Abstract: To reduce the possibility of falling into the local optima during the search process of the original Particle Swarm Optimization (PSO) and avoid destroying the population diversity, a hybrid two-norm particle swarm optimization algorithm with crossover term, namely HTPSO, was proposed. Firstly, the two-norm was employed to measure the Euclidean distance between current particle and its individual history best one. Then, the Euclidean distance was incorporated into the velocity updating formula in order to affect the influence of social term on particles' velocity, and inertia weight was randomly distributed in accordance with certain rules. Based on these operations, what's more, HTPSO was simplified and the crossover operator in the Differential Evolution (DE) algorithm was incorporated into the algorithm, which enables each particle to intersect with its individual history best one under a certain probability. In order to verify the excellent performance of HTPSO, four improved PSOs were introduced, including Particle Swarm Optimization algorithm for improved weight using Sine function (SinPSO), Self-adjusted Particle Swarm Optimization algorithm (SelPSO), Mean Particle Swarm Optimization algorithm based on Adaptive inertia Weight (MAWPSO) and Simple Particle Swarm Optimization algorithm (SPSO). The optima of eight commonly used benchmark functions in different dimensions were compared, the results of five algorithms were analyzed by T-test, success rate and average iteration times. Compared with the contrast algorithms, HTPSO has strong convergence, and the particles' movements are very flexible.

Key words: Particle Swarm Optimization algorithm (PSO), Differential Evolution (DE) algorithm, swarm intelligence, two-norm, benchmark function

摘要： 针对原始粒子群优化算法（PSO）在搜索过程中容易陷入局部最优点的问题，并尽量避免破坏种群多样性，提出一种含交叉项的混合二范数粒子群优化算法HTPSO。首先，利用二范数原理计算当前粒子与个体历史最优粒子间的欧氏距离；其次，将欧氏距离引入速度迭代公式以影响社交项对粒子速度的作用，并按照一定规律随机分布惯性权重；最后，在此基础上简化粒子群算法，并将差分进化（DE）算法中的交叉算子融入该算法中，使粒子能在一定概率下与个体历史最优粒子交叉。为了验证HTPSO的性能，与利用正弦函数改进惯性权重的粒子群优化算法（SinPSO）、自适应粒子群优化算法（SelPSO）、基于自适应惯性权重的均值粒子群优化算法（MAWPSO）和简化粒子群优化算法（SPSO）在不同维度下解决8个常用基准函数，并根据T-test、成功率和平均迭代次数分析了各算法的优化结果。实验结果表明，HTPSO具有较优秀的收敛能力，且粒子运动非常灵活。

关键词: 粒子群优化算法, 差分进化算法, 群体智能, 二范数, 基准函数