{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:54:26Z","timestamp":1760151266832,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,3,11]],"date-time":"2022-03-11T00:00:00Z","timestamp":1646956800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key-Area Research and Development Program of Guangdong Province","award":["2020B090921003"],"award-info":[{"award-number":["2020B090921003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Many transport systems in the real world can be modeled as networked systems. Due to limited resources, only a few nodes can be selected as seeds in the system, whose role is to spread required information or control signals as widely as possible. This problem can be modeled as the influence maximization problem. Most of the existing selection strategies are based on the invariable network structure and have not touched upon the condition that the network is under structural failures. Related studies indicate that such strategies may not completely tackle complicated diffusion tasks in reality, and the robustness of the information diffusion process against perturbances is significant. To give a numerical performance criterion of seeds under structural failure, a measure has been developed to define the robust influence maximization (RIM) problem. Further, a memetic optimization algorithm (MA) which includes several problem-orientated operators to improve the search ability, termed RIMMA, has been presented to deal with the RIM problem. Experimental results on synthetic networks and real-world networks validate the effectiveness of RIMMA, its superiority over existing approaches is also shown.<\/jats:p>","DOI":"10.3390\/s22062191","type":"journal-article","created":{"date-parts":[[2022,3,13]],"date-time":"2022-03-13T21:44:17Z","timestamp":1647207857000},"page":"2191","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Memetic Algorithm for Solving the Robust Influence Maximization Problem on Complex Networks against Structural Failures"],"prefix":"10.3390","volume":"22","author":[{"given":"Delin","family":"Huang","sequence":"first","affiliation":[{"name":"School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaojun","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nanjie","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengping","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Intelligent Systems Engineering, Sun Yat-sen University, Shenzhen 518107, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Newman, M.E.J. (2010). Networks: An Introduction, Oxford University Press.","DOI":"10.1093\/acprof:oso\/9780199206650.003.0001"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wang, J., Luo, H., and Tan, X. (2021). Path Planning for Automatic Guided Vehicles (AGVs) Fusing MH-RRT with Improved TEB. Actuators, 10.","DOI":"10.3390\/act10120314"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Albert","year":"1999","journal-title":"Science"},{"key":"ref_4","first-page":"17","article-title":"On the evolution of random graphs","volume":"5","year":"1960","journal-title":"Publ. Math. Inst. Hung. Acad. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1016\/j.ins.2016.07.012","article-title":"Influence maximization in social networks based on discrete particle swarm optimization","volume":"367","author":"Gong","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Wang, C., Ma, X., Jiang, W., Zhao, L., Lin, N., and Shi, J. (2019, January 10\u201312). IMCR: Influence Maximisation-Based Cluster Routing Algorithm for SDVN. Proceedings of the 2019 IEEE 21st International Conference on High Performance Computing and Communications; IEEE 17th International Conference on Smart City; IEEE 5th International Conference on Data Science and Systems (HPCC\/SmartCity\/DSS), Zhangjiajie, China.","DOI":"10.1109\/HPCC\/SmartCity\/DSS.2019.00361"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhao, B., Xu, C., Liu, S., Zhao, J., and Li, L. (2019, January 9\u201312). A Congestion Diffusion Model with Influence Maximization for Traffic Bottlenecks Identification in Metrocity Scales. Proceedings of the 2019 IEEE International Conference on Big Data (Big Data), Los Angeles, CA, USA.","DOI":"10.1109\/BigData47090.2019.9006472"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Kempe, D., Kleinberg, J., and Tardos, \u00c9. (2003, January 24\u201327). Maximizing the spread of influence through a social network. Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, DC, USA.","DOI":"10.1145\/956750.956769"},{"key":"ref_9","unstructured":"Chen, W., Wang, Y., and Yang, S. (July, January 28). Efficient influence maximization in social networks. Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Paris, France."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1016\/j.eswa.2014.09.037","article-title":"A fast algorithm for finding most influential people based on the linear threshold model","volume":"42","author":"Rahimkhani","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Lee, J.-R., and Chung, C.-W. (2014, January 7\u201311). A fast approximation for influence maximization in large social networks. Proceedings of the 23rd International Conference on World Wide Web, Seoul, Korea.","DOI":"10.1145\/2567948.2580063"},{"key":"ref_12","first-page":"539","article-title":"A two-phase multiobjective evolutionary algorithm for enhancing the robustness of scale-free networks against multiple malicious attacks","volume":"47","author":"Zhou","year":"2017","journal-title":"IEEE Trans. Cybern."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"582","DOI":"10.1109\/JSYST.2018.2835642","article-title":"Constructing robust community structure against edge-based attacks","volume":"13","author":"Wang","year":"2019","journal-title":"IEEE Syst. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"056109","DOI":"10.1103\/PhysRevE.65.056109","article-title":"Attack vulnerability of complex networks","volume":"65","author":"Holme","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.physa.2017.12.094","article-title":"Comparison analysis on vulnerability of metro networks based on complex network","volume":"496","author":"Zhang","year":"2018","journal-title":"Phys. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"49025","DOI":"10.1109\/ACCESS.2021.3063928","article-title":"Model and analyze the cascading failure of scale-Free network considering the selective forwarding attack","volume":"9","author":"Yin","year":"2021","journal-title":"IEEE Access"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1109\/JCN.2020.000010","article-title":"Malicious relay detection using sentinels: A stochastic geometry framework","volume":"22","author":"Tefek","year":"2020","journal-title":"J. Commun. Netw."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"022810","DOI":"10.1103\/PhysRevE.88.022810","article-title":"Enhancing community integrity of networks against multilevel targeted attacks","volume":"88","author":"Ma","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_19","unstructured":"Lupt\u00e1kov\u00e1, D., and Posp\u00edchal, J. (2017, January 12\u201314). Community cut-off attack on malicious networks. Proceedings of the Conference on Creativity in Intelligent Technologies and Data Science, Volgograd, Russia."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3838","DOI":"10.1073\/pnas.1009440108","article-title":"Mitigation of malicious attacks on networks","volume":"108","author":"Schneider","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1025","DOI":"10.1038\/nature08932","article-title":"Catastrophic cascade of failures in interdependent networks","volume":"464","author":"Buldyrev","year":"2010","journal-title":"Nature"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.physa.2014.05.002","article-title":"A memetic algorithm for enhancing the robustness of scale-free networks against malicious attacks","volume":"410","author":"Zhou","year":"2014","journal-title":"Phys. A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/TNSE.2017.2742522","article-title":"A multi-objective evolutionary algorithm for promoting the emergence of cooperation and controllable robustness on directed networks","volume":"5","author":"Wang","year":"2018","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Wang, J., Li, J., Shi, Y., Lai, J., and Tan, X. (2022). AM3Net: Adaptive mutual-learning-based multimodal data fusion network. IEEE Trans. Circuits Syst. Video Technol., Early Access.","DOI":"10.1109\/TCSVT.2022.3148257"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/MCI.2016.2572538","article-title":"An efficient memetic algorithm for influence maximization in social networks","volume":"11","author":"Gong","year":"2016","journal-title":"IEEE Comput. Intell. Mag."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1016\/j.ins.2015.03.034","article-title":"Super mediator\u2014A new centrality measure of node importance for information diffusion over social network","volume":"329","author":"Saito","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.neucom.2017.03.003","article-title":"Positive influence maximization in signed social networks based on simulated annealing","volume":"260","author":"Li","year":"2017","journal-title":"Neurocomputing"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1016\/j.physa.2017.02.067","article-title":"Maximizing influence in a social network: Improved results using a genetic algorithm","volume":"478","author":"Zhang","year":"2017","journal-title":"Phys. A"},{"key":"ref_29","unstructured":"Chen, W., Lin, T., Tan, Z., Zhao, M., and Zhou, X. (2016, January 13\u201317). Community cut-off attack on malicious networks. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3233227","article-title":"Stability and robustness in influence maximization","volume":"12","author":"He","year":"2018","journal-title":"ACM Trans. Knowl. Disc. Data (TKDD)"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"066130","DOI":"10.1103\/PhysRevE.85.066130","article-title":"Enhancing network robustness against malicious attacks","volume":"85","author":"Zeng","year":"2012","journal-title":"Phys. Rev. E"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.trb.2019.11.004","article-title":"An epidemiological diffusion framework for vehicular messaging in general transportation networks","volume":"131","author":"Kim","year":"2020","journal-title":"Transp. Res. Part B Methodol."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1109\/MNET.2004.1316760","article-title":"Movement control algorithms for realization of fault-tolerant ad hoc robot networks","volume":"18","author":"Baus","year":"2004","journal-title":"IEEE Netw."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/s10846-013-0003-8","article-title":"Methodologies to optimize automated guided vehicle scheduling and routing problems: A review study","volume":"77","author":"Fazlollahtabar","year":"2015","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2912","DOI":"10.1109\/TIE.2014.2363632","article-title":"A recursive receding horizon planning for unmanned vehicles","volume":"62","author":"Zhang","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1016\/j.asoc.2019.01.045","article-title":"Community robustness and its enhancement in interdependent networks","volume":"77","author":"Wang","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of \u2018small-world\u2019 networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40551-015-0012-9","article-title":"Symmetrica: Test case for transportation electrification research","volume":"2","author":"Farid","year":"2015","journal-title":"Infrastruct. Complex."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.physa.2016.04.035","article-title":"Robustness of single and interdependent scale-free interaction networks with various parameters","volume":"460","author":"Wang","year":"2016","journal-title":"Phys. A"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"125989","DOI":"10.1016\/j.physa.2021.125989","article-title":"Cascading failures of overload behaviors on interdependent networks","volume":"574","author":"Wang","year":"2021","journal-title":"Phys. A"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/6\/2191\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:35:02Z","timestamp":1760135702000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/6\/2191"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,11]]},"references-count":40,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["s22062191"],"URL":"https:\/\/doi.org\/10.3390\/s22062191","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,3,11]]}}}