一种改进的量子遗传算法及其应用

An Improved Quantum Genetic Algorithm and Its Application

基于量子位测量的二进制量子遗传算法,在用于连续问题优化时,频繁的解码运算会降低优化效率。为解决该问题,提出一种改进的量子遗传算法。基于Bloch球面建立搜索机制,使用量子位描述个体,采用泡利矩阵建立旋转轴,通过量子位在Bloch球面上的绕轴旋转实现进化搜索,利用Hadamard门实现个体变异,以避免早熟收敛,使当前量子位沿着Bloch球面上的大圆逼近目标量子位。实例结果表明,该算法在经历大约26步迭代后,绝对误差积分指标值最小为4.122,优化能力优于基于量子位Bloch坐标的量子遗传算法和带精英保留策略的遗传算法。

Due to frequent decoding operations, the efficiency of optimization is severely reduced when the binary Quanm Genetic Algorithm（QGA） based on qubits measure is applied to the continuous space optimization. To solve this problem, an improved QGA is proposed in this paper. In this algorithm, the search mechanism is built based on Bloch sphere. The individuals are expressed with qubits, the axis of revolution is established with Pauli matrix, and the evolution search is realized with the rotation of qubits in Bloch sphere. In order to avoid premature convergence, the mutation of individuals is achieved with Hadamard gates. Such rotation can make the current qubits approximate the target qubits along with the biggest circle on the Bloch sphere. Example results show that the Integral Time Absolute Error（ITAE） value of this algorithm can meet minimum 4.122 after about 26 step iteration, optimization ability is better than the QGA based on quantum bits Bloch coordinates and Genetic Algorithm（GA） with elite reserving strategy.