The optimization of high-dimensional functions is an important problem in both science and engineering. Particle swarm optimization is a technique often used for computing the global optimum of a multivariable function. In this paper, we develop a new particle swarm optimization algorithm that can accurately compute the optimal value of a high-dimensional function. The iteration process of the algorithm is comprised of a number of large iteration steps, where a large iteration step consists of two stages. In the first stage, an expansion procedure is utilized to effectively explore the high-dimensional variable space. In the second stage, the traditional particle swarm optimization algorithm is employed to compute the global optimal value of the function. A translation step is applied to each particle in the swarm after a large iteration step is completed to start a new large iteration step. Based on this technique, the variable space of a function can be extensively explored. Our analysis and testing results on high-dimensional benchmark functions show that this algorithm can achieve optimization results with significantly improved accuracy, compared with traditional particle swarm optimization algorithms and a few other state-of-the-art optimization algorithms based on particle swarm optimization.

中文翻译：

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用高效粒子群算法优化高维函数

高维函数的优化是科学和工程学中的重要问题。粒子群优化是一种经常用于计算多变量函数的全局最优的技术。在本文中，我们开发了一种新的粒子群优化算法，可以准确地计算高维函数的最优值。该算法的迭代过程由多个大迭代步骤组成，其中大迭代步骤由两个阶段组成。在第一阶段，利用扩展程序有效地探索高维变量空间。在第二阶段，采用传统的粒子群优化算法来计算函数的全局最优值。在完成较大的迭代步骤后，将平移步骤应用于群集中的每个粒子，以开始新的较大的迭代步骤。基于此技术，可以广泛地探索函数的可变空间。我们对高维基准函数的分析和测试结果表明，与传统的粒子群优化算法和其他一些基于粒子群优化的最新优化算法相比，该算法可以显着提高精度，从而获得优化结果。