{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T22:33:21Z","timestamp":1777415601434,"version":"3.51.4"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T00:00:00Z","timestamp":1747094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Laboratory of Ethnic Language Intelligent Analysis and Security Governance, Ministry of Education","award":["OPC-202401"],"award-info":[{"award-number":["OPC-202401"]}]},{"name":"Key Laboratory of Ethnic Language Intelligent Analysis and Security Governance, Ministry of Education","award":["BATLAB202403"],"award-info":[{"award-number":["BATLAB202403"]}]},{"name":"Foundation of Key Laboratory of Big Data &amp; Artificial Intelligence in Transportation (Beijing Jiaotong University), Ministry of Education","award":["OPC-202401"],"award-info":[{"award-number":["OPC-202401"]}]},{"name":"Foundation of Key Laboratory of Big Data &amp; Artificial Intelligence in Transportation (Beijing Jiaotong University), Ministry of Education","award":["BATLAB202403"],"award-info":[{"award-number":["BATLAB202403"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the continuous expansion of application scenarios for cloud computing, large-scale service deployments in cloud data centers are accompanied by a significant increase in resource consumption. Virtual machines (VMs) in data centers are allocated to physical machines (PMs) and require the resources provided by PMs to run various services. Apparently, a simple solution to minimize energy consumption is to allocate VMs as compactly as possible. However, the above virtual machine placement (VMP) strategy may lead to system performance degradation and service failures due to imbalanced resource load, thereby reducing the robustness of the cloud data center. Therefore, an effective VMP solution that comprehensively considers both energy consumption and other performance metrics in data centers is urgently needed. In this paper, we first construct a multi-objective VMP model aiming to simultaneously optimize energy consumption, resource utilization, load balancing, and system robustness, and we then build a joint optimization function with resource constraints. Subsequently, a novel energy-aware Cauchy particle swarm optimization (EA-CPSO) algorithm is proposed, which implements particle asymmetric disturbances and an energy-efficient population iteration strategy, aiming to minimize the value of the joint optimization function. Finally, our extensive experiments demonstrated that EA-CPSO outperforms existing methods.<\/jats:p>","DOI":"10.3390\/sym17050742","type":"journal-article","created":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T09:26:48Z","timestamp":1747128408000},"page":"742","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multi-Objective Cauchy Particle Swarm Optimization for Energy-Aware Virtual Machine Placement in Cloud Datacenters"],"prefix":"10.3390","volume":"17","author":[{"given":"Xuan","family":"Liu","sequence":"first","affiliation":[{"name":"Key Laboratory of Ethnic Language Intelligent Analysis and Security Governance of MOE, Minzu University of China, Beijing 100081, China"},{"name":"Key Laboratory of Big Data & Artificial Intelligence in Transportation, Ministry of Education (Beijing Jiaotong University), Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chenyan","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Ethnic Language Intelligent Analysis and Security Governance of MOE, Minzu University of China, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shan","family":"Jiang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Ethnic Language Intelligent Analysis and Security Governance of MOE, Minzu University of China, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6766-0703","authenticated-orcid":false,"given":"Yutong","family":"Gao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Ethnic Language Intelligent Analysis and Security Governance of MOE, Minzu University of China, Beijing 100081, China"},{"name":"Key Laboratory of Big Data & Artificial Intelligence in Transportation, Ministry of Education (Beijing Jiaotong University), Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"family":"Chaomurilige","sequence":"additional","affiliation":[{"name":"Key Laboratory of Ethnic Language Intelligent Analysis and Security Governance of MOE, Minzu University of China, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bo","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Computer Science (National Pilot Software Engineering School), Beijing University of Posts and Telecommunications, Beijing 100081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Al Hwaitat, A.K., and Fakhouri, H.N. 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