Could we use a million cores to solve an integer program?

Koch, Thorsten; Ralphs, Ted K.; Shinano, Yuji

doi:10.1007/s00186-012-0390-9

Cited by 34 publications

(15 citation statements)

References 46 publications

(39 reference statements)

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“…This is particularly interesting when a large number of parallel processors is available. Indeed, it is known that in this situation the performance of parallel MIP solvers scale-up with some difficulty [16], while randomization can play a role in improving scalability.…”

Section: Erraticism In Mip Solversmentioning

confidence: 99%

“…Taking full advantage of the new architecture is far from trivial, in particular because the branching nodes produced in the earliest "ramp up" phase of the enumeration cannot be distributed in a balanced way among the processors. Racing ramp-up is a technique proposed in [17,16] with the aim of avoiding idle processors: a same MIP solver is initially run with different settings, in parallel, until a stopping criterion is reached. Then it is decided which of the generated trees performed best according to some criterion (not described in full details).…”

Section: Introductionmentioning

confidence: 99%

“…The nodes of this tree are then distributed among the parallel processors, while all the other results, with the exception of primal solutions, are discarded. According to [16], however, so far these approaches have not proven to be effective enough in terms of number of subproblems solved per thread per second in the initial parts of the search.…”

Section: Introductionmentioning

confidence: 99%

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Exploiting Erraticism in Search

Fischetti

Monaci

2014

Operations Research

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High-sensitivity to initial conditions is generally viewed as a drawback of tree search methods, as it leads to an erratic behavior to be mitigated somehow. In this paper we investigate the opposite viewpoint, and consider this behavior as an opportunity to exploit. Our working hypothesis is that erraticism is in fact just a consequence of the exponential nature of tree search, that acts as a chaotic amplifier, so it is largely unavoidable. We propose a bet-and-run approach to actually turn erraticism to one's advantage. The idea is to make a number of short sample runs with randomized initial conditions, to bet on the "most promising" run selected according to certain simple criteria, and to bring it to completion. Computational results on a large testbed of mixed-integer linear programs from the literature are presented, showing the potential of this approach even when embedded in a proof-of-concept implementation.

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Section: Erraticism In Mip Solversmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exploiting Erraticism in Search

Fischetti

Monaci

2014

Operations Research

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“…Large scale solvers for Mixed Integer Programs (MIPs) have been studied before [5], [6]. The difficulty in achieving high efficiencies has been documented.…”

Section: Prior Workmentioning

confidence: 99%

Parallel branch-and-bound for two-stage stochastic integer optimization

Langer

Venkataraman

Palekar

et al. 2013

20th Annual International Conference on High Performance Computing

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Abstract---Many real-world planning problems require searching for an optimal solution in the face of uncertain input. One approach to is to express them as a two-stage stochastic optimization problem where the search for an optimum in one stage is informed by the evaluation of multiple possible scenarios in the other stage. If integer solutions are required, then branchand-bound techniques are the accepted norm. However, there has been little prior work in parallelizing and scaling branchand-bound algorithms for stochastic optimization problems.In this paper, we explore the parallelization of a two-stage stochastic integer program solved using branch-and-bound. We present a range of factors that influence the parallel design for such problems. Unlike typical, iterative scientific applications, we encounter several interesting characteristics that make it challenging to realize a scalable design. We present two design variations that navigate some of these challenges. Our designs seek to increase the exposed parallelism while delegating sequential linear program solves to existing libraries.We evaluate the scalability of our designs using sample aircraft allocation problems for the US airfleet. It is important that these problems be solved quickly while evaluating large number of scenarios. Our attempts result in strong scaling to hundreds of cores for these datasets. We believe similar results are not common in literature, and that our experiences will feed usefully into further research on this topic.

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“…Depending on the implementation, this may yield a deterministic or a nondeterministic algorithm, with the deterministic option being in general less efficient because of synchronization overhead. In any case, a non-negligible amount of communication and synchronization is needed among the workers, with negative effects on scalability [8,9].…”

Section: Introductionmentioning

confidence: 99%

Self-splitting of Workload in Parallel Computation

Fischetti¹,

Monaci²,

Salvagnin³

2014

Integration of AI and OR Techniques in Constraint Programming

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Abstract. Parallel computation requires splitting a job among a set of processing units called workers. The computation is generally performed by a set of one or more master workers that split the workload into chunks and distribute them to a set of slave workers. In this setting, communication among workers can be problematic and/or time consuming. Tree search algorithms are particularly suited for being applied in a parallel fashion, as different nodes can be processed by different workers in parallel. In this paper we propose a simple mechanism to convert a sequential tree-search code into a parallel one. In the new paradigm, called SelfSplit, each worker is able to autonomously determine, without any communication with the other workers, the job parts it has to process. Computational results are reported, showing that SelfSplit can achieve an almost linear speedup for hard Constraint Programming applications, even when 64 workers are considered.

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Could we use a million cores to solve an integer program?

Cited by 34 publications

References 46 publications

Exploiting Erraticism in Search

Exploiting Erraticism in Search

Parallel branch-and-bound for two-stage stochastic integer optimization

Self-splitting of Workload in Parallel Computation

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