Constructive algorithms have been shown to be
an effective solution approach.
However, decoding the representation as a
permutation of pieces and the layout of the
solution is not a 1-1 mapping
Hypothesis: there exists significant redundancy in
the search algorithm as a result of reproducing
the same solution from a different representatio

Bennell, Julia A.

English

Southampton (e-Prints Soton)

1Local search  Local search framework framework for irregular  for irregular shaped stock shaped stock- - cutting cuttingJulia A BennellCentre for Operational Research, Management Science and Information SystemsUniversity of Southampton, UK1st Meeting, Germany, March 18-20 2004Aims and motivationDevelop an understanding of how well various problem specific decisions work in a local search framework for the irregular cutting problem.§Investigate the performance of various local search   neighbourhoods for irregular stock- cutting§Use iterated local search to minimise parameterrefinement§Remove all problem specific enhancements§Not to beat the best but to learn more about the relationship between local search and such problems2Aims and motivationMost of the successful implementations in the literatureemploy problem specific enhancements and/or complexoptimisation procedures§Single or multiple (conflicting) objectives§Different representations of the solution§Computationally expensive enhancements§Complex neighbourhood move criteriaWhy they work is often conjectureThis studyConstructive algorithms have been shown to be an effective solution approach.However, decoding the representation as a permutation of pieces and the layout of the solution is not a 1-1 mappingHypothesis: There exists significant redundancy in the search algorithm as a result of reproducing the same solution from a different representation3Iterated local search1. randomly generate initial solution (S0) with cost C(S0)let Sbest= S02. If termination conditions are satisfied STOP3. Let Si ˛ N(S0) i=1,nfor all i if C(Si) < C(S0) accept S0 = Siif C(S0) < C(Sbest) Sbest = S0return to 2 4 if i=n perform kick S0 = Skreturn 2ENDIterated local search and iteratively construct solution§solution represented by permutation of pieces§initial solution randomly generated§neighbourhood of piece j all possible insert moves §piece j selected without replacement§solution constructed using a outer-left strategy§cost = length of constructed layout§kick = K random insert or swap move4Investigation of data with construction algorithmStep 1 : record searched neighbourhood moves (piece m inserted in locationj) where C(Si) = C(S0)Step 2 : identify distance moved in permutation (abs(pos(m) – j)Step 3 : identify no. of changed co-ordinate positions of placed pieces in solution layoutStep 4 : identify piece type of m for each identified movex 15x 15x 8x 15x 15x 15x 8x 8Data set: Shirt patterns, Dowsland et al (1998)99 pieces, stock sheet width = 405D cost <0 D cost >0 D cost =0D cost <0 D cost >0 D cost =06Over all piece types00.10.20.30.40.50.60.71 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30No. of positions away in permutationproportion 1234No. of different co-ordinate positions by move distanceOver all distances in permutation00.020.040.060.080.10.120.140.160.180.23 4 8 12 18 63 78 108enclosing piece areaproportion 1234No. of different co-ordinate positions by piece area7Shirt - peice type 201020304050607080-65-62-59-56-53-50-47-44-41-38-35-32-29-26-23-20-17-14-11 -8 -5 -2 2 5 81114172023262932Position differencecost differencecost diffco-ord diffShirt - peice type 3010203040506070801 4 7101316192225283134374043464952555861646770737679828588919497Position differencecost differencecost diffco-ord diff8Shirt - peice type 5-1001020304050607080-11-8 -5 -2 2 5 81114172023262932353841444750535659626568717477808386Position differencecost differencecost diffco-ord diffShirt - peice type 7010203040506070-66-63-60-57-54-51-48-45-42-39-36-33-30-27-24-21-18-15-12 -9 -6-3 1 4 71013161922252831Position differencecost differencecost diffco-ord diff9Summary• Construction algorithms are successful but slow• There is no 1-1 mapping between the solution representation and the physical solution• Short cuts need to be made to establish local optima and make a broad search of the neighbourhood• There exist systematic interactions between the data and the search neighbourhood• These, if discovered, can be exploited to reduce redundancy

Local search framework for irregular shaped stock-cutting

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