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Anomalies in Parallel BranchandBound Algorithms
, 1984
"... We consider the effects of parallelizing branchandbound algorithms by expanding several live nodes simultaneously. It is shown that it is quite possible for a parallel branchandbound algorithm using n 2 processors to take more time than one using n 1 processors even though n 1 < n 2 . Furthermor ..."
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Cited by 50 (3 self)
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We consider the effects of parallelizing branchandbound algorithms by expanding several live nodes simultaneously. It is shown that it is quite possible for a parallel branchandbound algorithm using n 2 processors to take more time than one using n 1 processors even though n 1 < n 2 . Furthermore, it is also possible to achieve speedups that are in excess of the ratio n 2 /n 1 . Experimental results with the 0/1Knapsack and Traveling Salesperson problems are also presented.
EVBDDbased algorithms for integer linear programming, spectral transformation, and function decomposition
 IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems
, 1994
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Parallel Branch, Cut, and Price For Largescale Discrete Optimization
, 2003
"... In discrete optimization, most exact solution approaches are based on branch and bound, which is conceptually easy to parallelize in its simplest forms. More sophisticated variants, such as the socalled branch, cut, and price algorithms, are more difficult to parallelize because of the need to sh ..."
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Cited by 18 (5 self)
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In discrete optimization, most exact solution approaches are based on branch and bound, which is conceptually easy to parallelize in its simplest forms. More sophisticated variants, such as the socalled branch, cut, and price algorithms, are more difficult to parallelize because of the need to share large amounts of knowledge discovered during the search process. In the first part of the paper, we survey the issues involved in parallelizing such algorithms. We then review the implementation of SYMPHONY and COIN/BCP, two existing frameworks for implementing parallel branch, cut, and price. These frameworks have limited scalability, but are effective on small numbers of processors. Finally, we briefly describe our nextgeneration framework, which improves scalability and further abstracts many of the notions inherent in parallel BCP, making it possible to implement and parallelize more general classes of algorithms.
A Library Hierarchy for Implementing Scalable Parallel Search Algorithms
 The Journal of Supercomputing
, 2001
"... This report describes the design of the Abstract Library for Parallel Search (ALPS), a framework for implementing scalable, parallel algorithms based on tree search. ALPS is specically designed to support data intensive algorithms, in which large amounts of data are required to describe each node ..."
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Cited by 16 (5 self)
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This report describes the design of the Abstract Library for Parallel Search (ALPS), a framework for implementing scalable, parallel algorithms based on tree search. ALPS is specically designed to support data intensive algorithms, in which large amounts of data are required to describe each node in the search tree. Implementing such algorithms in a scalable manner is dicult due to data storage requirements. This report also describes the design of two other libraries built on top of ALPS, the rst of which is the Branch, Constrain, and Price Software (BiCePS) library, a framework that supports the implementation of parallel branch and bound algorithms in which the bounding is based on some type of relaxation, usually Lagrangean. In this layer, the notion of global data objects associated with the variables and constraints is introduced. These global objects provide a connection between the various subproblems in the search tree and present further diculties in designing scalable algorithms. Finally, we will discuss the BiCePS Linear Integer Solver (BLIS), a concretization of BiCePS, in which linear programming is used to obtain bounds in each search tree node.
Solving largescale QAP problems in parallel with the search library ZRAM
 Journal of Parallel and Distributed Computing
, 1998
"... Program libraries are one tool to make the cooperation between specialists from various elds successful: the separation of applicationspeci c knowledge from applicationindependent tasks ensures portability, maintenance, extensibility, and exibility. The current paper demonstrates the success in com ..."
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Cited by 13 (1 self)
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Program libraries are one tool to make the cooperation between specialists from various elds successful: the separation of applicationspeci c knowledge from applicationindependent tasks ensures portability, maintenance, extensibility, and exibility. The current paper demonstrates the success in combining problemspeci c knowledge for the quadratic assignment problem (QAP) with the raw computing power o ered by contemporary parallel hardware by using the library of parallel search algorithms ZRAM. Solutions of previously unsolved large standard testinstances of the QAP are presented. 1
Parallel Branch and Cut for Capacitated Vehicle Routing
, 2002
"... Combinatorial optimization problems arise commonly in logistics applications. The most successful approaches to date for solving such problems involve modeling them as integer programs and then applying some variant of the branch and bound algorithm. Although branch and bound is conceptually easy t ..."
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Cited by 12 (2 self)
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Combinatorial optimization problems arise commonly in logistics applications. The most successful approaches to date for solving such problems involve modeling them as integer programs and then applying some variant of the branch and bound algorithm. Although branch and bound is conceptually easy to parallelize, achieving scalability can be a challenge. In more sophisticated variants, such as branch and cut, large amounts of data must be shared among the processors, resulting in increased parallel overhead. In this paper, we review the branch and cut algorithm for solving combinatorial optimization problems and describe the implementation of SYMPHONY, a library for implementing these algorithms in parallel. We then describe a solver for the vehicle routing problem that was implemented using SYMPHONY and analyze its parallel performance on a Beowulf cluster.
Parallel BestFirst BranchandBound in Discrete Optimization: a Framework
 IN SOLVING COMBINATORIAL OPTIMIZATION PROBLEMS IN PARALLEL
, 1995
"... In discrete optimization problems, we search for an optimal solution among all vectors in a discrete solution space that satisfy a set of constraints, and the search efficiency is of considerable importance since exhaustive search is often impracticable. The method called branchandbound (noted B&B ..."
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Cited by 8 (1 self)
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In discrete optimization problems, we search for an optimal solution among all vectors in a discrete solution space that satisfy a set of constraints, and the search efficiency is of considerable importance since exhaustive search is often impracticable. The method called branchandbound (noted B&B) is a heuristic tree search algorithm used in this context. Its principle lies in successive decompositions of the original problem in smaller disjoint subproblems until an optimal solution is found, and the search avoids visiting some subproblems which are known not to contain an optimal solution. Given that disjoint subproblems can be decomposed simultaneously and independently, parallel processing has been widely considered as an additional source of improvement in search efficiency, using the set of processors to concurrently decompose several subproblems at each iteration. Parallel B&B is traditionally considered as an irregular parallel algorithm due to the fact that the structure o...
Tcgd: A TimeConstrained Approximate Guided DepthFirst Search Algorithm
 Tsing Hua Univ
, 1990
"... In this paper, we develop TCGD, a problemindependent, timeconstrained, approximate guided depthfirst search (GDFS) algorithm. The algorithm is designed to achieve the best ascertained approximation degree under a fixed time constraint. We consider only searches with finite search space and admiss ..."
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Cited by 6 (3 self)
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In this paper, we develop TCGD, a problemindependent, timeconstrained, approximate guided depthfirst search (GDFS) algorithm. The algorithm is designed to achieve the best ascertained approximation degree under a fixed time constraint. We consider only searches with finite search space and admissible heuristic functions. We study NPhard combinatorial optimization problems with polynomialtime computable feasible solutions. For the problems studied, we observe that the execution time increases exponentially as approximation degree decreases, although anomalies may happen. The algorithms we study are evaluated by simulations using the symmetric travelingsalesperson problem. Keywords: A , TCA , TCGD, approximate branchandbound algorithm, bestfirst search, guided depthfirst search, iterative deepening, time constraint, symmetric travelingsalesman problem. Research was supported partially by National Science Foundation Grants MIP 8810584, MIP 9218715 and MIP 9632316 a...
Asynchronous Parallel Branch and Bound and Anomalies
, 1995
"... The parallel execution of branch and bound algorithms can result in seemingly unreasonable speedups or slowdowns. Almost never the speedup is equal to the increase in computing power. For synchronous parallel branch and bound, these effects have been studied extensively. For asynchronousparallelizat ..."
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Cited by 6 (0 self)
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The parallel execution of branch and bound algorithms can result in seemingly unreasonable speedups or slowdowns. Almost never the speedup is equal to the increase in computing power. For synchronous parallel branch and bound, these effects have been studied extensively. For asynchronousparallelizations, only little is known. In this paper, we derive sufficient conditions to guarantee that an asynchronous parallel branch and bound algorithm (with elimination by lower bound tests and dominance) will be at least as fast as its sequential counterpart. The technique used for obtaining the results seems to be more generally applicable. The essential observations are that, under certain conditions, the parallel algorithm will always work on at least one node, that is branchedfrom by the sequential algorithm, and that the parallel algorithm, after elimination of all such nodes, is able to conclude that the optimal solution has been found. Finally, some of the theoretical results are brought i...