Optimizing 2-opt-based heuristics on GPU for solving the single-row facility layout problem
The optimization of most combinatorial problems is NP-hard, which can be solved by heuristic algorithms to obtain approximately optimal solutions, especially for large-scale problems. Many heuristic algorithms can apply the 2-opt local search to find better solutions. In complete 2-opt local search,...
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| Vydáno v: | Future generation computer systems Ročník 126; s. 91 - 109 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.01.2022
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| ISSN: | 0167-739X, 1872-7115 |
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| Abstract | The optimization of most combinatorial problems is NP-hard, which can be solved by heuristic algorithms to obtain approximately optimal solutions, especially for large-scale problems. Many heuristic algorithms can apply the 2-opt local search to find better solutions. In complete 2-opt local search, every valid neighboring solutions of swapping mechanism will be compared, which is very time consuming especially when a sequential algorithm is adopted. Nowadays, graphic processing units (GPUs) have evolved into powerful and flexible parallel computation platforms that have been widely used to accelerate the solving of NP-hard problems. Therefore, in this study, we focus on how to use GPUs to solve the single-row facility layout problem (SRFLP) with the 2-opt-based simulated annealing (SA) heuristic algorithm. As far as we know, this study is the first to solve SRFLP by using a GPU. After analyzing the fitness function and the move gains calculation between parent and child solutions, we propose a prefix-sum formula table to eliminate a large amount of replicated computation. To calculate move gains for the 2-opt local search during each iteration, many GPU threads are created and they construct and lookup the table in parallel. According to experimental results, if the prefix-sum formula table is not adopted, the GPU version outperforms the sequential CPU counterpart with the best speedup of 123. However, if the table is used in the GPU version, the best speedup can reach up to 3208. Because the proposed parallelization approach with the prefix-sum formula table is based on the features of the 2-opt local search and the SRFLP fitness function, it can be applied to any 2-opt-based heuristic algorithm for solving SRFLP even though the SA algorithm is used in this study.
•The 2-opt operation is often the performance bottleneck in many heuristics.•GPU is adopted to parallelize the 2-opt operations for a shorter execution time.•The single row facility layout problem is used to detail the proposed algorithm.•A prefix-sum formula table is constructed to eliminate the replicated computations.•The best speedup our approach can provide is 3208, compared with the CPU version.•Thanks to the proposed table, at best the GPU performance can be improved 129 times. |
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| AbstractList | The optimization of most combinatorial problems is NP-hard, which can be solved by heuristic algorithms to obtain approximately optimal solutions, especially for large-scale problems. Many heuristic algorithms can apply the 2-opt local search to find better solutions. In complete 2-opt local search, every valid neighboring solutions of swapping mechanism will be compared, which is very time consuming especially when a sequential algorithm is adopted. Nowadays, graphic processing units (GPUs) have evolved into powerful and flexible parallel computation platforms that have been widely used to accelerate the solving of NP-hard problems. Therefore, in this study, we focus on how to use GPUs to solve the single-row facility layout problem (SRFLP) with the 2-opt-based simulated annealing (SA) heuristic algorithm. As far as we know, this study is the first to solve SRFLP by using a GPU. After analyzing the fitness function and the move gains calculation between parent and child solutions, we propose a prefix-sum formula table to eliminate a large amount of replicated computation. To calculate move gains for the 2-opt local search during each iteration, many GPU threads are created and they construct and lookup the table in parallel. According to experimental results, if the prefix-sum formula table is not adopted, the GPU version outperforms the sequential CPU counterpart with the best speedup of 123. However, if the table is used in the GPU version, the best speedup can reach up to 3208. Because the proposed parallelization approach with the prefix-sum formula table is based on the features of the 2-opt local search and the SRFLP fitness function, it can be applied to any 2-opt-based heuristic algorithm for solving SRFLP even though the SA algorithm is used in this study.
•The 2-opt operation is often the performance bottleneck in many heuristics.•GPU is adopted to parallelize the 2-opt operations for a shorter execution time.•The single row facility layout problem is used to detail the proposed algorithm.•A prefix-sum formula table is constructed to eliminate the replicated computations.•The best speedup our approach can provide is 3208, compared with the CPU version.•Thanks to the proposed table, at best the GPU performance can be improved 129 times. |
| Author | Wu, Chao-Chin Sun, Xue Koong, Chorng-Shiuh Chen, Liang-Rui Chou, Ping |
| Author_xml | – sequence: 1 givenname: Xue surname: Sun fullname: Sun, Xue organization: College of Urban Rail Transit and Logistics, Joint Jiaotong College of Beijing Union University & Russian University of Transport, Beijing Union University, Beijing 100101, China – sequence: 2 givenname: Ping surname: Chou fullname: Chou, Ping organization: Department of Management Information Systems, National Chengchi University, Taipei 11605, Taiwan – sequence: 3 givenname: Chorng-Shiuh surname: Koong fullname: Koong, Chorng-Shiuh organization: Department of Computer Science, National Taichung University of Education, Taichung 40359, Taiwan – sequence: 4 givenname: Chao-Chin surname: Wu fullname: Wu, Chao-Chin email: ccwu@cc.ncue.edu.tw organization: Department of Computer Science and Information Engineering, National Changhua University of Education, Changhua 50007, Taiwan – sequence: 5 givenname: Liang-Rui surname: Chen fullname: Chen, Liang-Rui organization: Department of Electrical Engineering, National Changhua University of Education, Changhua 50007, Taiwan |
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| Keywords | Facility layout Heuristic algorithm 2-opt local search Graphic processing unit (GPU) Simulated annealing |
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