Finding the best assignment (or plan) is a multiattribute optimization problem  Also want to generate qualitatively different plans that represent tradeoffs among the criteria, and help users visualize these tradeoffs  Search space is very large: O(s p ), where  s is the number of schools (12 high schools; 30 elementary)  p is the number of polygons (~263)  Currently in Howard County, Maryland, the process is almost entirely manual

5. July 18, 2006 5 Evaluation Criteria  Educational benefits for students  Frequency with which students are redistricted  Number and distance of students bused  Total busing cost  Demographics and academic performance of schools  Number of students redistricted  Maintenance of feeder patterns  Changes in school capacity  Impact on specialized programs  Functional and operational capacity of school infrastructure  Building utilization

6. July 18, 2006 6 Evaluation Criteria  Educational benefits for students  Frequency with which students are redistricted  Number and distance of students bused  Total busing cost  Demographics and academic performance of schools  Number of students redistricted  Maintenance of feeder patterns  Changes in school capacity  Impact on specialized programs  Functional and operational capacity of school infrastructure  Building utilization

7. July 18, 2006 7 Evaluation Criteria 1.Number of students bused  Students who can walk to a school should be assigned to that school 2.Busing cost  Estimated as a population-weighted sum of polygon-school distances 3.Demographics  FARM (Free and Reduced Meal) ratio at each school should ideally be the same as that of the county as a whole 4.Academic performance  MSA (Maryland State Assessment) scores at each school should ideally be the same as those of the county as a whole 5.Capacity  Each school should be between 90% and 110% of available capacity  Penalty functions are defined for each of the five criteria above  per-polygon, per-school, per-plan cost measure from 0 (good) to 1 (bad)

8. July 18, 2006 8 Selecting Multiple Plans: Diversity  One plan dominates another if it is better along all dimensions  Two plans are incomparable if each is better than the other along at least one dimension  A good set of plans should:  contain no dominated plans  consist of qualitatively different plans  We measure “qualitatively different” using Euclidean distance in the evaluation space:  Div(P) = 1/|P|  p i, p j  P Dist(p i, p j )

9. July 18, 2006 9 Closest-School Plan Marriottsville High (new)

10. July 18, 2006 10 Closest [outer] vs. Recommended [inner]

11. July 18, 2006 11 Searching for Good Plans

12. July 18, 2006 12 Multiattribute Optimization  Previous approaches to multiattribute optimization:  Weighted methods: Combine attributes into a single weighted sum  Priority-based methods: Optimize one attribute, then perform constrained optimization on the other attributes  MOA* (and variations): Find all nondominated solutions using heuristic search  Evolutionary methods: Use genetic search to explore the population space using recombination and fitness-based selection  Redistricting domain:  No single set of weights or prioritization scheme  Very large search space  can’t find all (or even most) nondominated solutions  Use local search

13. July 18, 2006 13 Basic Hill-Climbing  Baseline:  Choose an initial plan as a starting point (seed)  then hill-climb through “[weighted] sum of criteria” space  Seed options:  closest-school plan  current plan  random plan  “breadth-first” assignment  “minimum-spanning-tree” assignment

14. July 18, 2006 14 Biased Hill-Climbing  General approach:  Choose an initial plan as a seed  Hill-climb through “dominated plan” space  Save “incomparable plans” as they are encountered  Stop at a local maximum  Restart search starting from a plan in the incomparable list  Blind bias:  At restart, choose a plan from the incomparable list at random  Diversity bias:  At restart, choose the plan that is farthest in evaluation space from the solutions found so far

15. July 18, 2006 15 Results

16. July 18, 2006 16 Quality of Generated Plans  Quality of generated plans is better than manually generated plans ...with respect to the particular evaluation criteria we’ve defined  Original-plan seed does better than closest-plan seed  leads to the “wrong” local maximum  Compared to recommended plan, generated plans generally perform: ...better with respect to capacity ...comparably with respect to socioeconomic and academic measures ...better with respect to busing costs ...comparably with respect to walk utilization Outer: Recommended Inner: Best generated

17. July 18, 2006 17 Diversity of Generated Plans  Baselines:  Manual plans: closest, recommended, and alternative (diversity measure = 0.223  )  Unweighted hill-climbing: multiple runs of basic hill-climbing with different initial seeds (diversity measure = 0.044  )  Weighted hill-climbing: multiple runs of basic hill-climbing with different weight vectors (diversity measure = 0.048  )  Biased hill-climbing:  with blind bias: diversity measure = 0.032   with diversity bias: diversity measure = 0.389  Note: Biased hill-climbing yields a somewhat worse average unweighted sum, so the plans are not quite “as good” in a direct comparison 

18. July 18, 2006 18 Future Work and Conclusions

19. July 18, 2006 19 Future Work  Modeling additional evaluation criteria:  Feeder statistics  Redistricting frequency  Incorporating projected future demographic shifts into evaluation, search, and visualization  Extensions to search methods:  Other definitions of diversity (e.g., dispersion, similar to k-means mean-squared error)  Other multiattribute optimization methods (particularly genetic methods)  Visualization extensions:  Visualizing feeder patterns  Computing and visualizing gradients in search space  Deployment and user testing

20. July 18, 2006 20 Conclusions  School redistricting is an important and challenging problem  The multiattribute optimization framework is a good paradigm for this application  Novel search techniques and evaluation methods are needed  Diversity-biased hill climbing is a promising initial approach