Prestress Optimization of Suspended Domes with Plant Growth Simulation Algorithm Based on Multi-Mechanism Fusion
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摘要:
针对模拟植物生长算法(PGSA)以固定步长搜索难以收敛于全局最优解、对初始生长点选取依赖性强和生长空间巨大的局限性，提出自适应变步长搜索、高斯扰动变异和生长空间筛选3种机制的新策略，建立基于多机制融合的模拟植物生长算法(多机制融合PGSA)，进一步采用多机制融合PGSA对弦支穹顶结构进行预应力优化，并与其他优化算法进行对比. 结果表明：与原PGSA相比，引入自适应变步长搜索机制，可避免算法陷入局部最优解，引入高斯扰动变异机制，可解决由于初始生长点的选取不当而造成优化结果不佳的问题，引入生长空间筛选机制，可在算法收敛后有效终止生长，显著缩小生长空间(降幅最大达97.64%)；与其他优化算法相比，多机制融合PGSA的迭代次数最少(仅为45次)，且优化得到的支座平均水平径向反力绝对值最小(仅为0.004 kN)，验证了该算法的适用性.
Abstract:To address the limitations of difficult convergence to the global optimal solution with fixed step search, strong dependence on the selection of initial growth point, and huge growth space for the plant growth simulation algorithm (PGSA), a new strategy for search mechanism of adaptive variable step, Gauss perturbation mutation mechanism, and screening mechanism of growth space was proposed. On this basis, the PGSA based on multi-mechanism fusion (multi-mechanism fusion PGSA) was established. The prestress optimization of suspended domes was further carried out by using the multi-mechanism fusion PGSA and compared with other algorithms. The results show that compared with the original PGSA, the introduction of search mechanism of adaptive variable step can avoid the algorithm falling into local optimal solutions; the introduction of Gauss perturbation mutation mechanism can solve the problem of poor optimization results caused by the improper selection of initial growth points, and the introduction of screening mechanism of growth space can effectively terminate the growth after the algorithm converges, thus significantly reducing the growth space by 97.64%. The number of iterations of multi-mechanism fusion PGSA is the smallest (only 45), and the absolute value of the average horizontal radial reaction of supports after optimization is minimal (only 0.004 kN) in comparison with other algorithms. Therefore, the applicability of this algorithm is verified.
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图 3 仅引入自适应变步长搜索机制的PGSA优化过程
Figure 3. PGSA optimization process introducing searching mechanism of adaptive variable step only
图 4 仅引入高斯扰动变异机制的PGSA优化过程
Figure 4. PGSA optimization process introducing Gauss perturbation mutation mechanism only
图 5 引入生长空间筛选机制的PGSA优化过程
Figure 5. PGSA optimization process introducing screening mechanism of growth space
表 1 仅引入自适应变步长搜索机制的PGSA优化结果
Table 1. PGSA optimization results introducing searching mechanism of adaptive variable step only
算法 收敛生长次数/次 优化结果 寻优耗时/s 生长空间 O 不收敛 18.00 60.742 6012 × 3A 7 0 301.199 24562 × 3注：算法O、A分别对应于图3中的原PGSA、自适应变步长PGSA 
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表 2 仅引入高斯扰动变异机制的PGSA优化结果
Table 2. PGSA optimization results introducing Gauss perturbation mutation mechanism only
算法 初始生长点 收敛生长次数/次 优化结果 寻优耗时/s 生长空间 O $ {x_j} = 3.6 $ 不收敛 18.00 60.742 6012 × 3B1 $ {x_j} = 3.6 $ 15 0 658.209 28472 × 3B2 $ {x_j} = 3.0 $ 14 0 681.205 29081 × 3B3 $ {x_j} = 2.6 $ 14 0 849.400 28687 × 3B4 $ {x_j} = - 3.6 $ 16 0 601.005 28286 × 3注：算法B1～B4分别对应于图4中的高斯扰动变异PGSA1～PGSA4
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表 3 引入生长空间筛选机制的PGSA优化结果
Table 3. PGSA optimization results introducing screening mechanism of growth space
算法 收敛生长次数 优化结果 寻优耗时/s 生长空间 O 不收敛 18.00 60.742 6012 × 3C 265 0 2.767 746 × 3 C + A 8 0 0.051 142 × 3 C + B 11 0 0.244 533 × 3 注：算法C、C + A和C + B分别对应于图5中的生长空间筛选PGSA、生长空间筛选 + 自适应变步长PGSA和生长空间筛选 + 高斯扰动变异PGSA
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表 4 多机制融合PGSA优化结果
Table 4. Optimization results of multi-mechanism fusion PGSA
算法 收敛生长次数/次 寻优效果 寻优耗时/s 生长空间 R-O 不收敛 18.00 60.742 6012 × 3R-A+B+C 10 0.00 0.185 489 × 3 Ac-O 85 0.00 45.011 4746 × 3Ac-A+B+C 11 0.00 0.279 644 × 3 注：算法R-A+B+C、Ac-A+B+C分别对应于图7中的R-多机制融合PGSA、Ac-多机制融合PGSA
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表 5 构件和材料规格
Table 5. Specifications of members and materials
结构部位 构件 材质 规格 上部单层
网壳凯威特
部分径向杆 Q355B ϕ245 × 14 环向杆 Q355B ϕ245 × 14 斜杆 Q355B ϕ219 × 12 联方
部分环向杆 Q355B ϕ219 × 12 斜杆 Q355B ϕ203 × 12 下部索杆
体系撑杆 Q355B ϕ180 × 8 环向索 内圈 平行钢丝束， 1670 级ϕ5 × 61 中圈 平行钢丝束， 1670 级ϕ5 × 91 外圈 平行钢丝束， 1670 级ϕ5 × 139 径向索 平行钢丝束， 1670 级ϕ5 × 55
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表 6 不同优化算法的关键参数设定
Table 6. Key parameter setting for different optimization algorithms
算法 关键参数 原 PGSA 步长为 5，Kmax = 1000 多机制融合PGSA dmin=0.1，d0=50，Kmax = 1000 ，s=0.3，Cs=100PSO 粒子个数为 10，惯性权重和全局增量均为 0.9 ASA 初始温度为 1.0，退火相对速率为 1.0，最大收敛步数为 5 MIGA 子群规模为 10，交叉概率为 1.0，变异概率为 0.01 Pointer 任务时间为 1，失败点的罚值和目标值均为1.0×1030
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