Meta-Heuristics for Reconstructing Cross Cut Shredded Text Documents Matthias Prandtstetter Günther R. Raidl Institute of Computer Graphics and Algorithms Vienna University of Technology, Austria www.ads.tuwien.ac.at GECCO 2009 Montréal, Canada July 2009
Reconstruction of Cross Cut Shredded Text Documents (RCCSTD) Given a set S of snippets {1,..., n} all of same height back face blank completely blank shreds removed n denoting a virtual shred cost functions c(i, j) and c(i, j)
Reconstruction of Cross Cut Shredded Text Documents (RCCSTD) Given a set S of snippets {1,..., n} all of same height back face blank completely blank shreds removed n denoting a virtual shred cost functions c(i, j) and c(i, j)
Given
Solution to RCCSTD
Solution to RCCSTD x = 1 x = 2 x = 3 x = 4 x = 5 x = 6 x = 7 x = 8 x = 9 x = 10 x = 11 x = 12... x = n 2 x = n 1 y = 1 y = 2 y = 3. y = n 1
Starting and Ending Shreds Starting Shred is a shred with a blank left edge Ending Shred is a shred with a blank right edge
Matching Heuristics Greedy Matching Heuristic (GMH) in each iteration find best matching pair of shreds repeat with matching pairs, etc. insert row break at ending shreds Variant: Perfect Matching Heuristic (PMH) computing perfect matchings Randomized version of GMH randomly select matching pairs
Row Building Heuristics (RBH) begin the next row with a starting shred continue with best fitting shred end row if an ending shred is reached repeat these steps until no more shreds are available Randomized version of RBH continue with randomly selected shred
Multiple Paths Heuristic (MPH) search a solution of minimum costs such that at least one row is built each shred is part of (exactly) one row modeled via an integer linear programming formulation solved using a Branch&Cut approach
Prim Based Heuristics (PBH) start with an arbitrarily chosen shred place the next shred adjacent (best fitting one) Randomized version of PBH randomly select the next shred
Experimental Results Comparison of Construction Heuristics
Experimental Results Example of Reconstruction
Variable Neighborhood Descent (VND) local search based meta-heuristic systematically changing neighborhood structures neighborhood structures based on swap move two chosen shreds are swapped with each other shift move one shred is moved to another position while all other shreds are shifted accordingly
Neighborhood Structures N 1 one single swap move N 2 one single shift move N 3 shifting a block of horizontally/vertically adjacent shreds N 4 shifting an arbitrarily large rectangle of shreds N 5 two shifts of one single shred N 6 two shifts of a block of horizontally/vertically adjacent shreds N 7 two shifts of an arbitrarily large rectangle of shreds
Variable Neighborhood Search simple and successful meta-heuristic (Hansen and Mladenovic 1999) using VND as local search procedure applying i 2 randomly chosen shift moves in the i-th perturbation neighborhood
Experimental Results Comparison VNS variants
Ant Colony Optimization tries to imitate the behavior of ants pheromone laid corresponds to likelihood of neighbor relations of shreds uniformly initialized based on the best solution obtained via GMH, PMH, RBH, MPH, and PBH pheromone update is done based on solutions generated by randomized versions of GMH, RBH, and PBH (using pheromone as decision support)
Experimental Results Comparison ACO variants
Experimental Results Comparison of VNS and ACO
Experimental Results Example of VNS
Experimental Results Example of ACO
Summary five different construction heuristics three randomized versions variable neighborhood search based approach ant colony optimization based approach ACO achieved better results in 34 out of 45 test instances additional neighborhood structures for VNS/VND should be examined further more problem specific construction heuristics to be used within ACO needed
Meta-Heuristics for Reconstructing Cross Cut Shredded Text Documents Matthias Prandtstetter Günther R. Raidl Institute of Computer Graphics and Algorithms Vienna University of Technology, Austria www.ads.tuwien.ac.at GECCO 2009 Montréal, Canada July 2009