Search Results for « Branch-and-bound »

We consider the effects of parallelizing branch-and-bound algorithms by expanding several live nodes simultaneously. It is shown that it is quite possible for a parallel branch-and-bound 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 speed-ups that are in excess of the ratio n 2 / n 1 . Experimental results with the 0 / 1-Knapsack and Traveling Salesman problems are also presented.

This paper shows how branch-and-bound methods can be used to reduce storage and, possibly, computational requirements in discrete dynamic programs. Relaxations and fathoming criteria are used to identify and to eliminate states whose corresponding subpolicies could not lead to optimal policies. The general dynamic programming/branch-and-bound approach is applied to the traveling-salesman problem and the nonlinear knapsack problem. Our computational experience demonstrates that the hybrid approach yields dramatic savings in both computer storage and computational requirements.

A dominance relation D is a binary relation defined on the set of partial problems generated in a branch-and-bound algorithm, such that P i DP j (where P i and P j are partial problems) implies that P j can be excluded from consideration without loss of optimality of the given problem if P i has already been generated when P j is selected for the test. The branch-and-bound computation is usually enhanced by adding the test based on a dominance relation. A dominance relation D′ is said to be stronger than a dominance relation D if P i DP j always implies P i D′P j . Although it seems obvious that a stronger dominance relation makes the resulting algorithm more efficient, counterexamples can easily be constructed. In this paper, however, four classes of branch-and-bound algorithms are found in which a stronger dominance relation always gives a more efficient algorithm. This indicates that the monotonicity property of dominance relations would be observed in a rather wide class of branch-and-bound algorithms, thus encouraging the designer of a branch-and-bound algorithm to find the strongest possible dominance relation.

Quantum computers could significantly outperform their classical counterparts for solving hard optimization problems. One prominent classical technique for such problems is known as branch-and-bound. This work describes a quantum algorithm for accelerating general branch-and-bound methods, and gives an application to spin glasses.

We present a universal randomized method called Local Best-First Search for parallelizing sequential branch-and-bound algorithms. The method executes on a message-passing multiprocessor system, and requires no global data structures or complex communication protocols. We show that, uniformly on all instances, the execution time of the method is unlikely to exceed a certain inherent lower bound by more than a constant factor.

Distributed constraint optimization (DCOP) problems are a popular way of formulating and solving agent-coordination problems. A DCOP problem is a problem where several agents coordinate their values such that the sum of the resulting constraint costs is minimal. It is often desirable to solve DCOP problems with memory-bounded and asynchronous algorithms. We introduce Branch-and-Bound ADOPT (BnB-ADOPT), a memory-bounded asynchronous DCOP search algorithm that uses the message-passing and communication framework of ADOPT (Modi, Shen, Tambe, & Yokoo, 2005), a well known memory-bounded asynchronous DCOP search algorithm, but changes the search strategy of ADOPT from best-first search to depth-first branch-and-bound search. Our experimental results show that BnB-ADOPT finds cost-minimal solutions up to one order of magnitude faster than ADOPT for a variety of large DCOP problems and is as fast as NCBB, a memory-bounded synchronous DCOP search algorithm, for most of these DCOP problems. Additionally, it is often desirable to find bounded-error solutions for DCOP problems within a reasonable amount of time since finding cost-minimal solutions is NP-hard. The existing bounded-error approximation mechanism allows users only to specify an absolute error bound on the solution cost but a relative error bound is often more intuitive. Thus, we present two new bounded-error approximation mechanisms that allow for relative error bounds and implement them on top of BnB-ADOPT.

Universal randomized methods for parallelizing sequential backtrack search and branch-and-bound computation are presented.These methods execute on message-passing multiprocessor systems, and require no global data structures or complex communication protocols.For backtrack search, it is shown that, uniformly on all instances, the method described in this paper is likely to yield a speed-up within a small constant factor from optimal, when all solutions to the problem instance are required.For branch-and-bound computation, it is shown that, uniformly on all instances, the execution time of this method is unlikely to exceed a certain inherent lower bound by more than a constant factor.These randomized methods demonstrate the effectiveness of randomization in distributed parallel computation.