Abstract-An adaptive particle swarm optimization (APSO) that features better search efficiency than classical particle swarm optimization (PSO) is presented. More importantly, it can perform a global search over the entire search space with faster convergence speed. The APSO consists of two main steps. First, by evaluating the population distribution and particle fitness, a real-time evolutionary state estimation procedure is performed to identify one of the following four defined evolutionary states, including exploration, exploitation, convergence, and jumping out in each generation. It enables the automatic control of inertia weight, acceleration coefficients, and other algorithmic parameters at run time to improve the search efficiency and convergence speed. Then, an elitist learning strategy is performed when the evolutionary state is classified as convergence state. The strategy will act on the globally best particle to jump out of the likely local optima. The APSO has comprehensively been evaluated on 12 unimodal and multimodal benchmark functions. The effects of parameter adaptation and elitist learning will be studied. Results show that APSO substantially enhances the performance of the PSO paradigm in terms of convergence speed, global optimality, solution accuracy, and algorithm reliability. As APSO introduces two new parameters to the PSO paradigm only, it does not introduce an additional design or implementation complexity. Index Terms-Adaptive particle swarm optimization (APSO), evolutionary computation, global optimization, particle swarm optimization (PSO).

Virtual machine placement (VMP) and energy efficiency are significant topics in cloud computing research. In this paper, evolutionary computing is applied to VMP to minimize the number of active physical servers, so as to schedule underutilized servers to save energy. Inspired by the promising performance of the ant colony system (ACS) algorithm for combinatorial problems, an ACS-based approach is developed to achieve the VMP goal. Coupled with order exchange and migration (OEM) local search techniques, the resultant algorithm is termed an OEMACS. It effectively minimizes the number of active servers used for the assignment of virtual machines (VMs) from a global optimization perspective through a novel strategy for pheromone deposition which guides the artificial ants toward promising solutions that group candidate VMs together. The OEMACS is applied to a variety of VMP problems with differing VM sizes in cloud environments of homogenous and heterogeneous servers. The results show that the OEMACS generally outperforms conventional heuristic and other evolutionary-based approaches, especially on VMP with bottleneck resource characteristics, and offers significant savings of energy and more efficient use of different resources. Index Terms-Ant colony system (ACS), cloud computing, virtual machine placement (VMP). I. INTRODUCTION C LOUD computing is a large-scale distributed computing paradigm, driven by an increasing demand for various

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Abstract-An adaptive particle swarm optimization (APSO) that features better search efficiency than classical particle swarm optimization (PSO) is presented. More importantly, it can perform a global search over the entire search space with faster convergence speed. The APSO consists of two main steps. First, by evaluating the population distribution and particle fitness, a real-time evolutionary state estimation procedure is performed to identify one of the following four defined evolutionary states, including exploration, exploitation, convergence, and jumping out in each generation. It enables the automatic control of inertia weight, acceleration coefficients, and other algorithmic parameters at run time to improve the search efficiency and convergence speed. Then, an elitist learning strategy is performed when the evolutionary state is classified as convergence state. The strategy will act on the globally best particle to jump out of the likely local optima. The APSO has comprehensively been evaluated on 12 unimodal and multimodal benchmark functions. The effects of parameter adaptation and elitist learning will be studied. Results show that APSO substantially enhances the performance of the PSO paradigm in terms of convergence speed, global optimality, solution accuracy, and algorithm reliability. As APSO introduces two new parameters to the PSO paradigm only, it does not introduce an additional design or implementation complexity. Index Terms-Adaptive particle swarm optimization (APSO), evolutionary computation, global optimization, particle swarm optimization (PSO).

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