Statistical Stability Analysis for Particle Swarm Optimization Dynamics with Random Coefficients
Statistical Stability Analysis for Particle Swarm Optimization Dynamics with Random Coefficients
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DOI：
10.1541/ieejeiss.131.1020
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发表时间：
2011-05
影响因子：
--
通讯作者：
祐司 小熊;相吉 英太郎
中科院分区：
文献类型：
--
作者：
祐司 小熊;相吉 英太郎
粒子群优化（PSO）是一种具有启发式的全局优化方法，由于其算法简单、搜索能力强而受到人们的广泛关注。粒子群优化算法的更新公式中引入了随机数作为参数的系数，增强了粒子群优化算法搜索全局最优解的多样化能力。然而，随机性使得搜索点的稳定性难以用数学分析，并且用户需要通过尝试和错误来调整参数值。本文从数学上分析了粒子群优化算法随机动力学的稳定性，并给出了考虑随机性的精确稳定性条件，提出了一种新的评价粒子群优化算法动力学稳定性的指标--统计特征值。通过简单算例的数值模拟验证了该指标在稳定性判别中的准确性和有效性。
Particle Swarm Optimization (PSO), a meta-heuristic global optimization method, has attracted special interest for its simple algorithm and high searching ability. The updating formula of PSO involves coefficients with random numbers as parameters to enhance diversification ability in searching for the global optimum. However, the randomness makes stability of the searching points difficult to be analyzed mathematically, and the users need to adjust the parameter values by trial and error. In this paper, stability of the stochastic dynamics of PSO is analyzed mathematically and exact stability condition taking the randomness into consideration is presented with an index “statistical eigenvalue”, which is a new concept to evaluate the degree of the stability of PSO dynamics. Accuracy and effectiveness of the proposed stability discrimination using the presented index are certified in numerical simulation for simple examples.