Applying Ant Algorithms and the No Fit Polygon to the Nesting Problem

In previous work solutions for the nesting problem are produced using the no fit polygon (NFP), a new evaluation method and three evolutionary algorithms (simulated annealing (SA), tabu search (TS) and genetic algorithms (GA)). Tabu search has been shown to produce the best quality solutions for two problems. In this paper this work is developed. A relatively new type of search algorithm (ant algorithm) is developed and the results from this algorithm are compared against SA, TS and GA We discuss the ideas behind ant algorithms and describe how they have been implemented with regards to the nesting problem. The evaluation method used is described, as is the NFP. Computational results are given.

[1]  Nicos Christofides,et al.  An Algorithm for Two-Dimensional Cutting Problems , 1977, Oper. Res..

[2]  Graham Kendall,et al.  Applying Evolutionary Algorithms and the No Fit Polygon to the a Nesting Problem , 1999, IC-AI.

[3]  G. Di Caro,et al.  Ant colony optimization: a new meta-heuristic , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[4]  Luca Maria Gambardella,et al.  Ant Algorithms for Discrete Optimization , 1999, Artificial Life.

[5]  Alain Hertz,et al.  Ants can colour graphs , 1997 .

[6]  Richard F. Hartl,et al.  An improved Ant System algorithm for theVehicle Routing Problem , 1999, Ann. Oper. Res..

[7]  Marco Dorigo,et al.  The ant colony optimization meta-heuristic , 1999 .

[8]  José Fernando Oliveira,et al.  TOPOS – A new constructive algorithm for nesting problems , 2000, OR Spectr..

[9]  Marco Dorigo,et al.  Distributed Optimization by Ant Colonies , 1992 .

[10]  M. Dorigo,et al.  Aco Algorithms for the Traveling Salesman Problem , 1999 .

[11]  Marco Dorigo,et al.  Ant system for Job-shop Scheduling , 1994 .

[12]  Marco Dorigo,et al.  AntNet: Distributed Stigmergetic Control for Communications Networks , 1998, J. Artif. Intell. Res..

[13]  Marco Dorigo,et al.  An Investigation of some Properties of an "Ant Algorithm" , 1992, PPSN.

[14]  Vittorio Maniezzo,et al.  The Ant System Applied to the Quadratic Assignment Problem , 1999, IEEE Trans. Knowl. Data Eng..

[15]  Antonio Albano,et al.  Optimal Allocation of Two-Dimensional Irregular Shapes Using Heuristic Search Methods , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  Ray Cuninghame-Green Cut out waste! , 1992 .

[17]  Antonio Albano,et al.  NESTING TWO-DIMENSIONAL SHAPES IN RECTANGULAR MODULES , 1976 .

[18]  A. Wren,et al.  An Ant System for Bus Driver Scheduling 1 , 1997 .

[19]  Stefan Voß,et al.  Computer-Aided Scheduling of Public Transport , 2001 .

[20]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[21]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[22]  Emanuel Falkenauer,et al.  Genetic Algorithms and Grouping Problems , 1998 .

[23]  Richard Carl Art An approach to the two dimensional irregular cutting stock problem. , 1966 .

[24]  Graham Kendall,et al.  Applying Simulated Annealing and the No Fit Polygon to the Nesting Problem , 2000 .