A generalized utility for parallel branch and bound algorithms

Abstract

Branch and bound algorithms are general methods applied to various combinatorial optimization problems. Recently, parallelizations of these algorithms have been proposed. In spite of the generalzty of these methods, many of the parallelizations have been set up for a specific problem and a specific parallel computer. In this paper, a generalized utility P U B B (Parallelization Utility for Branch and Bound algorithms) is presented. It can be used on a network of workstations and enables us to easily apply parallelized branch and bound algorithms on any specific combinatorial optimization problem. A new selection rule (hybrid selection rule) was implemented during this study. Severalbranch and bound algorithms were experimentally parallelized with PUBB, using up to 111 networked workstations. The results of these experiments show that super-linear speedup in solving time m a y be achieved when the number of processing elements is increased and also indicate that the hybrid selection rule has an advantage over other selection rules.

Parallel skeletons for divide-and-conquer and branch-and-bound techniques

“…Also it has to maintain a queue of unsolved problems, Queue. The Master removes problems from this queue and assigns them to the slaves while there are problems and free slaves (lines [10][11][12]. The Master waits to receive the new subproblems that have been generated and inserts them in the queue (lines 22-24).…”

“…Similarly, in the combination phase the slaves receive a set of solutions from the Master (line 5), combine them (using the combination function given for the user) and return the solution to the Master (lines [11][12][13][14].…”

“…Several tools for the parallel implementation of general Branchand-Bound algorithms have been developed since 1995. PPBB (Portable Parallel Branch-and-Bound Library) [12] and PUBB (Parallelization Utility for Branch and Bound algorithms) [11] propose implementations in the C programming language. BOB [7], PICO (An Object-Oriented Framework for Parallel Branch-and-Bound) [3] and COIN (Common Optimization Interface for Optimization Research) [10] are developed in C ++ and in all cases a hierarchy of classes is provided and the user has to extend it to solve his/her particular problem.…”

Efficient Implementation of Branch-and-bound Method on Desktop Grids

“…Using parallel or distributed processing is one of the most popular ways to resolve this issue. The implementation of B&B algorithms on parallel machines was studied in numerous papers [11,13,15,20,[24][25][26]. All of these solvers are based on parallel computation frameworks that are flexible and only useful for tightly-coupled or shared-memory distributed systems.…”

A comparison between MPI and OpenMP Branch-and-Bound skeletons

“…For this paradigm have been developed several parallel tools. PPBB (Portable Parallel Branch-and-Bound Library) [13] and PUBB (Parallelization Utility for Branch and Bound algorithms) [10] propose implementations in the C programming language. BOB [5], PICO (An Object-Oriented Framework for Parallel Branch-and-Bound) [3] and COIN (Common Optimization Interface for Optimization Research) [8] are developed in C ++ and in all cases a hierarchy of classes is provided and the user has to extend it to solve his/her particular problem.…”