Parallel Branch-and-Branch Algorithms: Survey and Synthesis

We present a detailed and up-to-date survey of the literature on parallel branch-and-bound algorithms. We synthesize previous work in this area and propose a new classification of parallel branch-and-bound algorithms. This classification is used to analyze the methods proposed in the literature. To facilitate our analysis, we give a new characterization of branch-and-bound algorithms, which consists of isolating the performed operations without specifying any particular order for their execution.

[1]  Michael J. Flynn,et al.  Very high-speed computing systems , 1966 .

[2]  N. Agin Optimum Seeking with Branch and Bound , 1966 .

[3]  E. L. Lawler,et al.  Branch-and-Bound Methods: A Survey , 1966, Oper. Res..

[4]  Egon Balas,et al.  Letter to the Editor - A Note on the Branch-and-Bound Principle , 1968, Oper. Res..

[5]  L. G. Mitten Branch-and-Bound Methods: General Formulation and Properties , 1970, Oper. Res..

[6]  A. M. Geoffrion,et al.  Integer Programming Algorithms: A Framework and State-of-the-Art Survey , 1972 .

[7]  Kenneth Steiglitz,et al.  Characterization and Theoretical Comparison of Branch-and-Bound Algorithms for Permutation Problems , 1974, JACM.

[8]  A. Rinnooy On Mitten's Axioms for Branch-and-Bound , 1976 .

[9]  David R. Smith,et al.  Hierarchical multiprocessor organizations , 1977, ISCA '77.

[10]  Jan Karel Lenstra,et al.  BRANCHING FROM THE LARGEST UPPER BOUND: FOLKLORE AND FACTS , 1978 .

[11]  Toshihide Ibaraki,et al.  The Power of Dominance Relations in Branch-and-Bound Algorithms , 1977, JACM.

[12]  S.H. Fuller,et al.  Multi-microprocessors: An overview and working example , 1978, Proceedings of the IEEE.

[13]  Masaharu Imai,et al.  A Parallel Searching Scheme for Multiprocessor Systems and Its Application to Combinatorial Problems , 1979, IJCAI.

[14]  Edsger W. Dijkstra,et al.  Termination Detection for Diffusing Computations , 1980, Inf. Process. Lett..

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

[16]  Y. Sekiguchi A UNIFYING FRAMEWORK OF COMBINATORIAL OPTIMIZATION ALGORITHMS : TREE PROGRAMMING AND ITS VALIDITY , 1981 .

[17]  Benjamin W. Wah,et al.  MANIP-a parallel computer system for implementing branch and bound algorithms , 1981, ISCA '81.

[18]  Richard P. Hopkins,et al.  Data-Driven and Demand-Driven Computer Architecture , 1982, CSUR.

[19]  Joseph Mohan,et al.  A study in parallel computation : the traveling salesman problem , 1982 .

[20]  BRUCE W. WEIDE,et al.  Modeling Unusual Behavior of Parallel Algorithms , 1982, IEEE Transactions on Computers.

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

[22]  Benjamin W. Wah,et al.  How to Cope With Anomalies in Parallel Approximate Branch-and-Bound Algorithms , 1984, AAAI.

[23]  Benjamin W. Wah,et al.  MANIP—A Multicomputer Architecture for Solving Combinatonal Extremum-Search Problems , 1984, IEEE Transactions on Computers.

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

[25]  Jørgen Staunstrup,et al.  Experiments with a Multiprocessor , 1984 .

[26]  Vipin Kumar,et al.  Parallel Branch-and-Bound Formulations for AND/OR Tree Search , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[27]  V. Joseph Subash Mohan,et al.  Performance of parallel programs: model and analyses , 1984 .

[28]  Vipin Kumar,et al.  General Branch and Bound, and its Relation to A and AO , 1984, Artif. Intell..

[29]  Guo-Jie Li,et al.  The status of manip - a multicomputer architecture for solving, combinatorial extremum-search problems , 1984, ISCA 1984.

[30]  Alan P. Sprague,et al.  Performance of parallel branch-and-bound algorithms , 1985, IEEE Transactions on Computers.

[31]  Benjamin W. Wah,et al.  Multiprocessing of Combinatorial Search Problems , 1985, Computer.

[32]  Harry W. J. M. Trienekens,et al.  Experiments with Parallel Algorithms for Combinatorial Problems , 1985 .

[33]  Benjamin W. Wah,et al.  Coping with Anomalies in Parallel Branch-and-Bound Algorithms , 1986, IEEE Transactions on Computers.

[34]  Oliver Vornberger,et al.  Implementing Branch-and-Bound in a Ring of Processors , 1986, CONPAR.

[35]  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..

[36]  Benjamin W. Wah,et al.  How Good are Parallel and Ordered Depth-First Searches? , 1986, ICPP.

[37]  Jan Karel Lenstra,et al.  An introduction to parallelism in combinatorial optimization , 1986, Discret. Appl. Math..

[38]  Michael J. Quinn,et al.  An upper bound for the speedup of parallel best-bound branch-and-bound algorithms , 1986, BIT Comput. Sci. Sect..

[39]  H.W.J.M. Trienekens Parallel branch and bound on an MIMD system , 1986 .

[40]  Oliver Vornberger,et al.  Parallel Processing of Combinatorial Search , 1987, Parallel Algorithms and Architectures.

[41]  Udi Manber,et al.  DIB—a distributed implementation of backtracking , 1987, TOPL.

[42]  茨木 俊秀,et al.  Enumerative approaches to combinatorial optimization , 1987 .

[43]  David J. DeWitt,et al.  The Crystal Multicomputer: Design and Implementation Experience , 1987, IEEE Transactions on Software Engineering.

[44]  Geoffrey North Implementation and analysis , 1987, Nature.

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

[46]  Oliver Vornberger,et al.  Load Balancing in a Network of Transputers , 1987, WDAG.

[47]  Jan Karel Lenstra,et al.  Parallel computing in combinatorial optimization , 1988 .

[48]  Catherine Roucairol,et al.  A parallel branch and bound algorithm for the quadratic assignment problem , 1987, Discret. Appl. Math..

[49]  Vipin Kumar,et al.  Superlinear Speedup in Parallel State-Space Search , 1988, FSTTCS.

[50]  Richard M. Karp,et al.  A randomized parallel branch-and-bound procedure , 1988, STOC '88.

[51]  Vipin Kumar,et al.  Concurrent insertions and deletions in a priority queue , 1988 .

[52]  Alexander H. G. Rinnooy Kan,et al.  A simulation tool for the performance evaluation of parallel branch and bound algorithms , 1988, Math. Program..

[53]  Dharma P. Agrawal,et al.  A Randomized Parallel Backtracking Algorithm , 1988, IEEE Trans. Computers.

[54]  B. Gillett,et al.  A parallel integer linear programming algorithm , 1988 .

[55]  Vipin Kumar,et al.  Parallel Depth First Search on the Ring Architecture , 1988 .

[56]  L. F. Gulyanitskii,et al.  Discrete optimization methods for multiprocessor computer systems , 1988 .

[57]  Vipin Kumar,et al.  Concurrent Access of Priority Queues , 1988, IEEE Trans. Computers.

[58]  Vipin Kumar,et al.  Parallel Best-First Search of State-Space Graphs: A Summary of Results , 1988, AAAI.

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

[60]  E. Maehle,et al.  Implementation of a parallel branch-and-bound algorithm for the travelling salesman problem , 1989 .

[61]  J. M. Jansen,et al.  Parallel branch-and-bound algorithms , 1989, Future Gener. Comput. Syst..

[62]  E. W. Felten,et al.  Best-first branch-and bound on a hypercube , 1989, C3P.

[63]  Vipin Kumar,et al.  Floorplan optimization on multiprocessors , 1989, Proceedings 1989 IEEE International Conference on Computer Design: VLSI in Computers and Processors.

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

[65]  H. Trienekens Parallel branch and bound and anomalies , 1989 .

[66]  J. M. Troya,et al.  Live nodes distribution in parallel branch and bound algorithms , 1989, Microprocess. Microprogramming.

[67]  K. Schwan,et al.  Process and workload migration for a parallel branch-and-bound algorithm on a hypercube multicomputer , 1989, C3P.

[68]  Karsten Schwan,et al.  Global Data and Control in Multicomputers: Operating System Primitives and Experimentation with a Parallel Branch-and-Bound Algorithm , 1990, Concurrency Practice and Experience.

[69]  Reinhard Lüling,et al.  Two Strategies for Solving the Vertex Cover Problem on a Transputer Network , 1989, WDAG.

[70]  Trevor Mudge,et al.  Parallel processing of best-first branch and bound algorithms on distributed memory multiprocessors , 1989 .

[71]  T. N. Mudge,et al.  Parallel branch and bound algorithms on hypercube multiprocessors , 1989, C3P.

[72]  Panos M. Pardalos,et al.  A parallel algorithm for the quadratic assignment problem , 1989, Proceedings of the 1989 ACM/IEEE Conference on Supercomputing (Supercomputing '89).

[73]  Catherine Roucairol Parallel computing in combinatorial optimization , 1989 .

[74]  H.W.J.M. Trienekens Computational experiments with an asynchronous parallel branch and bound algorithm , 1989 .

[75]  R. P. Ma,et al.  A dynamic load balancer for a parallel branch and bound algorithm , 1989, C3P.

[76]  R. P. Pargas,et al.  Branch-and-bound algorithms on a hypercube , 1989, C3P.

[77]  J. M. Troya,et al.  A study of parallel branch-and-bound algorithms with best-bound-first search , 1989, Parallel Comput..

[78]  Afonso Ferreira,et al.  A. G. Ferreira Parallel branch and bound on fine-grained hypercube multiprocessors , 1990, Parallel Comput..

[79]  Abhiram G. Ranade A Simpler Analysis of the Karp-Zhang Parallel Branch-and-Bound Method , 1990 .

[80]  G. P. Rodgers Algorithms for unconstrained quadratic 0-1 programming and related problems on contemporary computer architectures , 1990 .

[81]  K. Hoffman,et al.  Large-scale 0–1 linear programming on distributed workstations , 1990 .

[82]  Q. Wang,et al.  An asynchronous multiprocessor design for branch-and-bound algorithms , 1990, [1990 Proceedings] The Third Symposium on the Frontiers of Massively Parallel Computation.

[83]  P. Pardalos,et al.  Parallel branch and bound algorithms for quadratic zero–one programs on the hypercube architecture , 1990 .

[84]  Vipin Kumar,et al.  Efficient parallel algorithms for search problems: applications in VLSI CAD , 1990, [1990 Proceedings] The Third Symposium on the Frontiers of Massively Parallel Computation.

[85]  Benjamin W. Wah,et al.  Computational Efficiency of Parallel Combinatorial OR-Tree Searches , 1990, IEEE Trans. Software Eng..

[86]  Michael J. Quinn,et al.  Analysis and Implementation of Branch-and Bound Algorithms on a Hypercube Multicomputer , 1990, IEEE Trans. Computers.

[87]  G. A. P. Kindervater Exercises in parallel combinatorial computing , 1991 .

[88]  Jesper Larsson Träff,et al.  Implementation of parallel branch-and-bound algorithms – experiences with the graph partitioning problem , 1991, Ann. Oper. Res..

[89]  Victor J. Rayward-Smith,et al.  Using a transputer network to solve branch-and-bound problems , 1991 .

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

[91]  Victor J. Rayward-Smith,et al.  Branch-and-bound as a higher-order function , 1991, Ann. Oper. Res..

[92]  Vipin Kumar,et al.  Automatic test pattern generation on parallel processors , 1991, Parallel Comput..

[93]  Onno J. Boxma,et al.  A Queueing Network Model for Analyzing a Class of Branch-and-Bound Algorithms on a Master-Slave Architecture , 1991, Oper. Res..

[94]  Chita R. Das,et al.  A parallel branch-and-bound algorithm for MIN-based multiprocessors , 1991, SIGMETRICS '91.

[95]  Reinhard Lüling,et al.  Load balancing for distributed branch & bound algorithms , 1992, Proceedings Sixth International Parallel Processing Symposium.

[96]  Teodor Gabriel Crainic,et al.  PARALLEL IMPLEMENTATIONS OF A BRANCH-AND-BOUND ALGORITHM FOR MULTICOMMODITY LOCATION WITH BALANCING REQUIREMENTS , 1992 .

[97]  Victor J. Rayward-Smith,et al.  Parallel branch-and-bound , 1992 .

[98]  Arie de Bruin,et al.  Towards a taxonomy of parallel branch and bound algorithms , 1992 .

[99]  Joseph F. Pekny,et al.  A parallel branch and bound algorithm for solving large asymmetric traveling salesman problems , 1992, Math. Program..

[100]  Panos M. Pardalos,et al.  Topics in parallel computing in mathematical programming , 1993, Applied discrete mathematics and theoretical computer science.

[101]  Victor J. Rayward-Smith,et al.  Efficiency considerations in the implementation of parallel branch-and-bound , 1993, Ann. Oper. Res..

[102]  Joseph F. Pekny,et al.  Commentary - The Role of Performance Metrics for Parallel Mathematical Programming Algorithms , 1993, INFORMS J. Comput..

[103]  Joseph F. Pekny,et al.  A distributed exact algorithm for the multiple resource constrained sequencing problem , 1993, Ann. Oper. Res..

[104]  Per S. Laursen Simple Approches to Parallel Branch and Bound , 1993, Parallel Comput..

[105]  Vipin Kumar,et al.  Scalable Load Balancing Techniques for Parallel Computers , 1994, J. Parallel Distributed Comput..

[106]  Jonathan Eckstein,et al.  Parallel Branch-and-Bound Algorithms for General Mixed Integer Programming on the CM-5 , 1994, SIAM J. Optim..

[107]  Per S. Laursen Can Parallel Branch and Bound without Communication Be Effective? , 1994, SIAM J. Optim..

[108]  Panos M. Pardalos,et al.  Parallel Processing of Discrete Optimization Problems , 1995 .

[109]  T. Mautor,et al.  A parallel depth first search branch and bound algorithm for the quadratic assignment problem , 1995 .

[110]  Vipin Kumar,et al.  Parallel depth first search. Part II. Analysis , 1987, International Journal of Parallel Programming.

[111]  Dharma P. Agrawal,et al.  A randomized parallel branch-and-bound algorithm , 1989, International Journal of Parallel Programming.