A GPU-based Branch-and-Bound algorithm using IntegerVectorMatrix data structure

Q: How many lanes of the warp are waiting for instruction to complete?

as the remaining 31 lanes of the warp are simply waiting for lane 0 to complete, no significant serialization of instructions occurs.

Q: How many warps are launched at each kernel call?

The number of warps launched at each kernel call is 960 for mapping static, which exceeds theoretical maximum of 13×64= 832 resident warps for the K20m.

Question

1. How many bytes are needed to store the position, end and direction vectors?

2. What future works have the authors mentioned in the paper "A gpu-based branch-and-bound algorithm using integer-vector-matrix data structure" ?

3. What have the authors contributed in "A gpu-based branch-and-bound algorithm using integer-vector-matrix data structure" ?

4. What is the main challenge to be faced when using GPU for the acceleration of B&B?

Accepted Answer

Moreover 3N bytes are needed to store the position-, end- and direction-vectors, 1 byte to store the integer, and N bytes to store permutations before calling the bounding operator.

Accepted Answer

As a future work the authors plan to investigate other work stealing strategies for the IVM-based GPU-B & B algorithm.. The authors also plan to extend their algorithm to a multi-GPU and to a hybrid multi-core/multi-GPU Branch-and-Bound algorithm capable of solving large instances of permutation-based combinatorial problems. [ 1 ]

Accepted Answer

To the best of their knowledge, the algorithm presented in this paper is the first GPU-based B & B algorithm that performs all four operators on the device and subsequently avoids the data transfer bottleneck between CPU and GPU.. This paper revisits the IVM-based B & B algorithm on the GPU, addressing the irregularity of the algorithm in terms of workload, memory access patterns and control flow.. Compared to a GPU-accelerated B & B based on a linked-list, the algorithm presented in this paper solves a set of standard flowshop instances on average 3. 3 times faster.

Accepted Answer

The reduction of the overhead induced by data transfers between host and device is another important challenge to be faced when using GPU for the acceleration of B&B.

Accepted Answer

In total, the IVM data structure requires a constant amount of 1+4N+N2 bytes of memory, i.e. 481 bytes per IVM for a 20-job instance.

Accepted Answer

In terms of node processing speed, the GPU-IVM algorithm decomposes on average 3.3 times more nodes per second than its linked-list counterpart.

Accepted Answer

Because of the irregular and unpredictable shape of the explored tree, dynamic load balancing is necessary to maintain the degree of parallelism induced by the parallel tree exploration model.

Accepted Answer

For a problem instance with N jobs, the storage of the matrix M requires N2 bytes of memory (for N < 127, using 1-byte integers).

Accepted Answer

as the remaining 31 lanes of the warp are simply waiting for lane 0 to complete, no significant serialization of instructions occurs.

Accepted Answer

The number of warps launched at each kernel call is 960 for mapping static, which exceeds theoretical maximum of 13×64= 832 resident warps for the K20m.

Accepted Answer

The average number of warps launched with mapping remap is 300 (average per kernel call and per instance), the average maximum (per instance) being 825 warps and the minimum 4.

Accepted Answer

The configurable size of the device’s shared memory/L1 cache is set to 48/16kB for kernels except bound, where the opposite configuration 16/48kB is used.

Accepted Answer

Although for the three instances the proposed 2D-Ring strategy scales nicely up to 1280 IVM structures, it apparently has a moment of inertia which makes the algorithm sensitive to rapid workload variations.

Accepted Answer

The algorithm’s performance for problem instances of different sizes is compared in terms of node processing speed (#decomposed nodes/second), which is computed from wallclock time.

Accepted Answer

Besides showing that the spaced mapping M2 is better adapted to the IVM-management kernels, the results presented in this subsection illustrate that performance metrics for thread divergence or control flow must be interpreted very carefully.

Accepted Answer

When enough parallel exploration processes are used, the number of generated subproblems per iteration approaches the maximum number of concurrent threads on the GPU.

Accepted Answer

The combined parallel tree exploration/parallel evaluation of bounds model (Figure 2) yields a much higher degree of parallelism than using one model alone.

Accepted Answer

On a lower level it efficiently uses up to 1280 IVM structures to perform the branching, selection and pruning operators in parallel, exploring different parts of the B&B tree simultaneously.

Accepted Answer

T is chosen as a multiple of 64, as the GK110 architecture allows up to 64 warps per SM and the management kernels reserve one warp per IVM.

Accepted Answer

the fact that at T = 1536 no sharp degradation of the IVM-efficiency occurs, confirms that the performance drop at T = 1536 is due to hardware limitations.

A GPU-based Branch-and-Bound algorithm using IntegerVectorMatrix data structure

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Most frequently asked questions

1. How many bytes are needed to store the position, end and direction vectors?

2. What future works have the authors mentioned in the paper "A gpu-based branch-and-bound algorithm using integer-vector-matrix data structure" ?

3. What have the authors contributed in "A gpu-based branch-and-bound algorithm using integer-vector-matrix data structure" ?

4. What is the main challenge to be faced when using GPU for the acceleration of B&B?

5. How many bytes of memory is required for a 20-job instance?

6. How much faster does the GPU-LL algorithm decompose?

7. Why is the parallel tree exploration model so unpredictable?

8. How many bytes of memory is needed for a problem instance?

9. How many lanes of the warp are waiting for instruction to complete?

10. How many warps are launched at each kernel call?

11. How many warps are launched with mapping remap?

12. How is the size of the shared memory/L1 cache set?

13. What is the reason why the algorithm is sensitive to rapid workload variations?

14. What is the performance of the algorithm for problem instances of different sizes?

15. What is the importance of the metric for thread divergence?

16. What is the maximum number of concurrent threads on the GPU?

17. What is the description of the parallel tree exploration/parallel evaluation of bounds model?

18. How many IVM structures are used to perform the branching, selection and pruning operators in parallel?

19. How many warps per SM is used in the GK110 architecture?

20. What is the reason why the performance drop at T = 1536 is due to hardware limitations?

Figures

Citations

A computationally efficient Branch-and-Bound algorithm for the permutation flow-shop scheduling problem

Optimization Techniques for GPU Programming

A comprehensive review of Branch-and-Bound algorithms: Guidelines and directions for further research on the flowshop scheduling problem

Parallel computational optimization in operations research: A new integrative framework, literature review and research directions

A data-driven method for pipeline scheduling optimization

References

Optimal two- and three-stage production schedules with setup times included

The Complexity of Flowshop and Jobshop Scheduling

Benchmarks for basic scheduling problems

Parallel Prefix Sum (Scan) with CUDA

Parallel branch-and-bound algorithms: survey and synthesis

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