基于混合量子进化计算的混沌系统参数估计

Hybrid quantum-inspired evolutionary algorithm-based parameter estimation for chaotic systems

混沌系统参数估计本质上是一多维参数优化问题.为精确估计混沌系统的未知参数,本文提出一种混合量子进化算法(HQEA)用于求解该优化问题,该方法采用实数量子角形式表示染色体,用量子比特的概率作为个体的当前位置信息;提出由差分进化计算更新量子位置状态的量子差分进化算法(QDE),并将其与实数编码量子进化算法(RQEA)相融合,以便令算法在解空间的全局探索和局部开发能力之间取得平衡.算法还引入量子非门算子,对当前最佳个体中按某个概率选中的量子比特位,进行变换操作,以便增强算法跳出局部最优解的能力.基准函数测试表明混合算法的全局搜索能力及可靠性都有很大改善.通过Lorenz混沌系统进行数值仿真,结果表明了该混合算法的有效性.

Parameter estimation of chaotic systems is essentially a multidimensional optimization problem. To estimate the unknown parameters of chaotic systems precisely, we present an effective hybrid quantum-inspired evolutionary algo- rithm （HQEA）, in which the real-valued quantum angle is used to express the Q-bits of chromosome, and the probability of each Q-bit is considered the position information of the chromosome. Combining the quantum differential evolutionary algorithm （QDE） which uses differential evolution to update the state of Q-bits with the real-coded quantum evolutionary algorithm （RQEA） which employs quantum rotation gate to update the state of Q-bits, we make a balance between the global exploration and the local exploitation. In addition, the HQEA performs the quantum non-gate operation in which the Q-bits selected from the current best chromosome with a certain probability are transformed to get rid of the premature local optimum. The experimental results of benchmark function tests show that the HQEA algorithm greatly improves the global optimization performance as well as the reliability performance. Numerical simulation results of the Lorenz system also demonstrate its effectiveness.