B. Gendron and T. G. Cranic, "Parallel Branch-and-Bound Algorithms: Survey and Synthesis", Operations Research 42 (6) (1994), p. 1042 - 1066. 27  Home/Search   Document Not in Database   Summary   Related Articles   Check

....programs (LPs) although this is the most typical scenario. A third layer, called the BiCePS Linear Integer Solver (BLIS) implements LP based branch and bound algorithms. A number of techniques for developing scalable, parallel branch and bound algorithms have been proposed in the literature [6, 11, 12, 16, 17, 32]. However, we know of no previous work speci cally addressing the development of scalable algorithms for data intensive applications. Standard techniques for parallel branch and bound break down when applied to BCP, primarily because they all depend on the ability to easily shuttle search tree ....

....particular, is rich and varied. We concentrate here on those works most closely related to our own. Kumar and Gupta provide an excellent general introduction to the analysis of parallel scalability in [21] Good overviews and taxonomies of parallel branch and bound algorithms are provided in both [16] and [35] Eckstein [13] also provides a good overview of the implementation of parallel branch and bound. A substantial number of papers have been written speci cally about the application of parallel branch and bound to discrete optimization problems, including [5, 9, 17, 24, 37] 6 3 ....

B. Gendron and T. G. Crainic, Parallel Branch and Bound Algorithms: Survey and Synthesis, Operations Research 42 (1994), 1042.

....design should allow them to be added cleanly, without major changes to the components already developed. The literature of parallel branch and bound is vast, and it is not possible to give a 3 comprehensive review here. Two fairly comprehensive but not particularly recent surveys may be found in [14] and [20, Chapter 8] 5] is a more recent but less comprehensive survey. The remainder of this paper describes the design of the current components of PICO. Section 2 describes PICO s overall design, including its class hierarchy and the separation of the package into serial and parallel layers. ....

B. Gendron and T. G. Crainic, Parallel branch-and-bound algorithms: survey and synthesis, Operations Research 42 (1994) 1042-1066.

....The master keeps track of unexplored nodes in the search tree and distributes them to the workers. The workers search their designated nodes of the tree and report unfathomed nodes back to the master. Many authors have used this centralized control mechanism for parallelizing B B algorithms [17]. The master worker paradigm is also perfectly suited to the dynamic and fault tolerant nature of the computational grid. As worker processors become available during the course of the computation they are assigned tasks. If a worker processor fails, the master reassigns its task to another ....

B. Gendron and T.G. Crainic. Parallel branch and bound algorithms: Survey and synthesis. Operations Research, 42:1042--1066, 1994.

....load balancing decisions. Loadserver is designed to support irregular parallel tree based applications, such as divide and conquer and branch and bound, where large numbers of independent tasks are generated dynamically and unpredictably. Though both these areas have been studied extensively (e.g. [5, 9]) little attention has been given to their common features, in this case the ability to use the same underlying load balancing technique. 2 Applications with Irregular Computational Structure We begin by characterising the classes of applications which motivate our work. 2.1 Divide and Conquer ....

....D C problem in parallel by means of a generic kernel which controls the subdivision and combining, and organises load balancing, communication and synchronisation as required [9] 2. 2 Branch and Bound Branch and bound (B B) is a well known technique for solving combinatorial search problems [5]. The basic scheme is to reduce the problem search space by dynamically pruning unsearched areas which can not yield better results than solutions already found. Branching is performed by recursively partitioning the problem into subproblems. A lower bound is computed for each subproblem to ....

B. Gendron and T. G. Crainic. Parallel Branch-and-Bound Algorithms: Survey and Synthesis. Operations Research, 42(6):1042--1066, Nov-Dec 1994.

....single central list of candidate subproblems to be processed, which is maintained by the tree manager. Most sequential implementations use such a single pool scheme. However, other schemes may be used in parallel implementations. For a description of various types of parallel branch and bound, see [43]. The master module begins by reading in the parameters and problem data. After initial I O is completed, subroutines for finding an initial upper bound and constructing the root node are executed. During construction of the root node, the user must designate the initial set of active cuts and ....

....branch and bound algorithms lend themselves well to parallelization. As a result, there is already a significant body of research on performing branch and bound in parallel environments. We again refer the reader to the survey of parallel branch and bound algorithms by Gendron and Crainic [43], as well as other references such as [35, 46, 80, 57] In parallel BCP, as in general branch and bound, there are two major sources of parallelism. First, it is clear that any group of subproblems on the current candidate list can be processed simultaneously. Once a subproblem has been added to ....

Gendron, B., and Crainic, T.G.: Parallel Branch and Bound Algorithms: Survey and Synthesis. Operations Research 42, 1042, 1994

....model has been already realized on renewed PUBB(Parallelization Utility for Branch and Bound algorithms) 9] though the precise speci cation of member functions were not presented in this paper, due to space restrictions. Many implementations for parallel branch and bound algorithms have appeared [2]. However, the situation is confused when we try to compare them with each other, because the two kinds of implementations are usually mixed. Therefore, we need a standard interface. If a standard interface could be provided, it would enable us not only to use the latest algorithms and technology ....

B.Gendron and T.G.Crainic. Parallel Branch-and-Bound Algorithms: Survey and Synthesis. Operations Research, 42(6):1042-1066, 1994.

....The leaves of the tree are infeasible problems, or pruned problems, or problems that lead to locally optimal solutions. The size and shape of the tree strongly depends on the quality of the heuristic function for the selection rule. In B B algorithms, parallelism can be achieved in different ways [14]. We consider the most general approach, in which the B B tree is built in parallel by performing operations on different subproblems simultaneously. Three design choices most influence the performance of parallel B B algorithms: the choice of a synchronous or an asynchronous algorithm, the work ....

....the selection and elimination rule and hence has an important effect on the size of the search space. 3. Related Work Many investigations of parallel B B for distributedmemory systems have adopted a centralized approach in which a single manager maintains the tree and hands out tasks to workers [14, 26]. While clearly not scalable, this approach simplifies the management of information and multiple processes. Scalability can be improved through a hierarchical organization of processes or by varying the size of work units, but the central manager remains an obstacle to both scalability and fault ....

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B. Gendron and T. G. Crainic. Parallel branch-and-bound algorithms: survey and synthesis. Operations Research, 42:1042--1066, 1994.

....The master keeps track of unexplored nodes in the search tree and distributes them to the workers. The workers search their designated nodes of the tree and report unfathomed nodes back to the master. Many authors have used this centralized control mechanism for parallelizing B B algorithms [16]. The master worker paradigm is also perfectly suited to the dynamic and fault tolerant nature of the computational grid. As worker processors become available during the course of the computation they are assigned tasks. If a worker processor fails, the master reassigns its task to another ....

B. Gendron and T.G. Crainic. Parallel branch and bound algorithms: Survey and synthesis. Operations Research, 42:1042--1066, 1994.

....possible fractional values. This paper discusses a new parallel mixed integer program solver, written in PVM, that runs in the opportunistic computing environment provided by the Condor resource management system. Parallel branch and bound algorithms for MIP have attracted many researchers (see [8, 12, 21] and references therein) Most parallel branch and bound programs were developed for large centralized mainframes or supercomputers that are typically very expensive. Users of these facilities usually only have a certain amount of time allotted to them and have to wait their turn to run their ....

B. Gendron and T. G. Crainic. Parallel Branch-and-Bound Algorithms: Survey and Synthesis. Operations Research, 42(6):1042--1060, 1994.

....second scenario results in a deceleration anomaly, occurring when a speedup of less than P is obtained due to excessive work. Parallel algorithms have been written for many related problems including: theorem proving using a divide and conquer strategy [8] local search [18] and branch and bound [16, 13]. Specifically, parallel algorithms have been written for the Satisfiability problem [19, 4] As of yet, there have been no documented parallel algorithms written for the Maximum Satisfiability problem. 19 2.9.1 Parallel Branch and Bound Several parallel algorithms have been written for solving ....

....have been written for the Satisfiability problem [19, 4] As of yet, there have been no documented parallel algorithms written for the Maximum Satisfiability problem. 19 2.9. 1 Parallel Branch and Bound Several parallel algorithms have been written for solving branch and bound problems [13, 16]. Since there are many different architectures, discussion of all the different branch and bound algorithm is beyond the scope of this work. For a more complete discussion, please refer to Gendron and Crainic [16] Here, we discuss a basic parallel branch and bound algorithm. Most parallel branch ....

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B. Gendron and T.G. Crainic. Parallel Branch and Bound Algorithms: Survey and Synthesis. Operations Research, 42:1042--1066, 1994.

....of [5] is not to study the parallelization of this method, but rather to develop an efficient load balancing strategy that uses priority of tasks. Therefore the chosen B B algorithm is sufficient for our purpose (for more information about B B algorithms and their parallelizations, refer to [4, 7, 3, 2, 11, 12]) The chosen B B algorithm uses a distributed queue organization to temporarily stock the generated subproblems. We chose to execute only one process per processor in the PVM machine. Each processor has a local queue in its local memory and executes the sequential B B algorithm using this ....

B. Gendron and T. G. Crainic. Parallel branch-and-bound algorithms: Survey and synthesis. Technical Report 913, Centre de recherche sur les transports, Montr'eal (Canada), May 1993.

....ffl it allows system adjustment to improve performance on a platform specific basis ffl it is portable ffl it is extendable. 3 Parino System Architecture The heart of Parino is a linear programming based branch and bound algorithm. A brief summary of the algorithm is given below (see [7, 8] for additional information) Branch and bound Node k of a branch and bound tree corresponds to a subproblem MIP(k) obtained by adding constraints to the original problem MIP(0) Frequently, these constraints are simply tighter bounds for the integer variables which, in the case of binary ....

B. Gendron, T. Crainic, "Parallel Branch-and-bound Algorithms: Survey and Synthesis, " Operations Research 42, 1042-1066, 1994.

....design should allow them to be added cleanly, without major changes to the components already developed. The literature of parallel branch and bound is vast, and it is not possible to give a comprehensive review here. Two fairly comprehensive but not particularly recent surveys may be found in [13] and [19, Chapter 8] 5] is more recent but less comprehensive survey. The remainder of this paper describes the design of current components of PICO. Section 2 describes the overall design of PICO, including its class hierarchy and the separation of the package into serial and parallel layers. ....

B. Gendron and T. G. Crainic, Parallel branch-and-bound algorithms: Survey and synthesis, Operations Research 42 (1994) 1042-1066.

....compete to be applied in a proof. Immediately after them are assigned to highest priority methods whose contradictions are all con rmed by methods in the preceding level. This idea is used by P 2 to de ne partial order on methods. A synchronous single pool parallel branch and bound algorithm ([3]) is used to drive the proof search: methods with the same priority are scheduled for concurrent matches with a given goal. A successful match produces a new branch in the search tree. 3. Conclusion The P 2 frame has two strong points: it can generate proof search strategies for arbitrary ....

Bernard Gendron and Teodor Gabriel Crainic, Parallel branch-and-bound algorithms: survey and synthesis, Operations Research 42 (1994), no. 6, 1042-1066.

....The leaves of the tree are infeasible problems, or pruned problems, or problems that lead to locally optimal solutions. The size and shape of the tree strongly depends on the quality of the heuristic function for the selection rule. In B B algorithms, parallelism can be achieved in di erent ways [11]. We consider the most general approach, in which the B B tree is built in parallel by performing operations on di erent subproblems simultaneously. Three design choices most in uence the performance of parallel B B algorithms: the choice of a synchronous or an asynchronous algorithm, the work ....

....the selection and elimination rule and hence has an important e ect on the size of the search space. 3 Related Work Many investigations of parallel B B for distributed memory systems have adopted a centralized approach in which a single manager maintains the tree and hands out tasks to workers [11, 29]. While clearly not scalable, this approach simpli es the management of information and multiple processes. Scalability can be improved through a hierarchical organization of processes or by varying the size of work units, but the central manager remains an obstacle to both scalability and fault ....

[Article contains additional citation context not shown here]

B. Gendron, T. Crainic. 1994. Parallel branch-and-bound algorithms: Survey and synthesis. Operations Research, 42(6):1042-1066.

....In parallel branch and bound computations, a load distribution algorithm is needed to distribute the subproblems among the processors at run time so that they can be executed in parallel. For an overview of different load balancing strategies in branch and bound algorithms see Gendron and Grainic [3]. Our approach is based on the direct neighbor load balancing approach by Tschoke, Luling, and Monien [6, 11] For cutting stock problems only few parallel algorithms are known (see [5] Previous parallel programming of branch and bound algorithms was machinedependent. In addition to ....

B. Gendron and T. G. Crainic. Parallel branch-and-bound algorithms: survey and synthesis. Operations Research 42 (1994), pp. 1042-1066.

....relationships amongst the variables, a large number of interesting examples can be e#ectively modeled using linear relationships along with integer variables. Such problems are typically called mixed integer programs [13] Typically, these problems are solved using a branch and bound approach [7]. First of all, the integer constraints are relaxed to simple bound constraints, resulting in a linear programming relaxation. This relaxation is solved, typically by a version of the simplex method, and the solution is tested to determine if the integrality constraints are satisfied. If not, one ....

B. Gendron and T. G. Crainic. Parallel branch-and-bound algorithms: Survey and synthesis. Operations Research, 42:1042--1060, 1994.

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B. Gendron and T.G. Crainic. Parallel Branch-and-Bound Algorithms: Survey and Synthesis. Operations Research, 42(6):1042--1066, 1994. 40

.... algorithms are referred to as cooperative search [3,4,19,20] multiple interacting walks [40] or population approaches [28] Procedures such as coarse grained parallel genetic algorithms (PGA) 17,33,35] and ne grained PGA [16,26,30] Memetic Algorithms [6,27,29] parallel Branchand Bound [13], tabu search algorithms [8,10,11,23] simulating annealing procedures [22,24,25] and special purpose Arti cial Intelligence (AI) cooperative searches [4,19] are examples of parallel search methods based on cooperation born from sharing gathered information among several sequential search ....

B. Gendron and T.G. Crainic. Parallel Branch-and-Bound Algorithms: Survey and Synthesis. Operations Research, 42(6):1042-1066, 1994.

No context found.

B. Gendron and T.G. Crainic. Parallel Branch-and-Bound Algorithms: Survey and Synthesis. Operations Research, 42(6):1042--1066, 1994.

....a subproblem, we implement high level parallelism of such algorithms, in which case all the existing subproblems are parallelized simultaneously provided that an adequate number of processors is available. Even though there are several criteria for classifying parallel branch and bound algorithms [1, 4, 9, 14], the most useful criterion is the search tree management. The search tree is managed with a single subproblem pool in the central control case(central control scheme) or with multiple subproblem pools in the distributed control case(distributed control scheme) Parallelization with a single ....

G. Gendron and T. G. Crainic. Parallel branch-and-bound algorithms:survey and synthesis. Operations Research, 42(6):1042--1066, 1994.

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B. Gendron and T. G. Cranic, "Parallel Branch-and-Bound Algorithms: Survey and Synthesis", Operations Research 42 (6) (1994), p. 1042 - 1066. 27

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Bernard Gendron and Teodor Gabriel Crainic. Parallel branchand -bound algorithms: Survey and synthesis. Operations Research, 42(6):1042 - 1066, November-December 1994.

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Gendron, B. and T.G. Crainic (1994): Parallel branch-and-bound algorithms: Survey and synthesis. Operations Research, Vol. 42, No. 6, pp. 1042-1066.

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B. Gendron and T.G. Crainic, Parallel Branch and Bound Algorithms: Survey and Synthesis, Operations Research 42 (1994), 1042.

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