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Published in Phillip A. Laplante, Dictionary of Computer Science, Engineering, and Technology, 2017
bidirectional search a search algorithm that replaces a single search graph, which is likely to grow exponentially, with two smaller graphs: one starting from the initial state and one starting from the goal state.
The routing algorithms for maximum probability paths under degree constraints in networks
Published in International Journal of Parallel, Emergent and Distributed Systems, 2023
Yinhui Liu, Shurong Zhang, Lin Chen, Kan He, Weihua Yang
Figure 2 shows the running time of GS, Bi-S, and NIMQ under the reference setting, respectively. The results are calculated from the average of random networks. As expected, Bi-S needs the longest running time. This is because the bidirectional search algorithm doubles the computation of the unidirectional search algorithm in the worst case. NIMQ algorithm shows the fastest computation speed when the success rate is in the range of (see Figure 2(a)). However, in the other ranges, GS algorithm is fastest. It can be seen that the running time of the three algorithms is proportional to N. Comparing (a), (b) and (c) in Figure 2, we can observe that the running time of the Bi-S and NIMQ algorithms are not sensitive to the range of the the success rate of communication establishment, GS algorithm is different from them. When the success rate is in the range of , the speed of the GS algorithm is the fastest, followed by and is slowest in .
Branch-and-price-and-cut methods for the electric vehicle routing problem with time windows
Published in International Journal of Production Research, 2022
Ece Naz Duman, Duygu Taş, Bülent Çatay
The results are similar for the SP instances: the performances of the two methods with both monodirectional and bidirectional labelling are comparable for the 50-customer instances with respect to the number of problems solved while, on average, HCG requires significantly less effort. Regarding 100-customer SP instances, HCG again outperforms TPA by solving five more problems using monodirectional search and eight more using bidirectional search. Overall, we see that the average run time of the HCG is considerably shorter than that of the TPA. Furthermore, bidirectional search improves the efficiency of both methods in solving large-size instances. It makes a significant contribution to the performance of the HCG in particular, allowing it to solve seven additional problems in both MP and SP variants.