Abstract

As the services in elastic optical networks (EONs) are bandwidth-intensive, unpredictable and dynamic, increasing network factors are emerging to affect the performance of network survivable planning and operation from network capacity to efficiency. Most of the traditional protection and restoration approaches may become before long inefficient due to the improvement of a particular network performance metric always at the expense of others. We argue that it would be more beneficial for comprehensive optimization of network performance to consider main network metrics jointly. Moreover, the highly dynamic features of EONs call for the new generation of machine learning-based solutions that are flexible and adaptable to cope with the dynamic nature of services to perform analytics. In this paper, we investigate the problem of global optimization of network performance under survivable EON environment. Specifically, a criterion, named the whole network cost-effectiveness value with survivability (WCES), is defined to measure the overall network performance by balancing the interaction among main network metrics. Then we propose a deep reinforcement learning (DRL) -based heuristic with the objective of improving overall network performance, in which two agents are utilized to provide working and protection schemes converging toward better survivable routing, modulation level and spectrum assignment (S-RMLSA) policies. Numerical results show that the proposed criterion can efficiently measure the overall network performance, and the double-agent DRL-based heuristic can greatly improve WCES while ensuring the network survivability and paying the acceptable extra consumption of request blocking probability.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (8)

H. Takeshita, T. Oguma, S. Fujisawa, Y. Suzuki, B. Yatabe, A. Tajima, H. Hasegawa, and K. Sato, “Enhancing protection performance by effectively using spectral slots of impairment-aware elastic optical networks [invited],” J. Opt. Commun. Netw. 10(1), A91–A101 (2018).
[Crossref]

M. Y. Namaad, A. G. Rahbar, and B. Alizadeh, “Adaptive modulation and flexible resource allocation in space-division- multiplexed elastic optical networks,” J. Opt. Commun. Netw. 10(3), 240–251 (2018).
[Crossref]

X. Luo, C. Shi, X. Chen, L. Wang, and T. Yang, “Global Optimization of All-Optical Hybrid-Casting in Inter-Datacenter Elastic Optical Networks,” IEEE Access 6, 36530–36543 (2018).
[Crossref]

P. Papanikolaou, K. Christodoulopoulos, and E. Varvarigos, “Optimization techniques for incremental planning of multilayer elastic optical networks,” J. Opt. Commun. Netw. 10(3), 183–194 (2018).
[Crossref]

W. Lu, X. Yin, X. Cheng, and Z. Zhu, “On cost-efficient integrated multilayer protection planning in IP-over-EONs,” J. Lightwave Technol. 36(10), 2037–2048 (2018).
[Crossref]

Q. Yao, H. Yang, R. Zhu, A. Yu, W. Bai, Y. Tan, J. Zhang, and H. Xiao, “Core, Mode, and Spectrum Assignment Based on Machine Learning in Space Division Multiplexing Elastic Optical Networks,” IEEE Access 6, 15898–15907 (2018).
[Crossref]

I. A. Alimi, A. L. Teixeira, and P. P. Monteiro, “Toward an Efficient C-RAN Optical Fronthaul for the Future Networks: A Tutorial on Technologies, Requirements, Challenges, and Solutions,” IEEE Comm. Surv. and Tutor. 20(1), 708–769 (2018).
[Crossref]

X. Guo, J. Huang, H. Liu, and Y. Chen, “Efficient P-cycle combination protection strategy based on improved genetic algorithm in elastic optical networks,” IET Optoelectron. 12(2), 73–79 (2018).
[Crossref]

2017 (5)

M. Moharrami, A. Fallahpour, H. Beyranvand, and J. A. Salehi, “Resource Allocation and Multicast Routing on Elastic Optical Networks,” IEEE Trans. Commun. 65(5), 2101–2113 (2017).
[Crossref]

S. Ba, B. C. Chatterjee, and E. Oki, “Defragmentation Scheme Based on Exchanging Primary and Backup Paths in 1+1 Path Protected Elastic Optical Networks,” IEEE/ACM Trans. Netw. 25(3), 1717–1731 (2017).
[Crossref]

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[Crossref] [PubMed]

J. Wu, Z. Ning, and L. Guo, “Energy-Efficient Survivable Grooming in Software-Defined Elastic Optical Networks,” IEEE Access 5, 6454–6463 (2017).
[Crossref]

M. Jinno, “Elastic Optical Networking: Roles and Benefits in Beyond 100-Gb/s Era,” J. Lightwave Technol. 35(5), 1116–1124 (2017).
[Crossref]

2016 (3)

G. Shen, H. Guo, and S. K. Bose, “Survivable elastic optical networks: survey and perspective (invited),” Photonic Netw. Commun. 31(1), 71–87 (2016).
[Crossref]

X. Li, S. Huang, S. Yin, B. Guo, Y. Zhao, J. Zhang, M. Zhang, and W. Gu, “Shared end-to-content backup path protection in k-node (edge) content connected elastic optical datacenter networks,” Opt. Express 24(9), 9446–9464 (2016).
[Crossref] [PubMed]

A. Cai, J. Guo, R. Lin, G. Shen, and M. Zukerman, “Multicast Routing and Distance-Adaptive Spectrum Allocation in Elastic Optical Networks With Shared Protection,” J. Lightwave Technol. 34(17), 4076–4088 (2016).
[Crossref]

2015 (5)

A. Fallahpour, H. Beyranvand, and J. A. Salehi, “Energy-Efficient Manycast Routing and Spectrum Assignment in Elastic Optical Networks for Cloud Computing Environment,” J. Lightwave Technol. 33(19), 4008–4018 (2015).
[Crossref]

B. C. Chatterjee, N. Sarma, and E. Oki, “Routing and Spectrum Allocation in Elastic Optical Networks: A Tutorial,” IEEE Comm. Surv. and Tutor. 17(3), 1776–1800 (2015).
[Crossref]

X. Chen, M. Tornatore, S. Zhu, F. Ji, W. Zhou, C. Chen, D. Hu, L. Jiang, and Z. Zhu, “Flexible Availability-Aware Differentiated Protection in Software-Defined Elastic Optical Networks,” J. Lightwave Technol. 33(18), 3872–3882 (2015).
[Crossref]

X. Chen, S. Zhu, L. Jiang, and Z. Zhu, “On Spectrum Efficient Failure-Independent Path Protection p-Cycle Design in Elastic Optical Networks,” J. Lightwave Technol. 33(17), 3719–3729 (2015).
[Crossref]

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

2014 (1)

X. Chen, F. Ji, and Z. Zhu, “Service availability oriented p-cycle protection design in elastic optical networks,” J. Opt. Commun. Netw. 6(10), 901–910 (2014).
[Crossref]

2008 (1)

R. Huelsermann, M. Gunkel, C. Meusburger, and D. A. Schupke, “Cost modeling and evaluation of capital expenditures in optical multilayer networks,” J. Opt. Netw. 7(9), 814–833 (2008).
[Crossref]

Alimi, I. A.

I. A. Alimi, A. L. Teixeira, and P. P. Monteiro, “Toward an Efficient C-RAN Optical Fronthaul for the Future Networks: A Tutorial on Technologies, Requirements, Challenges, and Solutions,” IEEE Comm. Surv. and Tutor. 20(1), 708–769 (2018).
[Crossref]

Alizadeh, B.

M. Y. Namaad, A. G. Rahbar, and B. Alizadeh, “Adaptive modulation and flexible resource allocation in space-division- multiplexed elastic optical networks,” J. Opt. Commun. Netw. 10(3), 240–251 (2018).
[Crossref]

Antonoglou, I.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Ba, S.

S. Ba, B. C. Chatterjee, and E. Oki, “Defragmentation Scheme Based on Exchanging Primary and Backup Paths in 1+1 Path Protected Elastic Optical Networks,” IEEE/ACM Trans. Netw. 25(3), 1717–1731 (2017).
[Crossref]

Bai, W.

Q. Yao, H. Yang, R. Zhu, A. Yu, W. Bai, Y. Tan, J. Zhang, and H. Xiao, “Core, Mode, and Spectrum Assignment Based on Machine Learning in Space Division Multiplexing Elastic Optical Networks,” IEEE Access 6, 15898–15907 (2018).
[Crossref]

Beattie, C.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Bellemare, M. G.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Beyranvand, H.

M. Moharrami, A. Fallahpour, H. Beyranvand, and J. A. Salehi, “Resource Allocation and Multicast Routing on Elastic Optical Networks,” IEEE Trans. Commun. 65(5), 2101–2113 (2017).
[Crossref]

A. Fallahpour, H. Beyranvand, and J. A. Salehi, “Energy-Efficient Manycast Routing and Spectrum Assignment in Elastic Optical Networks for Cloud Computing Environment,” J. Lightwave Technol. 33(19), 4008–4018 (2015).
[Crossref]

Bose, S. K.

G. Shen, H. Guo, and S. K. Bose, “Survivable elastic optical networks: survey and perspective (invited),” Photonic Netw. Commun. 31(1), 71–87 (2016).
[Crossref]

Cai, A.

A. Cai, J. Guo, R. Lin, G. Shen, and M. Zukerman, “Multicast Routing and Distance-Adaptive Spectrum Allocation in Elastic Optical Networks With Shared Protection,” J. Lightwave Technol. 34(17), 4076–4088 (2016).
[Crossref]

Chatterjee, B. C.

S. Ba, B. C. Chatterjee, and E. Oki, “Defragmentation Scheme Based on Exchanging Primary and Backup Paths in 1+1 Path Protected Elastic Optical Networks,” IEEE/ACM Trans. Netw. 25(3), 1717–1731 (2017).
[Crossref]

B. C. Chatterjee, N. Sarma, and E. Oki, “Routing and Spectrum Allocation in Elastic Optical Networks: A Tutorial,” IEEE Comm. Surv. and Tutor. 17(3), 1776–1800 (2015).
[Crossref]

Chen, C.

X. Chen, M. Tornatore, S. Zhu, F. Ji, W. Zhou, C. Chen, D. Hu, L. Jiang, and Z. Zhu, “Flexible Availability-Aware Differentiated Protection in Software-Defined Elastic Optical Networks,” J. Lightwave Technol. 33(18), 3872–3882 (2015).
[Crossref]

Chen, X.

X. Luo, C. Shi, X. Chen, L. Wang, and T. Yang, “Global Optimization of All-Optical Hybrid-Casting in Inter-Datacenter Elastic Optical Networks,” IEEE Access 6, 36530–36543 (2018).
[Crossref]

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[Crossref] [PubMed]

X. Chen, M. Tornatore, S. Zhu, F. Ji, W. Zhou, C. Chen, D. Hu, L. Jiang, and Z. Zhu, “Flexible Availability-Aware Differentiated Protection in Software-Defined Elastic Optical Networks,” J. Lightwave Technol. 33(18), 3872–3882 (2015).
[Crossref]

X. Chen, S. Zhu, L. Jiang, and Z. Zhu, “On Spectrum Efficient Failure-Independent Path Protection p-Cycle Design in Elastic Optical Networks,” J. Lightwave Technol. 33(17), 3719–3729 (2015).
[Crossref]

X. Chen, F. Ji, and Z. Zhu, “Service availability oriented p-cycle protection design in elastic optical networks,” J. Opt. Commun. Netw. 6(10), 901–910 (2014).
[Crossref]

Chen, Y.

X. Guo, J. Huang, H. Liu, and Y. Chen, “Efficient P-cycle combination protection strategy based on improved genetic algorithm in elastic optical networks,” IET Optoelectron. 12(2), 73–79 (2018).
[Crossref]

Cheng, X.

W. Lu, X. Yin, X. Cheng, and Z. Zhu, “On cost-efficient integrated multilayer protection planning in IP-over-EONs,” J. Lightwave Technol. 36(10), 2037–2048 (2018).
[Crossref]

Christodoulopoulos, K.

P. Papanikolaou, K. Christodoulopoulos, and E. Varvarigos, “Optimization techniques for incremental planning of multilayer elastic optical networks,” J. Opt. Commun. Netw. 10(3), 183–194 (2018).
[Crossref]

Fallahpour, A.

M. Moharrami, A. Fallahpour, H. Beyranvand, and J. A. Salehi, “Resource Allocation and Multicast Routing on Elastic Optical Networks,” IEEE Trans. Commun. 65(5), 2101–2113 (2017).
[Crossref]

A. Fallahpour, H. Beyranvand, and J. A. Salehi, “Energy-Efficient Manycast Routing and Spectrum Assignment in Elastic Optical Networks for Cloud Computing Environment,” J. Lightwave Technol. 33(19), 4008–4018 (2015).
[Crossref]

Fidjeland, A. K.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Fujisawa, S.

H. Takeshita, T. Oguma, S. Fujisawa, Y. Suzuki, B. Yatabe, A. Tajima, H. Hasegawa, and K. Sato, “Enhancing protection performance by effectively using spectral slots of impairment-aware elastic optical networks [invited],” J. Opt. Commun. Netw. 10(1), A91–A101 (2018).
[Crossref]

Graves, A.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Gu, W.

X. Li, S. Huang, S. Yin, B. Guo, Y. Zhao, J. Zhang, M. Zhang, and W. Gu, “Shared end-to-content backup path protection in k-node (edge) content connected elastic optical datacenter networks,” Opt. Express 24(9), 9446–9464 (2016).
[Crossref] [PubMed]

Gunkel, M.

R. Huelsermann, M. Gunkel, C. Meusburger, and D. A. Schupke, “Cost modeling and evaluation of capital expenditures in optical multilayer networks,” J. Opt. Netw. 7(9), 814–833 (2008).
[Crossref]

Guo, B.

X. Li, S. Huang, S. Yin, B. Guo, Y. Zhao, J. Zhang, M. Zhang, and W. Gu, “Shared end-to-content backup path protection in k-node (edge) content connected elastic optical datacenter networks,” Opt. Express 24(9), 9446–9464 (2016).
[Crossref] [PubMed]

Guo, H.

G. Shen, H. Guo, and S. K. Bose, “Survivable elastic optical networks: survey and perspective (invited),” Photonic Netw. Commun. 31(1), 71–87 (2016).
[Crossref]

Guo, J.

A. Cai, J. Guo, R. Lin, G. Shen, and M. Zukerman, “Multicast Routing and Distance-Adaptive Spectrum Allocation in Elastic Optical Networks With Shared Protection,” J. Lightwave Technol. 34(17), 4076–4088 (2016).
[Crossref]

Guo, L.

J. Wu, Z. Ning, and L. Guo, “Energy-Efficient Survivable Grooming in Software-Defined Elastic Optical Networks,” IEEE Access 5, 6454–6463 (2017).
[Crossref]

Guo, X.

X. Guo, J. Huang, H. Liu, and Y. Chen, “Efficient P-cycle combination protection strategy based on improved genetic algorithm in elastic optical networks,” IET Optoelectron. 12(2), 73–79 (2018).
[Crossref]

Hasegawa, H.

H. Takeshita, T. Oguma, S. Fujisawa, Y. Suzuki, B. Yatabe, A. Tajima, H. Hasegawa, and K. Sato, “Enhancing protection performance by effectively using spectral slots of impairment-aware elastic optical networks [invited],” J. Opt. Commun. Netw. 10(1), A91–A101 (2018).
[Crossref]

Hassabis, D.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Hu, D.

X. Chen, M. Tornatore, S. Zhu, F. Ji, W. Zhou, C. Chen, D. Hu, L. Jiang, and Z. Zhu, “Flexible Availability-Aware Differentiated Protection in Software-Defined Elastic Optical Networks,” J. Lightwave Technol. 33(18), 3872–3882 (2015).
[Crossref]

Huang, J.

X. Guo, J. Huang, H. Liu, and Y. Chen, “Efficient P-cycle combination protection strategy based on improved genetic algorithm in elastic optical networks,” IET Optoelectron. 12(2), 73–79 (2018).
[Crossref]

Huang, S.

X. Li, S. Huang, S. Yin, B. Guo, Y. Zhao, J. Zhang, M. Zhang, and W. Gu, “Shared end-to-content backup path protection in k-node (edge) content connected elastic optical datacenter networks,” Opt. Express 24(9), 9446–9464 (2016).
[Crossref] [PubMed]

Huelsermann, R.

R. Huelsermann, M. Gunkel, C. Meusburger, and D. A. Schupke, “Cost modeling and evaluation of capital expenditures in optical multilayer networks,” J. Opt. Netw. 7(9), 814–833 (2008).
[Crossref]

Ji, F.

X. Chen, M. Tornatore, S. Zhu, F. Ji, W. Zhou, C. Chen, D. Hu, L. Jiang, and Z. Zhu, “Flexible Availability-Aware Differentiated Protection in Software-Defined Elastic Optical Networks,” J. Lightwave Technol. 33(18), 3872–3882 (2015).
[Crossref]

X. Chen, F. Ji, and Z. Zhu, “Service availability oriented p-cycle protection design in elastic optical networks,” J. Opt. Commun. Netw. 6(10), 901–910 (2014).
[Crossref]

Jiang, L.

X. Chen, M. Tornatore, S. Zhu, F. Ji, W. Zhou, C. Chen, D. Hu, L. Jiang, and Z. Zhu, “Flexible Availability-Aware Differentiated Protection in Software-Defined Elastic Optical Networks,” J. Lightwave Technol. 33(18), 3872–3882 (2015).
[Crossref]

X. Chen, S. Zhu, L. Jiang, and Z. Zhu, “On Spectrum Efficient Failure-Independent Path Protection p-Cycle Design in Elastic Optical Networks,” J. Lightwave Technol. 33(17), 3719–3729 (2015).
[Crossref]

Jinno, M.

M. Jinno, “Elastic Optical Networking: Roles and Benefits in Beyond 100-Gb/s Era,” J. Lightwave Technol. 35(5), 1116–1124 (2017).
[Crossref]

Kavukcuoglu, K.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

King, H.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Kumaran, D.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Legg, S.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Li, J.

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[Crossref] [PubMed]

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[Crossref] [PubMed]

Li, X.

X. Li, S. Huang, S. Yin, B. Guo, Y. Zhao, J. Zhang, M. Zhang, and W. Gu, “Shared end-to-content backup path protection in k-node (edge) content connected elastic optical datacenter networks,” Opt. Express 24(9), 9446–9464 (2016).
[Crossref] [PubMed]

Li, Z.

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[Crossref] [PubMed]

Lin, R.

A. Cai, J. Guo, R. Lin, G. Shen, and M. Zukerman, “Multicast Routing and Distance-Adaptive Spectrum Allocation in Elastic Optical Networks With Shared Protection,” J. Lightwave Technol. 34(17), 4076–4088 (2016).
[Crossref]

Liu, H.

X. Guo, J. Huang, H. Liu, and Y. Chen, “Efficient P-cycle combination protection strategy based on improved genetic algorithm in elastic optical networks,” IET Optoelectron. 12(2), 73–79 (2018).
[Crossref]

Lu, W.

W. Lu, X. Yin, X. Cheng, and Z. Zhu, “On cost-efficient integrated multilayer protection planning in IP-over-EONs,” J. Lightwave Technol. 36(10), 2037–2048 (2018).
[Crossref]

Luo, X.

X. Luo, C. Shi, X. Chen, L. Wang, and T. Yang, “Global Optimization of All-Optical Hybrid-Casting in Inter-Datacenter Elastic Optical Networks,” IEEE Access 6, 36530–36543 (2018).
[Crossref]

Meusburger, C.

R. Huelsermann, M. Gunkel, C. Meusburger, and D. A. Schupke, “Cost modeling and evaluation of capital expenditures in optical multilayer networks,” J. Opt. Netw. 7(9), 814–833 (2008).
[Crossref]

Mnih, V.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Moharrami, M.

M. Moharrami, A. Fallahpour, H. Beyranvand, and J. A. Salehi, “Resource Allocation and Multicast Routing on Elastic Optical Networks,” IEEE Trans. Commun. 65(5), 2101–2113 (2017).
[Crossref]

Monteiro, P. P.

I. A. Alimi, A. L. Teixeira, and P. P. Monteiro, “Toward an Efficient C-RAN Optical Fronthaul for the Future Networks: A Tutorial on Technologies, Requirements, Challenges, and Solutions,” IEEE Comm. Surv. and Tutor. 20(1), 708–769 (2018).
[Crossref]

Namaad, M. Y.

M. Y. Namaad, A. G. Rahbar, and B. Alizadeh, “Adaptive modulation and flexible resource allocation in space-division- multiplexed elastic optical networks,” J. Opt. Commun. Netw. 10(3), 240–251 (2018).
[Crossref]

Ning, Z.

J. Wu, Z. Ning, and L. Guo, “Energy-Efficient Survivable Grooming in Software-Defined Elastic Optical Networks,” IEEE Access 5, 6454–6463 (2017).
[Crossref]

Oguma, T.

H. Takeshita, T. Oguma, S. Fujisawa, Y. Suzuki, B. Yatabe, A. Tajima, H. Hasegawa, and K. Sato, “Enhancing protection performance by effectively using spectral slots of impairment-aware elastic optical networks [invited],” J. Opt. Commun. Netw. 10(1), A91–A101 (2018).
[Crossref]

Oki, E.

S. Ba, B. C. Chatterjee, and E. Oki, “Defragmentation Scheme Based on Exchanging Primary and Backup Paths in 1+1 Path Protected Elastic Optical Networks,” IEEE/ACM Trans. Netw. 25(3), 1717–1731 (2017).
[Crossref]

B. C. Chatterjee, N. Sarma, and E. Oki, “Routing and Spectrum Allocation in Elastic Optical Networks: A Tutorial,” IEEE Comm. Surv. and Tutor. 17(3), 1776–1800 (2015).
[Crossref]

Ostrovski, G.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Papanikolaou, P.

P. Papanikolaou, K. Christodoulopoulos, and E. Varvarigos, “Optimization techniques for incremental planning of multilayer elastic optical networks,” J. Opt. Commun. Netw. 10(3), 183–194 (2018).
[Crossref]

Petersen, S.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Rahbar, A. G.

M. Y. Namaad, A. G. Rahbar, and B. Alizadeh, “Adaptive modulation and flexible resource allocation in space-division- multiplexed elastic optical networks,” J. Opt. Commun. Netw. 10(3), 240–251 (2018).
[Crossref]

Riedmiller, M.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Rusu, A. A.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Sadik, A.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Salehi, J. A.

M. Moharrami, A. Fallahpour, H. Beyranvand, and J. A. Salehi, “Resource Allocation and Multicast Routing on Elastic Optical Networks,” IEEE Trans. Commun. 65(5), 2101–2113 (2017).
[Crossref]

A. Fallahpour, H. Beyranvand, and J. A. Salehi, “Energy-Efficient Manycast Routing and Spectrum Assignment in Elastic Optical Networks for Cloud Computing Environment,” J. Lightwave Technol. 33(19), 4008–4018 (2015).
[Crossref]

Sarma, N.

B. C. Chatterjee, N. Sarma, and E. Oki, “Routing and Spectrum Allocation in Elastic Optical Networks: A Tutorial,” IEEE Comm. Surv. and Tutor. 17(3), 1776–1800 (2015).
[Crossref]

Sato, K.

H. Takeshita, T. Oguma, S. Fujisawa, Y. Suzuki, B. Yatabe, A. Tajima, H. Hasegawa, and K. Sato, “Enhancing protection performance by effectively using spectral slots of impairment-aware elastic optical networks [invited],” J. Opt. Commun. Netw. 10(1), A91–A101 (2018).
[Crossref]

Schupke, D. A.

R. Huelsermann, M. Gunkel, C. Meusburger, and D. A. Schupke, “Cost modeling and evaluation of capital expenditures in optical multilayer networks,” J. Opt. Netw. 7(9), 814–833 (2008).
[Crossref]

Shen, G.

G. Shen, H. Guo, and S. K. Bose, “Survivable elastic optical networks: survey and perspective (invited),” Photonic Netw. Commun. 31(1), 71–87 (2016).
[Crossref]

A. Cai, J. Guo, R. Lin, G. Shen, and M. Zukerman, “Multicast Routing and Distance-Adaptive Spectrum Allocation in Elastic Optical Networks With Shared Protection,” J. Lightwave Technol. 34(17), 4076–4088 (2016).
[Crossref]

Shi, C.

X. Luo, C. Shi, X. Chen, L. Wang, and T. Yang, “Global Optimization of All-Optical Hybrid-Casting in Inter-Datacenter Elastic Optical Networks,” IEEE Access 6, 36530–36543 (2018).
[Crossref]

Silver, D.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Song, C.

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[Crossref] [PubMed]

Suzuki, Y.

H. Takeshita, T. Oguma, S. Fujisawa, Y. Suzuki, B. Yatabe, A. Tajima, H. Hasegawa, and K. Sato, “Enhancing protection performance by effectively using spectral slots of impairment-aware elastic optical networks [invited],” J. Opt. Commun. Netw. 10(1), A91–A101 (2018).
[Crossref]

Tajima, A.

H. Takeshita, T. Oguma, S. Fujisawa, Y. Suzuki, B. Yatabe, A. Tajima, H. Hasegawa, and K. Sato, “Enhancing protection performance by effectively using spectral slots of impairment-aware elastic optical networks [invited],” J. Opt. Commun. Netw. 10(1), A91–A101 (2018).
[Crossref]

Takeshita, H.

H. Takeshita, T. Oguma, S. Fujisawa, Y. Suzuki, B. Yatabe, A. Tajima, H. Hasegawa, and K. Sato, “Enhancing protection performance by effectively using spectral slots of impairment-aware elastic optical networks [invited],” J. Opt. Commun. Netw. 10(1), A91–A101 (2018).
[Crossref]

Tan, Y.

Q. Yao, H. Yang, R. Zhu, A. Yu, W. Bai, Y. Tan, J. Zhang, and H. Xiao, “Core, Mode, and Spectrum Assignment Based on Machine Learning in Space Division Multiplexing Elastic Optical Networks,” IEEE Access 6, 15898–15907 (2018).
[Crossref]

Teixeira, A. L.

I. A. Alimi, A. L. Teixeira, and P. P. Monteiro, “Toward an Efficient C-RAN Optical Fronthaul for the Future Networks: A Tutorial on Technologies, Requirements, Challenges, and Solutions,” IEEE Comm. Surv. and Tutor. 20(1), 708–769 (2018).
[Crossref]

Tornatore, M.

X. Chen, M. Tornatore, S. Zhu, F. Ji, W. Zhou, C. Chen, D. Hu, L. Jiang, and Z. Zhu, “Flexible Availability-Aware Differentiated Protection in Software-Defined Elastic Optical Networks,” J. Lightwave Technol. 33(18), 3872–3882 (2015).
[Crossref]

Varvarigos, E.

P. Papanikolaou, K. Christodoulopoulos, and E. Varvarigos, “Optimization techniques for incremental planning of multilayer elastic optical networks,” J. Opt. Commun. Netw. 10(3), 183–194 (2018).
[Crossref]

Veness, J.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Wang, D.

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[Crossref] [PubMed]

Wang, L.

X. Luo, C. Shi, X. Chen, L. Wang, and T. Yang, “Global Optimization of All-Optical Hybrid-Casting in Inter-Datacenter Elastic Optical Networks,” IEEE Access 6, 36530–36543 (2018).
[Crossref]

Wierstra, D.

V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis, “Human-level control through deep reinforcement learning,” Nature 518(7540), 529–533 (2015).
[Crossref] [PubMed]

Wu, J.

J. Wu, Z. Ning, and L. Guo, “Energy-Efficient Survivable Grooming in Software-Defined Elastic Optical Networks,” IEEE Access 5, 6454–6463 (2017).
[Crossref]

Xiao, H.

Q. Yao, H. Yang, R. Zhu, A. Yu, W. Bai, Y. Tan, J. Zhang, and H. Xiao, “Core, Mode, and Spectrum Assignment Based on Machine Learning in Space Division Multiplexing Elastic Optical Networks,” IEEE Access 6, 15898–15907 (2018).
[Crossref]

Yang, H.

Q. Yao, H. Yang, R. Zhu, A. Yu, W. Bai, Y. Tan, J. Zhang, and H. Xiao, “Core, Mode, and Spectrum Assignment Based on Machine Learning in Space Division Multiplexing Elastic Optical Networks,” IEEE Access 6, 15898–15907 (2018).
[Crossref]

Yang, T.

X. Luo, C. Shi, X. Chen, L. Wang, and T. Yang, “Global Optimization of All-Optical Hybrid-Casting in Inter-Datacenter Elastic Optical Networks,” IEEE Access 6, 36530–36543 (2018).
[Crossref]

Yao, Q.

Q. Yao, H. Yang, R. Zhu, A. Yu, W. Bai, Y. Tan, J. Zhang, and H. Xiao, “Core, Mode, and Spectrum Assignment Based on Machine Learning in Space Division Multiplexing Elastic Optical Networks,” IEEE Access 6, 15898–15907 (2018).
[Crossref]

Yatabe, B.

H. Takeshita, T. Oguma, S. Fujisawa, Y. Suzuki, B. Yatabe, A. Tajima, H. Hasegawa, and K. Sato, “Enhancing protection performance by effectively using spectral slots of impairment-aware elastic optical networks [invited],” J. Opt. Commun. Netw. 10(1), A91–A101 (2018).
[Crossref]

Yin, S.

X. Li, S. Huang, S. Yin, B. Guo, Y. Zhao, J. Zhang, M. Zhang, and W. Gu, “Shared end-to-content backup path protection in k-node (edge) content connected elastic optical datacenter networks,” Opt. Express 24(9), 9446–9464 (2016).
[Crossref] [PubMed]

Yin, X.

W. Lu, X. Yin, X. Cheng, and Z. Zhu, “On cost-efficient integrated multilayer protection planning in IP-over-EONs,” J. Lightwave Technol. 36(10), 2037–2048 (2018).
[Crossref]

Yu, A.

Q. Yao, H. Yang, R. Zhu, A. Yu, W. Bai, Y. Tan, J. Zhang, and H. Xiao, “Core, Mode, and Spectrum Assignment Based on Machine Learning in Space Division Multiplexing Elastic Optical Networks,” IEEE Access 6, 15898–15907 (2018).
[Crossref]

Zhang, J.

Q. Yao, H. Yang, R. Zhu, A. Yu, W. Bai, Y. Tan, J. Zhang, and H. Xiao, “Core, Mode, and Spectrum Assignment Based on Machine Learning in Space Division Multiplexing Elastic Optical Networks,” IEEE Access 6, 15898–15907 (2018).
[Crossref]

X. Li, S. Huang, S. Yin, B. Guo, Y. Zhao, J. Zhang, M. Zhang, and W. Gu, “Shared end-to-content backup path protection in k-node (edge) content connected elastic optical datacenter networks,” Opt. Express 24(9), 9446–9464 (2016).
[Crossref] [PubMed]

Zhang, M.

D. Wang, M. Zhang, J. Li, Z. Li, J. Li, C. Song, and X. Chen, “Intelligent constellation diagram analyzer using convolutional neural network-based deep learning,” Opt. Express 25(15), 17150–17166 (2017).
[Crossref] [PubMed]

X. Li, S. Huang, S. Yin, B. Guo, Y. Zhao, J. Zhang, M. Zhang, and W. Gu, “Shared end-to-content backup path protection in k-node (edge) content connected elastic optical datacenter networks,” Opt. Express 24(9), 9446–9464 (2016).
[Crossref] [PubMed]

Zhao, Y.

X. Li, S. Huang, S. Yin, B. Guo, Y. Zhao, J. Zhang, M. Zhang, and W. Gu, “Shared end-to-content backup path protection in k-node (edge) content connected elastic optical datacenter networks,” Opt. Express 24(9), 9446–9464 (2016).
[Crossref] [PubMed]

Zhou, W.

X. Chen, M. Tornatore, S. Zhu, F. Ji, W. Zhou, C. Chen, D. Hu, L. Jiang, and Z. Zhu, “Flexible Availability-Aware Differentiated Protection in Software-Defined Elastic Optical Networks,” J. Lightwave Technol. 33(18), 3872–3882 (2015).
[Crossref]

Zhu, R.

Q. Yao, H. Yang, R. Zhu, A. Yu, W. Bai, Y. Tan, J. Zhang, and H. Xiao, “Core, Mode, and Spectrum Assignment Based on Machine Learning in Space Division Multiplexing Elastic Optical Networks,” IEEE Access 6, 15898–15907 (2018).
[Crossref]

Zhu, S.

X. Chen, M. Tornatore, S. Zhu, F. Ji, W. Zhou, C. Chen, D. Hu, L. Jiang, and Z. Zhu, “Flexible Availability-Aware Differentiated Protection in Software-Defined Elastic Optical Networks,” J. Lightwave Technol. 33(18), 3872–3882 (2015).
[Crossref]

X. Chen, S. Zhu, L. Jiang, and Z. Zhu, “On Spectrum Efficient Failure-Independent Path Protection p-Cycle Design in Elastic Optical Networks,” J. Lightwave Technol. 33(17), 3719–3729 (2015).
[Crossref]

Zhu, Z.

W. Lu, X. Yin, X. Cheng, and Z. Zhu, “On cost-efficient integrated multilayer protection planning in IP-over-EONs,” J. Lightwave Technol. 36(10), 2037–2048 (2018).
[Crossref]

X. Chen, M. Tornatore, S. Zhu, F. Ji, W. Zhou, C. Chen, D. Hu, L. Jiang, and Z. Zhu, “Flexible Availability-Aware Differentiated Protection in Software-Defined Elastic Optical Networks,” J. Lightwave Technol. 33(18), 3872–3882 (2015).
[Crossref]

X. Chen, S. Zhu, L. Jiang, and Z. Zhu, “On Spectrum Efficient Failure-Independent Path Protection p-Cycle Design in Elastic Optical Networks,” J. Lightwave Technol. 33(17), 3719–3729 (2015).
[Crossref]

X. Chen, F. Ji, and Z. Zhu, “Service availability oriented p-cycle protection design in elastic optical networks,” J. Opt. Commun. Netw. 6(10), 901–910 (2014).
[Crossref]

Zukerman, M.

A. Cai, J. Guo, R. Lin, G. Shen, and M. Zukerman, “Multicast Routing and Distance-Adaptive Spectrum Allocation in Elastic Optical Networks With Shared Protection,” J. Lightwave Technol. 34(17), 4076–4088 (2016).
[Crossref]

IEEE Access (3)

X. Luo, C. Shi, X. Chen, L. Wang, and T. Yang, “Global Optimization of All-Optical Hybrid-Casting in Inter-Datacenter Elastic Optical Networks,” IEEE Access 6, 36530–36543 (2018).
[Crossref]

J. Wu, Z. Ning, and L. Guo, “Energy-Efficient Survivable Grooming in Software-Defined Elastic Optical Networks,” IEEE Access 5, 6454–6463 (2017).
[Crossref]

Q. Yao, H. Yang, R. Zhu, A. Yu, W. Bai, Y. Tan, J. Zhang, and H. Xiao, “Core, Mode, and Spectrum Assignment Based on Machine Learning in Space Division Multiplexing Elastic Optical Networks,” IEEE Access 6, 15898–15907 (2018).
[Crossref]

IEEE Comm. Surv. and Tutor. (2)

B. C. Chatterjee, N. Sarma, and E. Oki, “Routing and Spectrum Allocation in Elastic Optical Networks: A Tutorial,” IEEE Comm. Surv. and Tutor. 17(3), 1776–1800 (2015).
[Crossref]

I. A. Alimi, A. L. Teixeira, and P. P. Monteiro, “Toward an Efficient C-RAN Optical Fronthaul for the Future Networks: A Tutorial on Technologies, Requirements, Challenges, and Solutions,” IEEE Comm. Surv. and Tutor. 20(1), 708–769 (2018).
[Crossref]

IEEE Trans. Commun. (1)

M. Moharrami, A. Fallahpour, H. Beyranvand, and J. A. Salehi, “Resource Allocation and Multicast Routing on Elastic Optical Networks,” IEEE Trans. Commun. 65(5), 2101–2113 (2017).
[Crossref]

IEEE/ACM Trans. Netw. (1)

S. Ba, B. C. Chatterjee, and E. Oki, “Defragmentation Scheme Based on Exchanging Primary and Backup Paths in 1+1 Path Protected Elastic Optical Networks,” IEEE/ACM Trans. Netw. 25(3), 1717–1731 (2017).
[Crossref]

IET Optoelectron. (1)

X. Guo, J. Huang, H. Liu, and Y. Chen, “Efficient P-cycle combination protection strategy based on improved genetic algorithm in elastic optical networks,” IET Optoelectron. 12(2), 73–79 (2018).
[Crossref]

J. Lightwave Technol. (6)

X. Chen, S. Zhu, L. Jiang, and Z. Zhu, “On Spectrum Efficient Failure-Independent Path Protection p-Cycle Design in Elastic Optical Networks,” J. Lightwave Technol. 33(17), 3719–3729 (2015).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Process of agent training at each time step t.
Fig. 2
Fig. 2 The structure of Q-network.
Fig. 3
Fig. 3 Convergence performance with different (a) learning rates and (b) the sizes of mini-batch.
Fig. 4
Fig. 4 Average values of WCES under different values of (a) T, (b) β and (c) α.
Fig. 5
Fig. 5 Average values of WCES under different traffic loads.
Fig. 6
Fig. 6 Request blocking probabilities under different traffic loads.
Fig. 7
Fig. 7 Survivable request success probabilities under different traffic loads.

Tables (2)

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Table 1 Typical cost and power consumption of network elements

Tables Icon

Table 2 Main simulation parameter settings

Equations (18)

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W C E S = W N T C W N S A S N C
W N T C = α i I p s ( C i l i ) + i I n p s ( C i l i ) i I b l ( C i l i )
W N S A = 1 + β ( | I s | | I m e a n | ) | I m e a n |
S N C = cos t C a p E x + cos t O p E x
cos t C a p E x = cos t C a p E x T i I s t i T
cos t O p E x = p u ( i I p s P C i + i I n p s P C i )
V π ( s t ) = E [ R ( s 0 , a 0 ) + γ R ( s 1 , a 1 ) + γ 2 R ( s 2 , a 2 ) + ... | π , s 0 = s t , a 0 = a t ] ;
V π ( s t ) = E { R ( s 0 , a 0 ) + γ [ R ( s 1 , a 1 ) + γ R ( s 2 , a 2 ) + ... ] | π , s 0 = s t , a 0 = a t } ;
V π ( s t ) = R ( s 0 , a 0 ) + γ s 0 [ P s 0 π ( s 0 ) ( s 1 ) V π ( s 1 ) ] , s 0 = s t ;
V * ( s t ) = max π V π ( s t ) = R ( s t , a t ) + max a t { γ s t + 1 [ P s t s t + 1 ( a t ) V * ( s t + 1 ) ] } , s t S ;
π * = arg max π V π ( s t ) = arg max a t { γ s t + 1 [ P s t s t + 1 ( a t ) V * ( s t + 1 ) ] } , s t S ;
Q * ( s , a ) = max π E [ R ( s 0 , a 0 ) + γ R ( s 1 , a 1 ) + γ 2 R ( s 2 , a 2 ) + ... | π , s 0 = s , a 0 = a ] = R ( s , a ) + max a { γ s ' [ P s s ' ( a ) V * ( s ' ) ] } = R ( s , a ) + γ max a ' Q ( s ' , a ' ) , s , s ' S ;
Q t + 1 ( s , a ) = Q t ( s , a ) + η { R ( s , a ) + E [ max a Q t ( s ' , a ' ) Q t ( s , a ) ] } ;
L o s s ( θ j ) = E { [ R ( s , a ) + γ max a ' Q ( s ' , a ' , θ j ) Q ( s , a , θ j ) ] 2 } ;
s ( t ) = { [ B d , e t ] } , d = 1 , 2 , ... , | E | ; e = 1 , 2 , ... , F ;
W A ( t ) = { [ a W , k 1 ( t ) ] } , k 1 = 1 , 2 , ... , K 1 ;
P A ( t ) = { [ a P , k 2 ( t ) ] } , k 2 = 1 , 2 , ... , K 2 ;
r ( t ) = W N T C W N S A S N C

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