{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T13:05:01Z","timestamp":1784898301488,"version":"3.55.0"},"reference-count":47,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100007724","name":"Wuhan University of Technology","doi-asserted-by":"publisher","award":["40120596"],"award-info":[{"award-number":["40120596"]}],"id":[{"id":"10.13039\/501100007724","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72101193"],"award-info":[{"award-number":["72101193"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72474167"],"award-info":[{"award-number":["72474167"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Expert Systems with Applications"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.eswa.2026.131935","type":"journal-article","created":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T16:15:06Z","timestamp":1772900106000},"page":"131935","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["Optimal budget allocation and influencer scheduling for product promotion within multilayer social networks"],"prefix":"10.1016","volume":"317","author":[{"given":"Rui","family":"Zheng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-1183-5918","authenticated-orcid":false,"given":"Fang","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.eswa.2026.131935_b0005","doi-asserted-by":"crossref","DOI":"10.1063\/5.0023427","article-title":"Sequential seeding in multilayer networks","volume":"31","author":"Br\u00f3dka","year":"2021","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"key":"10.1016\/j.eswa.2026.131935_b0010","doi-asserted-by":"crossref","unstructured":"Bucur, D., & Iacca, G. (2016). Influence maximization in social networks with genetic algorithms. In: Applications of Evolutionary Computation: 19th European Conference, EvoApplications 2016, Porto, Portugal, March 30--April 1, 2016, Proceedings, Part I 19 (pp. 379-392): Springer.","DOI":"10.1007\/978-3-319-31204-0_25"},{"key":"10.1016\/j.eswa.2026.131935_b0015","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1007\/s13278-025-01454-7","article-title":"Rank-refining seed selection methods for budget constrained influence maximisation in multilayer networks under linear threshold model","volume":"15","author":"Czuba","year":"2025","journal-title":"Social Network Analysis and Mining"},{"key":"10.1016\/j.eswa.2026.131935_b0020","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1007\/s10489-017-0987-z","article-title":"Minimum positive influence dominating set and its application in influence maximization: A learning automata approach","volume":"48","author":"Daliri Khomami","year":"2018","journal-title":"Applied Intelligence"},{"key":"10.1016\/j.eswa.2026.131935_b0025","doi-asserted-by":"crossref","first-page":"4151","DOI":"10.1007\/s10115-024-02084-9","article-title":"Influential users identification under the non-progressive LTIRS model","volume":"66","author":"Devi","year":"2024","journal-title":"Knowledge and Information Systems"},{"key":"10.1016\/j.eswa.2026.131935_b0030","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1109\/TCSS.2022.3140779","article-title":"Modeling influencer marketing campaigns in social networks","volume":"10","author":"Doshi","year":"2023","journal-title":"IEEE Transactions on Computational Social Systems"},{"key":"10.1016\/j.eswa.2026.131935_b0035","doi-asserted-by":"crossref","first-page":"39","DOI":"10.2501\/jar-41-3-39-48","article-title":"Selecting celebrity endorsers: The practitioner\u2019s perspective","volume":"41","author":"Erdogan","year":"2001","journal-title":"Journal of advertising research"},{"key":"10.1016\/j.eswa.2026.131935_b0040","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1016\/j.physa.2016.06.050","article-title":"Effect of individual behavior on the interplay between awareness and disease spreading in multiplex networks","volume":"461","author":"Fan","year":"2016","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"key":"10.1016\/j.eswa.2026.131935_b0045","doi-asserted-by":"crossref","DOI":"10.1016\/j.engappai.2023.106719","article-title":"Modeling public opinion dissemination in a multilayer network with SEIR model based on real social networks","volume":"125","author":"Geng","year":"2023","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"10.1016\/j.eswa.2026.131935_b0050","unstructured":"Geyser. (2025). Influencer Rates: How Much Do Influencers Really Cost in 2025? In (Vol. 2025)."},{"key":"10.1016\/j.eswa.2026.131935_b0055","doi-asserted-by":"crossref","DOI":"10.1038\/s41598-019-46507-y","article-title":"Centrality in complex networks with overlapping community structure","volume":"9","author":"Ghalmane","year":"2019","journal-title":"Scientific Reports"},{"key":"10.1016\/j.eswa.2026.131935_b0060","doi-asserted-by":"crossref","unstructured":"Goyal, A., Lu, W., & Lakshmanan, L. (2011). CELF++: Optimizing the greedy algorithm for influence maximization in social networks (Vol. 47-48).","DOI":"10.1145\/1963192.1963217"},{"key":"10.1016\/j.eswa.2026.131935_b0065","first-page":"643","article-title":"Influence maximization on multiple social networks","volume":"39","author":"Guoliang","year":"2016","journal-title":"Chinese Journal of Computers"},{"key":"10.1016\/j.eswa.2026.131935_b0070","doi-asserted-by":"crossref","first-page":"4012","DOI":"10.1016\/j.physa.2012.02.033","article-title":"Identifying all-around nodes for spreading dynamics in complex networks","volume":"391","author":"Hou","year":"2012","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"key":"10.1016\/j.eswa.2026.131935_b0075","doi-asserted-by":"crossref","DOI":"10.3390\/e22040450","article-title":"Identifying Influencers in Social Networks","volume":"22","author":"Huang","year":"2020","journal-title":"Entropy"},{"key":"10.1016\/j.eswa.2026.131935_b0080","doi-asserted-by":"crossref","unstructured":"Hub, I. M. (2025). Influencer Marketing Benchmark Report 2025. In (Vol. 2025).","DOI":"10.69645\/AEBN4669"},{"key":"10.1016\/j.eswa.2026.131935_b0085","article-title":"A method to detect influencers in social networks based on the combination of amplification factors and content creation","volume":"17","author":"Huynh","year":"2022","journal-title":"PLoS One1"},{"key":"10.1016\/j.eswa.2026.131935_b0090","doi-asserted-by":"crossref","DOI":"10.1016\/j.physa.2021.126480","article-title":"An improved influence maximization method for social networks based on genetic algorithm","volume":"586","author":"Jabari Lotf","year":"2022","journal-title":"Physica A: Statistical Mechanics and its Applications"},{"key":"10.1016\/j.eswa.2026.131935_b0095","series-title":"Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining","first-page":"137","article-title":"Maximizing the spread of influence through a social network","author":"Kempe","year":"2003"},{"key":"10.1016\/j.eswa.2026.131935_b0100","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s41109-019-0150-3","article-title":"Influence spread in two-layer interdependent networks: Designed single-layer or random two-layer initial spreaders?","volume":"4","author":"Khamfroush","year":"2019","journal-title":"Applied Network Science"},{"key":"10.1016\/j.eswa.2026.131935_b0105","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1007\/s11747-021-00829-4","article-title":"Online influencer marketing","volume":"50","author":"Leung","year":"2022","journal-title":"Journal of the Academy of Marketing Science"},{"key":"10.1016\/j.eswa.2026.131935_b0110","doi-asserted-by":"crossref","DOI":"10.1016\/j.heliyon.2024.e40031","article-title":"Budget-aware local influence iterative algorithm for efficient influence maximization in social networks","volume":"10","author":"Li","year":"2024","journal-title":"Heliyon"},{"key":"10.1016\/j.eswa.2026.131935_b0115","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/j.ins.2016.12.027","article-title":"Clustering coefficients of large networks","volume":"382","author":"Li","year":"2017","journal-title":"Information Sciences"},{"key":"10.1016\/j.eswa.2026.131935_b0120","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.knosys.2015.03.026","article-title":"The node importance in actual complex networks based on a multi-attribute ranking method","volume":"84","author":"Liu","year":"2015","journal-title":"Knowledge-Based Systems"},{"key":"10.1016\/j.eswa.2026.131935_b0125","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2016.06.007","article-title":"Vital nodes identification in complex networks","volume":"650","author":"L\u00fc","year":"2016","journal-title":"Physics reports"},{"key":"10.1016\/j.eswa.2026.131935_b0130","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1287\/mnsc.2020.3899","article-title":"A framework for analyzing influencer marketing in social networks: Selection and scheduling of influencers","volume":"68","author":"Mallipeddi","year":"2022","journal-title":"Management Science"},{"key":"10.1016\/j.eswa.2026.131935_b0135","doi-asserted-by":"crossref","first-page":"127407","DOI":"10.1109\/ACCESS.2021.3112344","article-title":"Research on the dynamic multisocial networks influence maximization problem based on common users","volume":"9","author":"Meng","year":"2021","journal-title":"IEEE Access"},{"key":"10.1016\/j.eswa.2026.131935_b0140","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1007\/s40747-025-02070-w","article-title":"Personal brand value extraction method to identify micro-influencer for effective digital marketing","volume":"11","author":"Nguyen","year":"2025","journal-title":"Complex & Intelligent Systems"},{"key":"10.1016\/j.eswa.2026.131935_b0145","doi-asserted-by":"crossref","DOI":"10.1063\/5.0096740","article-title":"Two-step seeding strategy in multiplex networks with inter-layer conversion cost of influence","volume":"32","author":"Ni","year":"2022","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"key":"10.1016\/j.eswa.2026.131935_b0150","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.tre.2018.02.006","article-title":"A simulation\u2013optimization approach for a service-constrained multi-echelon distribution network","volume":"114","author":"Noordhoek","year":"2018","journal-title":"Transportation Research Part E: Logistics and Transportation Review"},{"key":"10.1016\/j.eswa.2026.131935_b0155","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2020.113183","article-title":"Evolutionary multiobjective optimization to target social network influentials in viral marketing","volume":"147","author":"Robles","year":"2020","journal-title":"Expert Systems with Applications"},{"key":"10.1016\/j.eswa.2026.131935_b0160","unstructured":"Rogers, E. M., Singhal, A., & Quinlan, M. M. (2014). Diffusion of innovations. In: An integrated approach to communication theory and research (pp. 432-448): Routledge."},{"key":"10.1016\/j.eswa.2026.131935_b0165","doi-asserted-by":"crossref","unstructured":"Romero, D. M., Galuba, W., Asur, S., & Huberman, B. A. (2011). Influence and passivity in social media. In: Proceedings of the 20th international conference companion on World wide web (pp. 113\u2013114). Hyderabad, India: Association for Computing Machinery.","DOI":"10.1145\/1963192.1963250"},{"key":"10.1016\/j.eswa.2026.131935_b0170","unstructured":"Santora, J. (2024). 35 Influencer Marketing Statistics Shaping 2024. In (Vol. 2024)."},{"key":"10.1016\/j.eswa.2026.131935_b0175","series-title":"Proceedings of the 2015 IEEE\/ACM International Conference on Advances in Social Networks Analysis and Mining 2015","first-page":"629","article-title":"Improving information spread through a scheduled seeding approach","author":"Sela","year":"2015"},{"key":"10.1016\/j.eswa.2026.131935_b0180","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.ejor.2015.03.008","article-title":"Innovation diffusion of repeat purchase products in a competitive market: An agent-based simulation approach","volume":"245","author":"Stummer","year":"2015","journal-title":"European Journal of Operational Research"},{"key":"10.1016\/j.eswa.2026.131935_b0185","doi-asserted-by":"crossref","first-page":"2919","DOI":"10.1007\/s10878-021-00815-0","article-title":"Measuring the influence and amplification of users on social network with unsupervised behaviors learning and efficient interaction-based knowledge graph","volume":"44","author":"Tran","year":"2022","journal-title":"Journal of Combinatorial Optimization"},{"key":"10.1016\/j.eswa.2026.131935_b0190","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1111\/ijcs.12647","article-title":"Social media influencer marketing: A systematic review, integrative framework and future research agenda","volume":"45","author":"Vrontis","year":"2021","journal-title":"International Journal of Consumer Studies"},{"key":"10.1016\/j.eswa.2026.131935_b0195","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2025.126649","article-title":"Multi-channel advertising budget allocation: A novel method using Q-learning and mutual learning-based artificial bee colony","volume":"271","author":"Wang","year":"2025","journal-title":"Expert Systems with Applications"},{"key":"10.1016\/j.eswa.2026.131935_b0200","doi-asserted-by":"crossref","DOI":"10.1016\/j.jocs.2022.101924","article-title":"A new centrality ranking method for multilayer networks","volume":"66","author":"Wang","year":"2023","journal-title":"Journal of Computational Science"},{"key":"10.1016\/j.eswa.2026.131935_b0205","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1109\/TEVC.2016.2555315","article-title":"Data-driven surrogate-assisted multiobjective evolutionary optimization of a trauma system","volume":"20","author":"Wang","year":"2016","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"10.1016\/j.eswa.2026.131935_b0210","series-title":"TwitterRank: finding topic-sensitive influential twitterers","first-page":"261","author":"Weng","year":"2010"},{"key":"10.1016\/j.eswa.2026.131935_b0215","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1287\/ijoc.2014.0626","article-title":"Optimal budget allocation across search advertising markets","volume":"27","author":"Yang","year":"2015","journal-title":"INFORMS Journal on Computing"},{"key":"10.1016\/j.eswa.2026.131935_b0220","series-title":"2016 IEEE 17th International Conference on Information Reuse and Integration (IRI)","first-page":"67","article-title":"Discover Tipping users for Cross Network Influencing (Invited Paper)","author":"Zhan","year":"2016"},{"key":"10.1016\/j.eswa.2026.131935_b0225","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1109\/TEVC.2021.3065707","article-title":"Surrogate-assisted evolutionary multitask genetic programming for dynamic flexible job shop scheduling","volume":"25","author":"Zhang","year":"2021","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"10.1016\/j.eswa.2026.131935_b0230","doi-asserted-by":"crossref","DOI":"10.1155\/2021\/5535923","article-title":"Sales disclosure and pricing policies in the presence of social learning","volume":"2021","author":"Zheng","year":"2021","journal-title":"Mathematical Problems in Engineering"},{"key":"10.1016\/j.eswa.2026.131935_b0235","first-page":"1157","article-title":"Classification and literature review on the integration of simulation and optimization in maritime logistics studies","volume":"53","author":"Zhou","year":"2021","journal-title":"IISE Transactions"}],"container-title":["Expert Systems with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0957417426008481?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0957417426008481?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T12:39:37Z","timestamp":1784896777000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0957417426008481"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":47,"alternative-id":["S0957417426008481"],"URL":"https:\/\/doi.org\/10.1016\/j.eswa.2026.131935","relation":{},"ISSN":["0957-4174"],"issn-type":[{"value":"0957-4174","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Optimal budget allocation and influencer scheduling for product promotion within multilayer social networks","name":"articletitle","label":"Article Title"},{"value":"Expert Systems with Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.eswa.2026.131935","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"131935"}}