求解大规模优化问题的改进正弦余弦算法

Improved sine cosine algorithm for large-scale optimization problems

针对正弦余弦算法(sine cosine algorithm,SCA)在求解大规模优化问题时收敛精度低、收敛速度慢和易陷入“维数灾难”的不足,提出一种带Lévy飞行的正弦余弦算法(sine cosine algorithm with Lévy flight,SCAL).SCAL算法通过将Lévy飞行分布与正弦余弦种群个体位置向量进行对应元素相乘运算,使Lévy飞行分布的特征和信息融入正弦余弦种群个体信息中,使其拥有Lévy飞行随机游走的特性,增强了个体局部开发和逃离局部极值的能力;采用基于空间距离的非线性参数调整方法,平衡算法的局部开发和全局搜索,提高了算法的收敛速度.在14个经典测试函数上,维度分别为100、1 000和5 000维时,与SCA、花授粉算法(flower pollination algorithm,FPA)、粒子群优化(particle swarm optimization,PSO)算法、麻雀搜索算法(sparrow search algorithm,SSA)和鲸鱼优化算法(whale optimization algorithm,WOA)5种群体智能算法进行仿真对比实验.结果表明,SCAL算法在收敛精度、收敛速度和鲁棒性上较5种群体智能算法优势明显.与解决大规模优化问题的改进狼群算法(improved wolf pack algorithm,IWPA)、改进花授粉算法(improved flower pollination algorithm,IFPA)、鲸鱼算法的两种改进版本IWOA(improved whale optimization algorithm)和MWOA(modified whale optimization algorithm)进行比较,发现SCAL的整体寻优结果优于对比算法,在求解大规模优化问题上具有显著优势和竞争力.

Aiming at the shortcomings of the sine cosine algorithm(SCA) in solving the large-scale optimization problems, such as low accuracy, slow convergence speed, and being easy to fall into the dimension disaster, we propose an sine cosine algorithm with Lévy flight(SCAL). By using the element-by-element multiplication of the Lévy flight distribution with the individual position vector of sine and cosine population, the characteristics and information of Lévy flight distribution are integrated into the individual information, so that it can possess the characteristic of random walk of Lévy flight and enhances the ability of local exploitation to escape from local extremum. A novel nonlinear parameter adjustment method based on spatial distance is adopted to balance the local exploitation and global exploration, which improves the convergence speed of the algorithm. On 14 classic test functions with dimensions of 100, 1 000 and 5 000 respectively, SCAL is compared with five swarm intelligence algorithms including SCA, flower pollination algorithm(FPA), particle swarm optimization(PSO) algorithm, sparrow search algorithm(SSA) and whale optimization algorithm(WOA). The experimental results indicate that SCAL has a significant advantage over the five swarm intelligence algorithms in terms of convergence accuracy, convergence speed and robustness. Compared with the improved wolf pack algorithm(IWPA), the improved flower pollination algorithm(IFPA), the improved whale optimization algorithm(IWOA), and the modified whale optimization algorithm(MWOA), which are suitable for solving large scale optimization problems, it is found that the overall optimization result of SCAL is better than the comparison algorithms and thus demonstrate that the proposed algorithm has the obvious advantages and competitiveness for solving large-scale optimization problems.