A parallel branch and bound algorithm for solving large asymmetric traveling salesman problems

A parallel branch and bound algorithm that solves the asymmetric traveling salesman problem to optimality is described. The algorithm uses an assignment problem based lower bounding technique, subtour elimination branching rules, and a subtour patching algorithm as an upper bounding procedure. The algorithm is organized around a new data flow framework for parallel branch and bound. Computational results are presented for problem sizes from 500 to 7500 cities with cost matrix elements randomly drawn from a uniform distribution of integers in the range [0,1000] and [0,10000].

[1]  G. Nemhauser,et al.  Branch-and-bound and parallel computation: A historical note , 1988 .

[2]  N. Biggs.  THE TRAVELING SALESMAN PROBLEM A Guided Tour of Combinatorial Optimization , 1986 .

[3]  Egon Balas,et al.  A PARALLEL SHORTEST PATH ALGORITHM FOR THE ASSIGNMENT PROBLEM , 1989 .

[4]  P. Toth,et al.  Some New Branching and Bounding Criteria for the Asymmetric Travelling Salesman Problem , 1980 .

[5]  Richard M. Karp,et al.  A Patching Algorithm for the Nonsymmetric Traveling-Salesman Problem , 1979, SIAM J. Comput..

[6]  M. Padberg,et al.  Addendum: Optimization of a 532-city symmetric traveling salesman problem by branch and cut , 1990 .

[7]  Paolo Toth,et al.  Linear Assignment Problems , 1987 .

[8]  J. Pekny,et al.  Results from a parallel branch and bound algorithm for the asymmetric traveling salesman problem , 1989 .

[9]  Gerald L. Thompson,et al.  Computational Performance of Three Subtour Elimination Algorithms for Solving Asymmetric Traveling Salesman Problems. , 1977 .

[10]  Donald L. Miller,et al.  Solution of large dense transportation problems using a parallel primal algorithm , 1990 .

[11]  Jan Karel Lenstra,et al.  Parallel algorithms in combinatorial optimization: an annotated bibliography , 1983 .

[12]  K. G. Murty.  An Algorithm for Ranking All the Assignment in Order of Increasing Cost , 1968 .

[13]  Eugene L. Lawler,et al.  The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization , 1985 .

[14]  Joseph Mohan,et al.  Experience with Two Parallel Programs Solving the Traveling Salesman Problem , 1983, ICPP.

[15]  H. A. Luther,et al.  Applied numerical methods , 1969 .

[16]  D. Bertsekas,et al.  Distributed asynchronous relaxation methods for convex network flow problems , 1987 .

[17]  Robert S. Garfinkel,et al.  Technical Note - On Partitioning the Feasible Set in a Branch-and-Bound Algorithm for the Asymmetric Traveling-Salesman Problem , 1973, Oper. Res..

[18]  Donald M. Shapiro,et al.  Algorithms for the solution of the optimal cost and bottle-neck travelingsalesman problems. , 1966 .

[19]  Kai Hwang,et al.  Computer architecture and parallel processing , 1984, McGraw-Hill Series in computer organization and architecture.

[20]  Alan P. Sprague,et al.  A Note on Anomalies in Parallel Branch-and-Bound Algorithms with One-to-One Bounding Functions , 1986, Inf. Process. Lett..

[21]  Sartaj Sahni,et al.  Anomalies in Parallel Branch-and-Bound Algorithms , 1984 .

[22]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[23]  Egon Balas,et al.  A parallel shortest augmenting path algorithm for the assignment problem , 1991, JACM.

[24]  Mandell Bellmore,et al.  Pathology of Traveling-Salesman Subtour-Elimination Algorithms , 1971, Oper. Res..

[25]  C. Ribeiro.  Parallel Computer Models and Combinatorial Algorithms , 1987 .

[26]  Egon Balas,et al.  A restricted Lagrangean approach to the traveling salesman problem , 1981, Math. Program..

[27]  Selmer M. Johnson,et al.  On a Linear-Programming, Combinatorial Approach to the Traveling-Salesman Problem , 1959 .

[28]  Kenneth Steiglitz,et al.  Some Examples of Difficult Traveling Salesman Problems , 1978, Oper. Res..

[29]  Matteo Fischetti,et al.  An Additive Bounding Procedure for Combinatorial Optimization Problems , 1989, Oper. Res..

[30]  Wing H. Huen,et al.  Distributed Enumeration on Between Computers , 1980, IEEE Transactions on Computers.

[31]  Randall Rettberg,et al.  Contention is no obstacle to shared-memory multiprocessing , 1986, CACM.

[32]  Paolo Toth,et al.  Primal-dual algrorithms for the assignment problem , 1987, Discret. Appl. Math..