Nodal ordering for bandwidth reduction using ant system algorithm

Purpose – For the solution of equations with sparse matrices, the problem of bandwidth reduction is an important issue. Though graph theoretical algorithms are available, the purpose of this paper is to examine the feasibility of ant systems (AS).Design/methodology/approach – For band optimization an ant colony algorithm based on AS is utilized. In this algorithm a local search procedure is also included to improve the solution.Findings – AS algorithms are found to be suitable for bandwidth optimization.Originality/value – Application of AS to the bandwidth reduction is the main purpose of this paper, which is successfully performed. The results are compared to those of a graph theoretical bandwidth optimization algorithm.

[1]  Ali Kaveh,et al.  Ordering for wavefront optimization , 2000 .

[2]  Ali Kaveh,et al.  Optimal Structural Analysis , 1997 .

[3]  Ian P. King,et al.  An automatic reordering scheme for simultaneous equations derived from network systems , 1970 .

[4]  Andrew Lim,et al.  Integrated Genetic Algorithm with Hill Climbing for Bandwidth Minimization Problem , 2003, GECCO.

[5]  Ali Kaveh,et al.  Structural Mechanics: Graph and Matrix Methods , 1995 .

[6]  M. Dorigo,et al.  Ant System: An Autocatalytic Optimizing Process , 1991 .

[7]  Andrew Lim,et al.  Ant colony optimization with hill climbing for the bandwidth minimization problem , 2006, Appl. Soft Comput..

[8]  Ali Kaveh,et al.  A novel nodal ordering algorithm for profile optimization by efficient solution of a differential equation , 2007 .

[9]  Ali Kaveh,et al.  Comparative study of finite element nodal ordering methods , 1998 .

[10]  S. Sloan An algorithm for profile and wavefront reduction of sparse matrices , 1986 .

[11]  Ian Burgess,et al.  A new node renumbering algorithm for bandwidth reduction , 1986 .

[12]  Fred W. Glover,et al.  Reducing the bandwidth of a sparse matrix with tabu search , 2001, Eur. J. Oper. Res..

[13]  William G. Poole,et al.  An algorithm for reducing the bandwidth and profile of a sparse matrix , 1976 .

[14]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[15]  E. Cuthill,et al.  Reducing the bandwidth of sparse symmetric matrices , 1969, ACM '69.

[16]  Kuo-Young Cheng Note on minimizing the bandwidth of sparse, symmetric matrices , 2005, Computing.

[17]  Ali Kaveh,et al.  A connectivity coordinate system for node and element ordering , 1991 .

[18]  Ali Kaveh ORDERING FOR BANDWIDTH REDUCTION , 1986 .

[19]  R. Grimes,et al.  A new algorithm for finding a pseudoperipheral node in a graph , 1990 .

[20]  Ali Kaveh Multiple use of a shortest route tree for ordering , 1986 .