仝秋娟 李萌 趙豈
摘 ?要: 針對(duì)粒子群算法存在收斂速度慢、收斂精度低且易收斂到局部極值的問(wèn)題,提出一種基于分類思想的粒子群改進(jìn)算法。該算法將粒子適度值和適度值均值做差與適度值標(biāo)準(zhǔn)差進(jìn)行比較,從而將粒子所在區(qū)域劃分為拒絕域、親近域、合理域。根據(jù)不同區(qū)域中粒子的特點(diǎn)選取不同慣性權(quán)重和學(xué)習(xí)因子,使粒子高效地選擇自身經(jīng)驗(yàn)或種群經(jīng)驗(yàn),合理增強(qiáng)或減弱粒子全局搜索能力和局部搜索能力。數(shù)值實(shí)驗(yàn)結(jié)果表明,與其他粒子群改進(jìn)算法相比,新的分類粒子群算法有效加快了粒子的收斂速度,提高了算法的收斂精度,有效改善了算法尋優(yōu)性能。
關(guān)鍵詞: 粒子群優(yōu)化; 參數(shù)改進(jìn); 適度值; 適度值均值; 適度值標(biāo)準(zhǔn)差; 粒子分類; 有效經(jīng)驗(yàn)
中圖分類號(hào): TN911.1?34; TP18 ? ? ? ? ? ? ? ? ? ? 文獻(xiàn)標(biāo)識(shí)碼: A ? ? ? ? ? ? ? ? ? 文章編號(hào): 1004?373X(2019)19?0011?04
Abstract: In order to solve the problems of slow convergence speed, low convergence precision and easy convergence to local extremum, an improved particle swarm optimization algorithm based on classification is proposed. The difference between the moderate value and the mean of moderate value is compared with the standard deviation of moderate value in this algorithm, then the region where the particles are located is divided into rejection domain, close proximity domain, and reasonable domain. According to the characteristics of particles in different regions, different inertia weights and learning factors are selected to ensure that the particles can efficiently select their own experience or population experience, and reasonably enhance or weaken the global search ability and the local search ability of the particles. The numerical results show that, in comparison with other particle swarm optimization algorithms, the proposed particle swarm optimization algorithm can more effectively accelerate the convergence speed of particles, and improve the convergence precision and optimization performance of the algorithm.
Keywords: particle swarm optimization; parameter improvement; moderate value; mean of the moderate value; standard deviation of moderate value; particle classification; effective experience
粒子群優(yōu)化算法(Particle Swarm Optimization,PSO)是受到鳥(niǎo)魚(yú)群搜索食物策略的啟發(fā)而提出的一種群智能優(yōu)化算法[1]。它以隨機(jī)解為出發(fā)點(diǎn),用適度值評(píng)價(jià)解的優(yōu)劣,通過(guò)迭代尋找最優(yōu)解。相比其他智能算法,PSO算法設(shè)置參數(shù)少、迭代快、易理解、工程上易實(shí)現(xiàn)。目前PSO算法在函數(shù)優(yōu)化[2]、神經(jīng)網(wǎng)絡(luò)訓(xùn)練[3]、圖像處理[4]以及其他工程領(lǐng)域都得到了廣泛應(yīng)用。但該算法沒(méi)有嚴(yán)格的理論指導(dǎo),收斂精度低、易收斂到局部極值。對(duì)此,學(xué)者們提出各種改進(jìn)算法,有基于模式結(jié)構(gòu)的改進(jìn)、基于種群多樣性的改進(jìn)、基于參數(shù)改進(jìn)等[5?7]。其中,對(duì)算法參數(shù)的改進(jìn)是一個(gè)重要方向。文獻(xiàn)[8]先將慣性權(quán)重系數(shù)引入粒子速度更新公式中,后又加以改進(jìn),使慣性權(quán)重系數(shù)線性遞減[9],有效加快了算法收斂速度。文獻(xiàn)[10]提出基于時(shí)間變化的學(xué)習(xí)因子的改進(jìn),動(dòng)態(tài)調(diào)節(jié)前后期粒子的搜索策略,加快了算法的收斂速度,但在多峰函數(shù)中極易陷入局部最優(yōu)。文獻(xiàn)[11]提出一種用正弦函數(shù)調(diào)節(jié)慣性權(quán)重的改進(jìn)算法,提高了算法的收斂速度。但是這些方法在收斂精度上依然有所欠缺。
綜上所述,無(wú)論是在求解單峰函數(shù)還是復(fù)雜的多峰函數(shù),基于分類思想的改進(jìn)算法在收斂速度和收斂精度上整體優(yōu)于另外三種算法。
本文提出一種基于分類思想的粒子群優(yōu)化算法,改變了傳統(tǒng)算法中粒子采取統(tǒng)一迭代公式的做法,針對(duì)不同區(qū)域的粒子,利用不同的慣性權(quán)重系數(shù)和學(xué)習(xí)因子對(duì)粒子的全局尋優(yōu)能力和局部尋優(yōu)能力進(jìn)行合理地調(diào)整。實(shí)驗(yàn)結(jié)果表明,相比一些傳統(tǒng)的算法,新算法不僅收斂速度有所提升,收斂精度也有所提高,算法尋優(yōu)性能明顯改善。將此算法應(yīng)用到其他領(lǐng)域是下一步的研究方向。
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