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Applications of Tabu Search. OPIM 950 Gary Chen 9/29/03. Basic Tabu Search Overview. Pick an arbitrary point and evaluate an initial solution Compute next set of solutions within neighborhood of current solution Pick best solution from the set.

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applications of tabu search

Applications of Tabu Search

OPIM 950

Gary Chen

9/29/03

basic tabu search overview
Basic Tabu Search Overview
  • Pick an arbitrary point and evaluate an initial solution
  • Compute next set of solutions within neighborhood of current solution
  • Pick best solution from the set.
  • If solution is on Tabu (or forbidden) list, pick next best solution. Repeat until you come across solution not on Tabu list.
  • After solution is chosen, repeat from step 2 until optima is reached.
  • Parameters for tuning: Number of iterations, penalty points, size of Taboo list
applications
Applications
  • Bioengineering
  • Finance
  • Manufacturing
  • Scheduling
  • Political Districting

Many of the applications of Tabu Search are very similar to Simulated Annealing

application 1 student course scheduling
Application 1: Student Course Scheduling
  • Problem: Registering for classes required students waiting in long queues.
  • Solution: Allow course registration over the internet and using OR techniques (tabu search), give student satisfactory time schedule as well as balance section loads.
objectives and constraints
Objectives and Constraints
  • Main Objective: Find conflict-free time schedule for each student
  • Secondary Objectives:
    • Balance number of classes per day
    • Minimize gaps between classes
    • Respect language preferences
  • Student course selections must be respected
  • Section enrollment must be balanced
  • Section maximum capacity cannot be exceeded
implementation part 1

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Implementation - Part 1
  • Construct student timetable without considering section enrollments
  • Model course sections as undirected graphs
maximum cardinality independent sets
Maximum Cardinality Independent Sets
  • Objective: Find sets that contain one section of each course.
  • Algorithm
    • Find all cliques in the graphs.
    • Pick one node or no nodes from each clique. Check if it’s a valid schedule. If it is retain as a possible solution set.
    • repeat
implementation part 2
Implementation - Part 2
  • Balance out section enrollment
  • Each student has a set of possible time schedules.
  • “Optimal” time schedule for a student adheres to following criteria:
    • Balance number of classes per day
    • Minimize gaps between classes
    • Respect language preferences
tabu search
Tabu Search
  • Objective: Find satisfactory course schedule.
    • “Satisfactory” being a solution no more than a threshold cost distance from the “optimal” course scheduling.
    • Tabu list contains previously tried student course schedules.
  • Tabu search combined with strategic oscillation used.
strategic oscillation
Strategic Oscillation
  • Perform moves until hitting a boundary.
  • Modify objective constraints or extend neighborhood function to allow crossing over to infeasible region.
  • Proceed beyond boundary for a set depth
  • Turn around to enforce feasibility
strategic oscillation cont
Strategic Oscillation (Cont)
  • For course selection, class size is strategically oscillated.
application 2 tabu search for political districting
Application 2: Tabu Search for Political Districting
  • Problem: Partition a territory into voting districts. Political influence problems.
  • Solution: Using tabu search for deciding districts will result in a fair, unbiased answer
constraints
Constraints
  • Districts should be contiguous
  • Voting population should be close to evenly divided among the districts
  • Natural boundaries should be respected
  • Existing political subdivisions, such as townships, should be respected
  • Socio-economic homogeneity
  • Integrity of communities should be respected
general solution strategy
General Solution Strategy
  • Clustering approach
    • First pick several pre-determined centroid districts.
    • “Grow” districts outward.
  • Previous attempts
    • Branch-and-bound trees (NP-hard)
    • Simulated annealing
problem formulation
Problem Formulation
  • minimize
  • i are user-supplied multiplers
  • fpop(x) = population equality function
  • fcomp(x) = compactness function
  • fsoc(x) = socio-economic homogeneity function
  • fsim(x) = similarity to previous districting function
  • fint() = integrity of communities function
population equality
Population Equality

Pj(x) – represents population for each j district

- represents total population/#districts

 - represents user-defined constant fraction, 0  1

Require population in each district [(1-) , (1+) ]

Should equal 0 if each district lies in interval. Otherwise, will take a positive value

compactness
Compactness
  • Rj(x) = length of jth district boundary
  • R = perimeter of entire territory
socio economic homogeneity
Socio-Economic Homogeneity
  • Sj(x) = standard deviation of income in district j.
  • = average income in entire territory
similarity to previous districting
Similarity to Previous Districting
  • Oj(x) = largest overlay of district j and similar district in new solution
  • A = Entire territory area
integrity of communities
Integrity of Communities
  • Gj(x) = largest population of a given community (Chinese, latino, etc) in district j.
  • Pj(x) = total population in district j.
tabu search1
Tabu Search
  • Start with initial solution
    • Start with a seed unit for initializing a district.
    • “Grow” district by merging it with adjacent units until reached or no adjacent unit are available.
tabu search cont
Tabu Search (cont)
  • After initial solution created, two possible moves.
    • Give – give a basic unit from one district to another
    • Swap – swap basic units along boundary of two adjacent districts
  • Any basic units swapped or given are placed on a tabu list.
  • Algorithm stops when value of current best solution has no improvements from previously known best solution.
references
References
  • Alvarez-Valdes, R. et al. Assigning students to course sections using tabu search. Annals of Operations Research. Vol. 96 (2000) p. 1-16
  • Bozkaya, Burcin. A tabu search heuristic and adaptive memory procedure for political districting. European Journal of Operational Research. Vol. 144 (2003) p. 12-26.