# American Institute of Mathematical Sciences

July  2022, 18(4): 2805-2826. doi: 10.3934/jimo.2021092

## Collaborative mission optimization for ship rapid search by multiple heterogeneous remote sensing satellites

 Beijing Institute of Remote Sensing Information, Beijing 100089, China

* Corresponding author: Bitao Jiang

Received  February 2021 Revised  March 2021 Published  July 2022 Early access  April 2021

Fund Project: This paper is supported by the National Natural Science Foundation of China (Grant Nos: 91638301)

Multiple heterogeneous satellites mission optimization is a typical kind of non-deterministic polynomial-time hard (NP-hard) problem, and some complicated scenarios bring new challenges. A novel method of missing ship rapid search using multiple grouped heterogeneous satellites is introduced in this paper. The focus is on optimization of collaborative mission optimization for various satellites including low-earth orbit (LEO) satellite and geostationary orbit (GEO) satellites. A fast coverage of the wide sea area using imaging satellites with narrow coverage range has become the most important part to tackle this problem. However, due to different imaging mechanisms of heterogeneous satellites and other constraints, it brings a great challenge to construct the optimization model. A constrained optimization problem model considering the cooperation between LEO and GEO satellites is constructed. A solution strategy based on bi-level metaheuristic algorithm is designed. The time optimal solution of the collaborative task planning between LEO and GEO satellites can be obtained based on the optimal attitude maneuver path of GEO satellites. Thus, wide-area search for missing ships can be conducted in an effective way. The effectiveness of the proposed method is verified by an example.

Citation: Qian Zhao, Bitao Jiang, Xiaogang Yu, Yue Zhang. Collaborative mission optimization for ship rapid search by multiple heterogeneous remote sensing satellites. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2805-2826. doi: 10.3934/jimo.2021092
##### References:
 [1] N. Bianchessi, J.-F. Cordeau, J. Desrosiers, G. Laporte and V. Raymond, A heuristic for the multi-satellite, multi-orbit and multi-user management of Earth observation satellites, European Journal of Operational Research, 177 (2007), 750-762.  doi: 10.1016/j.ejor.2005.12.026. [2] R. Deutsch, Orbital Dynamics of Space Vehicles, Prentice-Hall, Inc., Englewood Cliffs, N.J. 1963. [3] M. Dorigo and C. Blum, Ant colony optimization theory: A survey, Theoret. Comput. Sci., 344 (2005), 243-278.  doi: 10.1016/j.tcs.2005.05.020. [4] M. Dorigo and G. Di Caro, Ant colony optimization: A new meta-heuristic, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), 2 (1999), 1470-1477.  doi: 10.1109/CEC.1999.782657. [5] M. Dorigo, M. Birattari and T. Stutzle, Ant colony optimization, IEEE Computational Intelligence Magazine, 1 (2006), 28-39. [6] J. Dungan, J. Frank, A. Jónsson, R. Morris and D. Smith, Advances in planning and scheduling of remote sensing instruments for fleets of earth orbiting satellites, In Earth Science Technology Conference, 2002. [7] S. D. Florio, T. Zehetbauer and T. Neff, Optimal operations planning for SAR satellite constellations [C], In Low Earth Orbit. 6th International Symposium on Reducing the Costs of Spacecraft Ground Systems and Operations, 2005. [8] F. T. Hwang, Y. Y. Yeh and S. Y. Li, Multi-objective optimization for multi-satellite scheduling system, In Proceedings of 31st Asian Conference on Remote Sensing, 2010. [9] J. Li, S. Zhang, X. Liu and R. He, Multi-objective evolutionary optimization for geostationary orbit satellite mission planning, Journal of Systems Engineering and Electronics, 28 (2017), 934-945.  doi: 10.21629/JSEE.2017.05.11. [10] K. T. Malladi, S. M. Minic, D. Karapetyan and A. P. Punnen, Satellite constellation image acquisition problem: A case study, In Space Engineering, Springer, Cham, (2016), 177–197. doi: 10.1007/978-3-319-41508-6_7. [11] K. T. Malladi, S. Mitrovic-Minic and A. P. Punnen, Clustered maximum weight clique problem: Algorithms and empirical analysis, Comput. Oper. Res., 85 (2017), 113-128.  doi: 10.1016/j.cor.2017.04.002. [12] M. Mitchell, An Introduction to Genetic Algorithms, MIT press, 1998.  doi: 10.7551/mitpress/3927.001.0001. [13] S. Mitrovic-Minic, D. Thomson, J. Berger and J. Secker, Collection planning and scheduling for multiple heterogeneous satellite missions: Survey, optimization problem, and mathematical programming formulation, Modeling and Optimization in Space Engineering, 144 (2019), 271-305. [14] M. D. Shuster, A survey of attitude representations, J. Astronaut. Sci., 41 (1993), 439-517. [15] S. N. Sivanandam and S. N. Deepa, Genetic algorithms, In Introduction to Genetic Algorithms, Springer, Berlin, Heidelberg, (2008), 15–37 [16] M. Vasquez and J.-K. Hao, A "logic-constrained" knapsack formulation and a tabu algorithm for the daily photograph scheduling of an Earth observation satellite, Comput. Optim. Appl., 20 (2001), 137-157.  doi: 10.1023/A:1011203002719. [17] X. Liu, B. Bai, Y. Chen and F. Yao, Multi satellites scheduling algorithm based on task merging mechanism, Appl. Math. Comput., 230 (2014), 687-700.  doi: 10.1016/j.amc.2013.12.109. [18] Y. Zhang, J. Wang, B. Yuan, C. Wang and L. Shi, Research on multi-satellite observation multi-region task planning based on genetic algorithm, In IOP Conference Series: Materials Science and Engineering, 685 (2019), 012002. doi: 10.1088/1757-899X/685/1/012002. [19] Y. Zhou, Y. Yan, X. Huang, Y. Yang and H. Zhang, Mission planning optimization for the visual inspection of multiple geosynchronous satellites, Engineering Optimization, 47 (2015), 1543-1563.  doi: 10.1080/0305215X.2014.979813. [20] X. Zhu, J. Chen, C. hang and B. Qiao, Optimal fuel station arrangement for multiple GEO spacecraft refueling mission, Advances in Space Research, 66 (2020), 1924-1936.

show all references

##### References:
 [1] N. Bianchessi, J.-F. Cordeau, J. Desrosiers, G. Laporte and V. Raymond, A heuristic for the multi-satellite, multi-orbit and multi-user management of Earth observation satellites, European Journal of Operational Research, 177 (2007), 750-762.  doi: 10.1016/j.ejor.2005.12.026. [2] R. Deutsch, Orbital Dynamics of Space Vehicles, Prentice-Hall, Inc., Englewood Cliffs, N.J. 1963. [3] M. Dorigo and C. Blum, Ant colony optimization theory: A survey, Theoret. Comput. Sci., 344 (2005), 243-278.  doi: 10.1016/j.tcs.2005.05.020. [4] M. Dorigo and G. Di Caro, Ant colony optimization: A new meta-heuristic, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), 2 (1999), 1470-1477.  doi: 10.1109/CEC.1999.782657. [5] M. Dorigo, M. Birattari and T. Stutzle, Ant colony optimization, IEEE Computational Intelligence Magazine, 1 (2006), 28-39. [6] J. Dungan, J. Frank, A. Jónsson, R. Morris and D. Smith, Advances in planning and scheduling of remote sensing instruments for fleets of earth orbiting satellites, In Earth Science Technology Conference, 2002. [7] S. D. Florio, T. Zehetbauer and T. Neff, Optimal operations planning for SAR satellite constellations [C], In Low Earth Orbit. 6th International Symposium on Reducing the Costs of Spacecraft Ground Systems and Operations, 2005. [8] F. T. Hwang, Y. Y. Yeh and S. Y. Li, Multi-objective optimization for multi-satellite scheduling system, In Proceedings of 31st Asian Conference on Remote Sensing, 2010. [9] J. Li, S. Zhang, X. Liu and R. He, Multi-objective evolutionary optimization for geostationary orbit satellite mission planning, Journal of Systems Engineering and Electronics, 28 (2017), 934-945.  doi: 10.21629/JSEE.2017.05.11. [10] K. T. Malladi, S. M. Minic, D. Karapetyan and A. P. Punnen, Satellite constellation image acquisition problem: A case study, In Space Engineering, Springer, Cham, (2016), 177–197. doi: 10.1007/978-3-319-41508-6_7. [11] K. T. Malladi, S. Mitrovic-Minic and A. P. Punnen, Clustered maximum weight clique problem: Algorithms and empirical analysis, Comput. Oper. Res., 85 (2017), 113-128.  doi: 10.1016/j.cor.2017.04.002. [12] M. Mitchell, An Introduction to Genetic Algorithms, MIT press, 1998.  doi: 10.7551/mitpress/3927.001.0001. [13] S. Mitrovic-Minic, D. Thomson, J. Berger and J. Secker, Collection planning and scheduling for multiple heterogeneous satellite missions: Survey, optimization problem, and mathematical programming formulation, Modeling and Optimization in Space Engineering, 144 (2019), 271-305. [14] M. D. Shuster, A survey of attitude representations, J. Astronaut. Sci., 41 (1993), 439-517. [15] S. N. Sivanandam and S. N. Deepa, Genetic algorithms, In Introduction to Genetic Algorithms, Springer, Berlin, Heidelberg, (2008), 15–37 [16] M. Vasquez and J.-K. Hao, A "logic-constrained" knapsack formulation and a tabu algorithm for the daily photograph scheduling of an Earth observation satellite, Comput. Optim. Appl., 20 (2001), 137-157.  doi: 10.1023/A:1011203002719. [17] X. Liu, B. Bai, Y. Chen and F. Yao, Multi satellites scheduling algorithm based on task merging mechanism, Appl. Math. Comput., 230 (2014), 687-700.  doi: 10.1016/j.amc.2013.12.109. [18] Y. Zhang, J. Wang, B. Yuan, C. Wang and L. Shi, Research on multi-satellite observation multi-region task planning based on genetic algorithm, In IOP Conference Series: Materials Science and Engineering, 685 (2019), 012002. doi: 10.1088/1757-899X/685/1/012002. [19] Y. Zhou, Y. Yan, X. Huang, Y. Yang and H. Zhang, Mission planning optimization for the visual inspection of multiple geosynchronous satellites, Engineering Optimization, 47 (2015), 1543-1563.  doi: 10.1080/0305215X.2014.979813. [20] X. Zhu, J. Chen, C. hang and B. Qiao, Optimal fuel station arrangement for multiple GEO spacecraft refueling mission, Advances in Space Research, 66 (2020), 1924-1936.
LEO satellite observation
GEO satellite observation
The relationship between ship speed and coverage area
Mesh generation considering ship moving
General structure of solution method
Coverage ratio of task area over 17:29:08
Results of outer layer optimization
LEO Mission Selected
Results of inner layer optimization problems
GEO Satellite Optimal Path
Satellite Orbit Parameters
 $\boldsymbol{a(km)}$ $\boldsymbol{e}$ $\boldsymbol{i(rad)}$ $\boldsymbol{raan(rad)}$ $\boldsymbol{ w(rad)}$ $\boldsymbol{GEO}$ 42166.3 0 0 2.6180 0 $\boldsymbol{LEO-1 }$ 6978 0 0.6981 0.7854 2.0944 $\boldsymbol{LEO-2 }$ 6978 0 0.6981 0.7854 4.1888 $\boldsymbol{LEO-3 }$ 6978 0 0.6981 0.7854 6.2832 $\boldsymbol{LEO-4 }$ 6978 0 0.6981 1.5708 2.0944 $\boldsymbol{LEO-5 }$ 6978 0 0.6981 1.5708 4.1888 $\boldsymbol{LEO-6 }$ 6978 0 0.6981 1.5708 6.2832 $\boldsymbol{LEO-7 }$ 6978 0 0.6981 2.3562 2.0944 $\boldsymbol{LEO-8 }$ 6978 0 0.6981 2.3562 4.1888 $\boldsymbol{LEO-9 }$ 6978 0 0.6981 2.3562 6.2832 $\boldsymbol{LEO-10 }$ 6978 0 0.6981 3.1416 2.0944 $\boldsymbol{LEO-11 }$ 6978 0 0.6981 3.1416 4.1888 $\boldsymbol{LEO-12 }$ 6978 0 0.6981 3.1416 6.2832 $\boldsymbol{LEO-13 }$ 6978 0 0.6981 3.9270 2.0944 $\boldsymbol{LEO-14 }$ 6978 0 0.6981 3.9270 4.1888 $\boldsymbol{LEO-15 }$ 6978 0 0.6981 3.9270 6.2832 $\boldsymbol{LEO-16 }$ 6978 0 0.6981 4.7124 2.0944 $\boldsymbol{LEO-17 }$ 6978 0 0.6981 4.7124 4.1888 $\boldsymbol{LEO-18 }$ 6978 0 0.6981 4.7124 6.2832 $\boldsymbol{LEO-19 }$ 6978 0 0.6981 5.4978 2.0944 $\boldsymbol{LEO-20 }$ 6978 0 0.6981 5.4978 4.1888 $\boldsymbol{LEO-21 }$ 6978 0 0.6981 5.4978 6.2832 $\boldsymbol{LEO-22 }$ 6978 0 0.6981 6.2832 2.0944 $\boldsymbol{LEO-23 }$ 6978 0 0.6981 6.2832 4.1888 $\boldsymbol{LEO-24 }$ 6978 0 0.6981 6.2832 6.2832
 $\boldsymbol{a(km)}$ $\boldsymbol{e}$ $\boldsymbol{i(rad)}$ $\boldsymbol{raan(rad)}$ $\boldsymbol{ w(rad)}$ $\boldsymbol{GEO}$ 42166.3 0 0 2.6180 0 $\boldsymbol{LEO-1 }$ 6978 0 0.6981 0.7854 2.0944 $\boldsymbol{LEO-2 }$ 6978 0 0.6981 0.7854 4.1888 $\boldsymbol{LEO-3 }$ 6978 0 0.6981 0.7854 6.2832 $\boldsymbol{LEO-4 }$ 6978 0 0.6981 1.5708 2.0944 $\boldsymbol{LEO-5 }$ 6978 0 0.6981 1.5708 4.1888 $\boldsymbol{LEO-6 }$ 6978 0 0.6981 1.5708 6.2832 $\boldsymbol{LEO-7 }$ 6978 0 0.6981 2.3562 2.0944 $\boldsymbol{LEO-8 }$ 6978 0 0.6981 2.3562 4.1888 $\boldsymbol{LEO-9 }$ 6978 0 0.6981 2.3562 6.2832 $\boldsymbol{LEO-10 }$ 6978 0 0.6981 3.1416 2.0944 $\boldsymbol{LEO-11 }$ 6978 0 0.6981 3.1416 4.1888 $\boldsymbol{LEO-12 }$ 6978 0 0.6981 3.1416 6.2832 $\boldsymbol{LEO-13 }$ 6978 0 0.6981 3.9270 2.0944 $\boldsymbol{LEO-14 }$ 6978 0 0.6981 3.9270 4.1888 $\boldsymbol{LEO-15 }$ 6978 0 0.6981 3.9270 6.2832 $\boldsymbol{LEO-16 }$ 6978 0 0.6981 4.7124 2.0944 $\boldsymbol{LEO-17 }$ 6978 0 0.6981 4.7124 4.1888 $\boldsymbol{LEO-18 }$ 6978 0 0.6981 4.7124 6.2832 $\boldsymbol{LEO-19 }$ 6978 0 0.6981 5.4978 2.0944 $\boldsymbol{LEO-20 }$ 6978 0 0.6981 5.4978 4.1888 $\boldsymbol{LEO-21 }$ 6978 0 0.6981 5.4978 6.2832 $\boldsymbol{LEO-22 }$ 6978 0 0.6981 6.2832 2.0944 $\boldsymbol{LEO-23 }$ 6978 0 0.6981 6.2832 4.1888 $\boldsymbol{LEO-24 }$ 6978 0 0.6981 6.2832 6.2832
Constant Parameters
 $\textbf{Parameters}$ $\boldsymbol{Value}$ $\boldsymbol{Unit}$ Orbit perturbation constant J2 0.001082629989052 — Gravity acceleration of earth's sea level ge 0.00980665 km/s$^2$ Gravitational constant $\mu$ 398600.4418 km$^2$/s$^2$ Radius of the earth Re 6.378137e3 km Ship maximum speed $v_{max}$ 20 km/hour Imaging width of LEO satellite $D_{LEO}$ 250km km Imaging width of GEO satellite $D_{GEO}$ 250km km Maximum angular velocity of GEO satellite $w_{max}$ 1e-4 deg/hour Single imaging time of GEO satellite $t_{single}$ 20 s
 $\textbf{Parameters}$ $\boldsymbol{Value}$ $\boldsymbol{Unit}$ Orbit perturbation constant J2 0.001082629989052 — Gravity acceleration of earth's sea level ge 0.00980665 km/s$^2$ Gravitational constant $\mu$ 398600.4418 km$^2$/s$^2$ Radius of the earth Re 6.378137e3 km Ship maximum speed $v_{max}$ 20 km/hour Imaging width of LEO satellite $D_{LEO}$ 250km km Imaging width of GEO satellite $D_{GEO}$ 250km km Maximum angular velocity of GEO satellite $w_{max}$ 1e-4 deg/hour Single imaging time of GEO satellite $t_{single}$ 20 s
Access calculation results
 $\textbf{Meta Mission No.}$ $\textbf{Satellite No.}$ $\textbf{Grid No.}$ ${\textbf{Observation Time (hour)}}$ $\boldsymbol{1}$ 4 1 0.119444 $\boldsymbol{2}$ 4 2 0.113889 $\boldsymbol{3}$ 4 3 0.108333 $\boldsymbol{4}$ 4 11 0.125 $\boldsymbol{5}$ 4 12 0.122222 $\boldsymbol{6}$ 4 21 0.133333 $\boldsymbol{7}$ 7 7 1.625 $\boldsymbol{8}$ 7 8 1.619444 $\boldsymbol{9}$ 7 16 1.636111 $\boldsymbol{10}$ 7 17 1.633333 $\boldsymbol{11}$ 7 18 1.627778 $\boldsymbol{12}$ 7 26 1.641667 $\boldsymbol{13}$ 7 27 1.641667 $\boldsymbol{14}$ 7 35 1.655556 $\boldsymbol{15}$ 7 36 1.652778 $\boldsymbol{16}$ 7 37 1.644444 $\boldsymbol{17}$ 7 45 1.663889 $\boldsymbol{18}$ 7 46 1.658333 $\boldsymbol{19}$ 7 54 1.675 $\boldsymbol{20}$ 7 55 1.669444
 $\textbf{Meta Mission No.}$ $\textbf{Satellite No.}$ $\textbf{Grid No.}$ ${\textbf{Observation Time (hour)}}$ $\boldsymbol{1}$ 4 1 0.119444 $\boldsymbol{2}$ 4 2 0.113889 $\boldsymbol{3}$ 4 3 0.108333 $\boldsymbol{4}$ 4 11 0.125 $\boldsymbol{5}$ 4 12 0.122222 $\boldsymbol{6}$ 4 21 0.133333 $\boldsymbol{7}$ 7 7 1.625 $\boldsymbol{8}$ 7 8 1.619444 $\boldsymbol{9}$ 7 16 1.636111 $\boldsymbol{10}$ 7 17 1.633333 $\boldsymbol{11}$ 7 18 1.627778 $\boldsymbol{12}$ 7 26 1.641667 $\boldsymbol{13}$ 7 27 1.641667 $\boldsymbol{14}$ 7 35 1.655556 $\boldsymbol{15}$ 7 36 1.652778 $\boldsymbol{16}$ 7 37 1.644444 $\boldsymbol{17}$ 7 45 1.663889 $\boldsymbol{18}$ 7 46 1.658333 $\boldsymbol{19}$ 7 54 1.675 $\boldsymbol{20}$ 7 55 1.669444
 [1] Xinwei Wang, Hai Wang, Hongyun Zhang, Min Wang, Lei Wang, Kaikai Cui, Chen Lu, Yu Ding. A mini review on UAV mission planning. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022089 [2] Zhihua Zhang, Naoki Saito. PHLST with adaptive tiling and its application to antarctic remote sensing image approximation. Inverse Problems and Imaging, 2014, 8 (1) : 321-337. doi: 10.3934/ipi.2014.8.321 [3] Min-Fan He, Li-Ning Xing, Wen Li, Shang Xiang, Xu Tan. Double layer programming model to the scheduling of remote sensing data processing tasks. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1515-1526. doi: 10.3934/dcdss.2019104 [4] A Voutilainen, Jari P. Kaipio. Model reduction and pollution source identification from remote sensing data. Inverse Problems and Imaging, 2009, 3 (4) : 711-730. doi: 10.3934/ipi.2009.3.711 [5] Wei Fu, Jun Liu, Yirong Lai. Collaborative filtering recommendation algorithm towards intelligent community. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 811-822. doi: 10.3934/dcdss.2019054 [6] Soheil Dolatabadi. Weighted vertices optimizer (WVO): A novel metaheuristic optimization algorithm. Numerical Algebra, Control and Optimization, 2018, 8 (4) : 461-479. doi: 10.3934/naco.2018029 [7] Linfei Wang, Dapeng Tao, Ruonan Wang, Ruxin Wang, Hao Li. Big Map R-CNN for object detection in large-scale remote sensing images. Mathematical Foundations of Computing, 2019, 2 (4) : 299-314. doi: 10.3934/mfc.2019019 [8] Graciela Canziani, Rosana Ferrati, Claudia Marinelli, Federico Dukatz. Artificial neural networks and remote sensing in the analysis of the highly variable Pampean shallow lakes. Mathematical Biosciences & Engineering, 2008, 5 (4) : 691-711. doi: 10.3934/mbe.2008.5.691 [9] Dequan Yue, Jun Yu, Wuyi Yue. A Markovian queue with two heterogeneous servers and multiple vacations. Journal of Industrial and Management Optimization, 2009, 5 (3) : 453-465. doi: 10.3934/jimo.2009.5.453 [10] Katherinne Salas Navarro, Jaime Acevedo Chedid, Whady F. Florez, Holman Ospina Mateus, Leopoldo Eduardo Cárdenas-Barrón, Shib Sankar Sana. A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1613-1633. doi: 10.3934/jimo.2019020 [11] Wenbo Fu, Debnath Narayan. Optimization algorithm for embedded Linux remote video monitoring system oriented to the internet of things (IOT). Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1341-1354. doi: 10.3934/dcdss.2019092 [12] Lou Caccetta, Elham Mardaneh. Joint pricing and production planning for fixed priced multiple products with backorders. Journal of Industrial and Management Optimization, 2010, 6 (1) : 123-147. doi: 10.3934/jimo.2010.6.123 [13] Yingying Li, Stanley Osher. Coordinate descent optimization for l1 minimization with application to compressed sensing; a greedy algorithm. Inverse Problems and Imaging, 2009, 3 (3) : 487-503. doi: 10.3934/ipi.2009.3.487 [14] Jian-Wu Xue, Xiao-Kun Xu, Feng Zhang. Big data dynamic compressive sensing system architecture and optimization algorithm for internet of things. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1401-1414. doi: 10.3934/dcdss.2015.8.1401 [15] Rodolfo Mendoza-Gómez, Roger Z. Ríos-Mercado, Karla B. Valenzuela-Ocaña. An iterated greedy algorithm with variable neighborhood descent for the planning of specialized diagnostic services in a segmented healthcare system. Journal of Industrial and Management Optimization, 2020, 16 (2) : 857-885. doi: 10.3934/jimo.2018182 [16] Zheng Chang, Haoxun Chen, Farouk Yalaoui, Bo Dai. Adaptive large neighborhood search Algorithm for route planning of freight buses with pickup and delivery. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1771-1793. doi: 10.3934/jimo.2020045 [17] Dariush Mohamadi Zanjirani, Majid Esmaelian. An integrated approach based on Fuzzy Inference System for scheduling and process planning through multiple objectives. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1235-1259. doi: 10.3934/jimo.2018202 [18] Nicolás M. Crisosto, Christopher M. Kribs-Zaleta, Carlos Castillo-Chávez, Stephen Wirkus. Community resilience in collaborative learning. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 17-40. doi: 10.3934/dcdsb.2010.14.17 [19] Chia-Huang Wu, Kuo-Hsiung Wang, Jau-Chuan Ke, Jyh-Bin Ke. A heuristic algorithm for the optimization of M/M/$s$ queue with multiple working vacations. Journal of Industrial and Management Optimization, 2012, 8 (1) : 1-17. doi: 10.3934/jimo.2012.8.1 [20] Jaedal Jung, Ertugrul Taciroglu. A divide-alternate-and-conquer approach for localization and shape identification of multiple scatterers in heterogeneous media using dynamic XFEM. Inverse Problems and Imaging, 2016, 10 (1) : 165-193. doi: 10.3934/ipi.2016.10.165

2021 Impact Factor: 1.411