
Applications of Tabu Search opim 950 Gary Chen

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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. 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 Bioengineering Finance Manufacturing Scheduling Political Districting Many of the applications of Tabu Search are very similar to Simulated Annealing
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 Main Objective: Find conflictfree time schedule for each student Secondary Objectives: Student course selections must be respected Section enrollment must be balanced Section maximum capacity cannot be exceeded
Implementation  Part 1 Construct student timetable without considering section enrollments Model course sections as undirected graphs
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 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 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 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
Strategic Oscillation (Cont) For course selection, class size is strategically oscillated.
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 Districts should be contiguous Voting population should be close to evenly divided among the districts Existing political subdivisions, such as townships, should be respected Socioeconomic homogeneity Integrity of communities should be respected
General Solution Strategy  First pick several predetermined centroid districts.
 “Grow” districts outward.
Previous attempts  Branchandbound trees (NPhard)
 Simulated annealing
Problem Formulation minimize i are usersupplied multiplers fpop(x) = population equality function fcomp(x) = compactness function fsim(x) = similarity to previous districting function fint() = integrity of communities function
Population Equality
Compactness Rj(x) = length of jth district boundary R = perimeter of entire territory
SocioEconomic Homogeneity Sj(x) = standard deviation of income in district j.
Similarity to Previous Districting Oj(x) = largest overlay of district j and similar district in new solution A = Entire territory area
Example
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 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) After initial solution created, two possible moves. 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.
Example
References AlvarezValdes, R. et al. Assigning students to course sections using tabu search. Annals of Operations Research. Vol. 96 (2000) p. 116 Bozkaya, Burcin. A tabu search heuristic and adaptive memory procedure for political districting. European Journal of Operational Research. Vol. 144 (2003) p. 1226.
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