Meta-Heuristics for Reconstructing Cross Cut Shredded Text Documents

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1 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 GECCO 2009 Montréal, Canada July 2009

Raidl Institute of Computer Graphics and Algorithms Vienna

2 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)

3 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)

4 Given

5 Solution to RCCSTD

6 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 = x = n 2 x = n 1 y = 1 y = 2 y = 3. y = n 1

7 Starting and Ending Shreds Starting Shred is a shred with a blank left edge Ending Shred is a shred with a blank right edge

8 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

insert row break at ending shreds Variant: Perfect Matching Heuristic

9 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

shred is reached repeat these steps until no more shreds are

10 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

shred is part of (exactly) one row modeled via an integer

11 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

12 Experimental Results Comparison of Construction Heuristics

13 Experimental Results Example of Reconstruction

14 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

based on swap move two chosen shreds are swapped with each other shift move

15 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

rectangle of shreds N 5 two shifts of one single shred N 6 two shifts of a block of

16 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

VND as local search procedure applying i 2 randomly

17 Experimental Results Comparison VNS variants

18 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)

solution obtained via GMH, PMH, RBH, MPH, and PBH pheromone update is done based on

19 Experimental Results Comparison ACO variants

20 Experimental Results Comparison of VNS and ACO

21 Experimental Results Example of VNS

22 Experimental Results Example of ACO

23 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

24 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 GECCO 2009 Montréal, Canada July 2009

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