HYBRID OPTIMIZATION ALGORITHM BASED ON DIFFERENTIAL EVOLUTION AND RBF RESPONSE SURFACE
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摘要: 针对气动优化等昂贵优化问题，提出了一种基于差分进化和RBF响应面的混合优化算法HSADE，该方法结合了差分进化算法的强全局寻优能力和RBF响应面方法的快速局部搜索能力，能够同时有效地提高算法的局部搜索效率和全局寻优能力.对各子算法中的策略和逻辑进行了多项改进，提出和应用了基于双败淘汰赛的竞赛赛制和参数自适应等改进策略.对HSADE使用多个典型算例进行了测试，并横向对比了NSGA-Ⅱ，MOPSO和多目标差分进化算法.测试结果表明，在大多数问题中HSADE在以世代距离表征的局部搜索效率和以超体积比表征的全局寻优能力两项指标上都优于其他算法，证实了以上混合策略及算法改进的有效性.将该算法应用于一个翼型优化问题和一个二维超声速喷管膨胀面优化问题，并横向对比未经改良的差分进化算法DE和另一种混合算法NARSGA，结果表明在接近1 000次的函数评估下，HSADE能相对其他算法进一步对翼型减阻0.5 count，在喷管优化中HSADE得到的结果也好于其他两种算法，表明该方法具有较强工程应用价值.Abstract: A new hybrid optimization algorithm HSADE (hybrid self-adaptive differential evolution) based on differential evolution and radial basis function response surface was proposed aiming at aerodynamic optimization problems. Through combing the merits of response surface method's fast local searching ability and differential evolution's powerful global searching ability, the overall local and global search efficiency of HSADE were simultaneously enhanced. Several improvements were made on certain logics and strategies embedded in the processes of each sub-algorithm by proposing and utilizing strategies such as selection strategy based on double elimination and self-adaptive parameters. Having applied HSADE and several other typical optimization algorithms-NSGA-Ⅱ, MOPSO and multi-objective differential evolution to several benchmark functions, the results indicated HSADE was superior to other algorithms in most of the cases regarding local search ability represented by generation distance and global search ability symbolled by hyper volume ratio, which validated the effectiveness of above improvements. Applying HSADE along with basic DE and NARSGA to an airfoil optimization problem and a hypersonic nozzle expansion surface optimization problem, the results showed HSADE was able to obtain airfoils with extra 0.5 count drag reduction and nozzles with better performance than other two algorithms under approximately 1000 function evaluations, which indicated high engineering application potential of HSADE.
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图 5 初始外形和3种算法得到的外形
Figure 5. Shapes of initial airfoil and optimal airfoils obtained by optimizers
图 7 3种算法的Pareto前缘对比
Figure 7. Comparisons of Pareto fronts obtained by HSADE, NARSGA and DE
图 9 喷管构型与3种算法获得的代表性个体外形
Figure 9. Nozzle concepts and representative optimal shapes obtained by HSADE, NARSGA and DE
表 1 径向基函数类型
Table 1. Different types of radial basis functions
表 2 几种响应面插值精度验证
Table 2. Examination of interpolation error of different response surfaces
表 3 几种算法在测试问题上的收敛性指标结果
Table 3. Convergence criteria of competing algorithms upon tested problems
表 4 几种算法在测试问题上的分布性指标结果
Table 4. Distribution criteria of competing algorithms upon tested problems
表 5 翼型优化问题的优化变量、目标和约束
Table 5. Variables, targets and constraints of the airfoil optimization problem
表 6 3种算法得到的最优翼型的性能参数和优化量
Table 6. Performance and optimization measurement of the optimal airfoils obtained by optimizers
表 7 喷管设计变量范围
Table 7. Variable ranges of the nozzle design
表 8 3种算法得到的代表个体的性能参数
Table 8. Performance of representative optimal shapes obtained by HSADE, NARSGA and DE
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