Evolutionary Optimization Framework Based on Transfer Learning of Similar Historical Information
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摘要: 现有进化算法大都从问题的零初始信息开始搜索最优解, 没有利用先前解决相似问题时获得的历史信息, 在一定程度上浪费了计算资源.将迁移学习的思想扩展到进化优化领域, 本文研究一种基于相似历史信息迁移学习的进化优化框架.从已解决问题的模型库中找到与新问题匹配的历史问题, 将历史问题对应的知识迁移到新问题的求解过程中, 以提高种群的搜索效率.首先, 定义一种基于多分布估计的最大均值差异指标, 用来评价新问题与历史模型之间的匹配程度; 接着, 将相匹配的历史问题的知识迁移到新问题中, 给出一种基于模型匹配程度的进化种群初始化策略, 以加快算法的搜索速度; 然后, 给出一种基于迭代聚类的代表个体保存策略, 保留求解过程中产生的优势信息, 用于更新历史模型库; 最后, 将自适应骨干粒子群优化算法嵌入到所提框架, 给出一种基于相似历史信息迁移学习的骨干粒子群优化算法.针对多个改进的典型测试函数, 实验结果表明, 所提迁移策略可以加速粒子群的搜索过程, 显著提高算法的收敛速度和搜索效率.Abstract: Most of existing evolutionary algorithms search optimal solutions from zero initial information of a given problem. Because of the lacking a mechanism to use historical information, this must waste computing resources to some extent when solving a problem similar to old ones. This paper extends the idea of transfer learning to the field of evolutionary optimization, and studies a new evolutionary optimization framework based the transfer learning of similar historical information. To improve the search efficiency of the population, the proposed framework finds out the history problem from the model library, which matches current new problem, and transfers the knowledge of the historical problem into optimization process of the new problem. First, a maximum mean discrepancy indicator based on multi-distribution estimation is defined to evaluate the matching degree between a new problem and historical models. Secondly, the knowledge of matched historical problem is transferred into the new problem, and a new initialization strategy of the population based on matching degree is given to accelerate the search speed of the algorithm. Next, a preservation strategy based on iterative clustering is presented to save good information generated during the evolutionary process, for updating the model library. Finally, embedding an adaptive bare-bones particle swarm optimization (PSO) into the proposed framework, a bare-bones PSO algorithm based on the transfer learning of similar historical information is presented. Testing on several improved typical functions, experimental results show that the proposed transfer strategy accelerates the search process of the particle swarm, and significantly improve the convergence speed and the search efficiency of the proposed PSO algorithm.
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Key words:
- Evolutionary optimization /
- transfer learning /
- particle swarm optimization (PSO) /
- model matching
1) 本文责任编委 魏庆来 -
图 1 所提基于迁移学习的进化算法框架
Fig. 1 Evolutionary algorithm framework based on transfer learning
图 2 优化第1组测试函数时ABPSO和TL-ABPSO算法的收敛曲线
Fig. 2 Convergence curves of ABPSO and TL-ABPSO algorithms for the first set of test functions
图 3 优化第1组测试函数时DE和TL-DE算法的收敛曲线
Fig. 3 Convergence curves of DE and TL-DE algorithms for the first set of test functions
图 4 在不同参数ck取值下, TL-ABPSO找到问题最优解所需平均迭代次数
Fig. 4 The average iteration time required by TL-ABPSO to find the optimal solution under different ck value
表 1 源域中保存的历史优化函数
Table 1 optimization functions saved in the source domain
函数名称 表达式 定义域 最优解 维数 Sphere $f(x) = \sum\limits_{i = 1}^n{x_i^2}$ $[-100, 100]$ 0 30 Rastrigin $f(x) = \sum\limits_{i = 1}^n {(x_i^2 - 10\cos (2\pi{x_i}) + 10)}$ $[-5.12, 5.12]$ 0 30 Ackley ${f(x) = - 20\exp ( - 0.2\sqrt {\frac{{\rm{1}}}{{{\rm{30}}}}\sum\limits_{i = 1}^n {x_i^2} } ){\kern 1pt} - \exp (\frac{1}{{30}}\sum\limits_{i = 1}^n {\cos 2\pi {x_i}} ) + 20 + e{\kern 1pt} }$ $[-32, 32]$ 0 30 Griewank $f(x) = \frac{1}{{4\, 000}}\sum\limits_{i = 1}^n{x_i^2} - \prod\limits_{i = 1}^n {\cos(\frac{{{x_i}}}{{\sqrt i }}) +1}$ $[-600, 600]$ 0 30 Rosenbrock $f(x) = \sum\limits_{i = 1}^n {(100{{({x_{i +1}} - x_i^2)}^2} + {{({x_i} - 1)}^2})}$ $[-30, 30]$ 0 30 
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表 2 目标域中新的优化函数
Table 2 New optimization functions in the target domain
函数名称 表达式 定义域 最优解 维数 F1: 修改后Sphere $f(x) = \sum\limits_{i = 1}^n {x_i^{10}} $ $[-100, 100] $ 0 30 F2:修改后Rastrigin $f(x) = \sum\limits_{i = 1}^n {(x_i^{10} - 10\sin(2\pi {x_i}))} $ $[-5.12, 5.12]$ 0 30 F3: 修改后Ackley $\begin{array}{*{20}{c}} {f(x) = - 20\exp \left( { - 0.2 \times \sqrt[{10}]{{\frac{1}{{30}}\sum\limits_{i = 1}^n {x_i^{10}} }}} \right) - }\\ {\exp \left( {\frac{1}{{30}}\sum\limits_{i = 1}^n {\sin } 2\pi {x_i}} \right) + 20 + 1} \end{array}$ $[-32, 32]$ 0 30 F4: 修改后Griewank $f(x) = \frac{1}{{4\, 000}}\sum\limits_{i = 1}^n {x_i^{10}} - \prod\limits_{i = 1}^n {{{\sin}}(\frac{{{x_i}}}{{\sqrt i }})} $ $[-600, 600] $ 0 30 F5: 修改Rosenbrock $f(x) = \sum\limits_{i = 1}^n {(100{{({x_{i + 1}} - x_i^{10})}^2} + {{({x_i} - 1)}^{10}})} $ $[-30, 30] $ 0 30 F6: Shifted Sphere 文献[32] $[-100, 100]$ $-450$ 30 F7: Shifted rotated Rastrigin 文献[32] $[-5, 5]$ $-330$ 30 F8: Shifted rotated Ackley 文献[32] $[-32, 32]$ $-140$ 30 F9: Shifted rotated Griewank 文献[32] $[-600, 600]$ $-180$ 300 F10: Shifted Rosenbrock 文献[32] $[-100, 100]$ 390 30
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表 3 比较算法优化第1组测试函数所得实验结果
Table 3 Experimental results obtained by comparison algorithm for the first set of test functions
优化函数 比较算法 指标SR (%) 指标Fave 指标Time (s) 指标AC SPSO 100 2.635 ×103 1.539 0 BBPSO-MC 66.67 - 2.960 1.8241×10-5 函数F1 BBJ 63.33 - 7.614 8.6800×10-6 ABPSO 100 3.730×103 3.150 0 TL-ABPSO 100 1.574×103 1.860 0 SPSO 0 - 9.722 5.169×101 BBPSO-MC 26.67 - 12.761 1.824×10-0 {函数F2} BBJ 0 - 20.169 8.680×10-6 ABPSO 72 - 21.083 7.067×10-5 TL-ABPSO 100 1.283×104 20.183 0 SPSO 0 - 12.769 1.494×100 BBPSO-MC 100 2.815×104 13.185 0 函数F3 BBJ 0 - 22.356 1.350 ×10-2 ABPSO 100 3.568×103 17.514 0 TL-ABPSO 100 2.214×103 7.9190 0 SPSO 0 - 8.726 3.312×10-4 BBPSO-MC 100 1.163×103 3.820 0 函数F4 BBJ 0 - 9.947 2.366×10-5 ABPSO 100 8.110×102 4.706 0 TL-ABPSO 100 2.310×102 3.370 0 SPSO 0 - 10.154 2.908×101 BBPSO-MC 0 - 15.651 2.277×101 函数F5 BBJ 0 - 25.425 1.861×101 ABPSO 0 - 31.817 1.281×101 TL-ABPSO 0 - 49.476 1.253×101
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表 4 比较算法优化第2组测试函数所得实验结果
Table 4 Experimental results obtained by comparison algorithm for the second set of test functions
优化函数 比较算法 指标SR (%) 指标Fave 指标Time (s) 指标AC SPSO 100 3.525×103 10.105 0 BBPSO-MC 66.67 - 12.132 0 函数F6 BBJ 0 - 14.835 0 ABPSO 100 1.066×103 7.451 0 TL-ABPSO 100 1.421×102 7.160 0 SPSO 0 - 36.853 4.279×101 BBPSO-MC 33.33 - 62.168 3.800×10-3 函数F7 BBJ 50 - 57.679 1.893×100 ABPSO 72 - 39.707 0 TL-ABPSO 100 7.467×103 22.704 0 SPSO 0 - 33.796 1.329×102 BBPSO-MC 26.67 - 61.905 2.095×101 函数F8 BBJ 0 - 62.813 2.094×101 ABPSO 44.33 - 166.905 8.231×10-2 TL-ABPSO 63.33 - 214.023 1.709×10-4 SPSO 0 - 39.021 5.483×102 BBPSO-MC 0 - 62.722 7.901×10-3 函数F9 BBJ 0 - 54.329 1.040×101 ABPSO 0 - 125.621 5.286×101 TL-ABPSO 0 - 183.422 9.567×10-4 SPSO 0 - 36.927 2.908×101 BBPSO-MC 0 - 61.933 2.674×101 函数F10 BBJ 0 - 51.946 3.597×101 ABPSO 0 - 122.359 1.922×101 TL-ABPSO 0 - 180.816 1.347×101
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