变分布的量子行为粒子群优化算法求解工程约束优化问题

针对工程形状设计领域中带有多个约束条件的非线性设计优化问题,提出了一种自适应的基于高斯分布的量子行为粒子群优化(AG-QPSO)算法。通过自适应地调整高斯分布,AG-QPSO算法能够在搜索的初始阶段有很强的全局搜索能力,随着搜索过程的进行,算法的局部搜索能力逐渐增强,从而满足了算法在搜索过程不同阶段的需要。为了验证算法的有效性,在压力容器和张弦设计问题这两个工程约束优化问题上进行50轮独立实验。实验结果表明,在满足所有约束条件的情况下,AG-QPSO算法在压力容器设计问题上取得了5890.9315的平均解和5885.3328的最优解,在张弦设计问题上取得了0.01096的平均解和0.01096的最优解,远优于标准粒子群优化(PSO)算法、具有量子行为的粒子群优化(QPSO)算法和高斯量子行为粒子群(G-QPSO)算法等现有的算法的结果,同时AG-QPSO算法取得的结果的方差较小,说明该算法具有很好的鲁棒性。

Adaptive distribution based quantum-behaved particle swarm optimization algorithm for engineering constrained optimization problem

Aiming at the nonlinear design optimization problems with multiple constraints in the field of engineering shape design, an Adaptive Gaussian Quantum-behaved Particle Swarm Optimization (AG-QPSO) algorithm was proposed. By adjusting the Gaussian distribution adaptively, AG-QPSO algorithm was able to have strong global search ability at the initial stage of search process, and with the search process continued, the algorithm was able to have stronger local search ability, so as to meet the demands of the algorithm at different stages of the search process. In order to verify the effectiveness of the algorithm, 50 rounds of independent experiments were carried out on the two engineering constraint optimization problems: pressure vessel design and tension string design. The experimental results show that AG-QPSO algorithm achieves the average result of 5 890.931 5 and the optimal result of 5 885.332 8 on the pressure vessel design problem, and achieves the average result of 0.010 96 and the optimal result of 0.010 96 on the tension string design problem, which are better than the results of the existing algorithms such as the standard Particle Swarm Optimization (PSO) algorithm, Quantum Particle Swarm Optimization (QPSO) algorithm and Gaussian Quantum-behaved Particle Swarm Optimization (G-QPSO) algorithm. At the same time, the small variance of the results obtained by AG-QPSO algorithm indicates that the algorithm is very robust.