Optimization of free surface measurement path based on improved differential evolution algorithm
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摘要: 为解决传统差分进化算法存在收敛速度慢、易陷入局部最优解以及由于个体选择的随机性导致求优稳定性差的问题，文章通过引入多重启动策略，多次运行算法并使用不同的随机种子，增加算法对空间的探索性，在一定程度上解决算法易陷入局部最优解问题；通过使用新的突变策略，在求优稳定性提高了约10%；通过引入参数自适应调节机制，动态地调整算法参数的取值，使收敛速度提高了约10%，并提高了算法的鲁棒性。Abstract: To address the issues of slow convergence and susceptibility to local optima in traditional differential evolution algorithms, as well as the poor optimization stability caused by the randomness in individual selection, a multi-restart strategy is introduced in this paper. The algorithm is executed multiple times with different random seeds, increasing the algorithm’s spatial exploratory capability and, to a certain extent, resolving the problem of easily falling into local optima. Through the incorporation of a new mutation strategy, the optimization stability is improved by approximately 10%. Additionally, a parameter self-adaptive tuning mechanism is introduced, dynamically adjusting the algorithm’s parameter values, resulting in an approximately 10% increase in convergence speed and enhancing the algorithm’s robustness.
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图 4 使用$ \mathit{D}\mathit{E}/\mathit{a}\mathit{v}\mathit{e}\mathit{r}\mathit{a}\mathit{g}\mathit{e}/2 $策略生成的优化路径和优化过程曲线
表 1 三维坐标点
序号 x y z 1 1.23 2.82 18.06 2 0.86 3.27 19.45 3 0.48 3.11 16.02 4 1.98 3.49 29.53 5 0.08 3.55 17.57 6 1.31 2.14 13.58 7 1.90 3.19 25.94 8 0.28 2.95 13.84 9 0.18 3.41 16.91 10 0.97 3.47 21.83 
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表 2 仿真对比实验数据
策略类别 $ DE/average/2 $ 1 2 3 路径长度/mm 135.2 147.19 143.76 优化时间/s 74 76 77 策略类别 新策略 1 2 3 路径长度/mm 126.75 128.73 124.23 优化时间/s 65 68 70
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表 3 实际检测实验对比数据表
数据
算法优化路径
长度/mm优化过程
耗时/s测量机检测
耗时/s“$ DE/average/2 $”策略 150.34 72 327 新策略 124.58 66 295
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