@article{scholars16167,
           title = {Chaotic Simulator for Bilevel Optimization of Virtual Machine Placements in Cloud Computing},
          number = {4},
          volume = {10},
            note = {cited By 5},
             doi = {10.1007/s40305-020-00326-5},
         journal = {Journal of the Operations Research Society of China},
       publisher = {Springer},
           pages = {703--723},
            year = {2022},
        abstract = {The drastic increase in engineering system complexity has spurred the development of highly efficient optimization techniques. Many real-world optimization problems have been identified as bilevel/multilevel as well as multiobjective. The primary aim of this work is to present a framework to tackle the bilevel virtual machine (VM) placement problem in cloud systems. This is done using the coupled map lattice (CML) approach in conjunction with the Stackelberg game theory and weighted-sum frameworks. The VM placement problem was modified from the original multiobjective (MO) problem to an MO bilevel formulation to make it more realistic albeit more complicated. Additionally comparative analysis on the performance of the CML approach was carried out against the particle swarm optimization method. A new bilevel metric called the cascaded hypervolume indicator is introduced and applied to measure the dominance of the solutions produced by both methods. Detailed analysis on the computational results is presented. {\^A}{\copyright} 2021, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature.},
        keywords = {Cloud computing; Crystal lattices; Lattice theory; Multiobjective optimization; Network security; Particle swarm optimization (PSO); Virtual machine, Bilevel; Bilevel multiobjective; Cascaded hypervolume indicator; Coupled map lattice; Coupled map lattices; Hypervolume indicators; Multi objective; Particle swarm; Particle swarm optimization; Stackelberg game theory; Stackelberg Games; Swarm optimization; Virtual machine placements, Game theory},
             url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85100778457&doi=10.1007\%2fs40305-020-00326-5&partnerID=40&md5=2afee8b1aba1f605012bfa9228243f11},
            issn = {2194668X},
          author = {Ganesan, T. and Vasant, P. and Litvinchev, I.}
}