基于分数阶位置状态的量子粒子群算法

An Improved Quantum Swarm Optimization with Fractional-order Position

摘要:

由量子力学的概念和粒子群优化算法的结合，量子行为粒子优化算法作为粒子群算法的一个变种，具有更好的全局搜索能力.为了提高量子粒子算法的全局搜索能力，结合分数阶微积分的概念，本文提出了一种新的算法.该算法将分数阶微积分中常用的GL定义引入了量子粒子算法的更新迭代公式中，利用分数阶微积分的长时记忆特性，通过记忆量子粒子在更新迭代过程中的历史位置和历史信息，增强算法的收敛速度和收敛精度.为了全面评估算法的基本性能，本文进行了一些关于基本测试函数的功能测试.通过对于不同阶次的分数阶量子粒子算法的对比实验和与其他粒子群改进算法的对比实验，实验结果表明，该算法具有更高的收敛精度.

Abstract:

Motivated by concepts in quantum mechanics and particle swarm optimization (PSO), quantumbehaved particle swarm optimization was proposed as a variant of PSO with better global search capability. This paper proposes a novel method for enhancing the global search capability of PSO and guiding its search with fractional calculus concepts. With the commonly used definitions of fractional differential known as GrünwaldLetnikov(GL), the authors introduce its discrete expression into the position update in QPSO to improve its convergence speed and accuracy. Some empirical studies on popular benchmark functions are performed in order to make a full evaluation on performance and comparison between standard QPSO and QPSO with different fractionalorder. The new algorithm, named fractionalorder Quantum particle swarm optimization, shows to perform well in finding optimal solutions with much higher convergence accuracy in many optimization problems.