基于改进多目标布谷鸟搜索算法的翼型气动优化设计
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摘要
布谷鸟搜索(CS)算法是一种新型的受自然现象启发的元启发式智能优化算法,其强大的全局搜索能力和收敛速度受到了广泛关注。多目标布谷鸟搜索(MOCS)算法是一种在单目标布谷鸟算法基础上发展的可以直接求解Pareto解集的多目标优化算法。针对原始MOCS算法的不足,采用一系列措施以提高算法的收敛精度、收敛速度以及解的均匀性:通过引入非支配排序与拥挤距离来改进解的适应度评估;通过改进随机游走策略来提高局部搜索能力;通过引入改进的自适应丢弃概率策略来提高算法的收敛速度;加入档案管理机制,提高解的均匀性。典型的多目标数值算例结果表明,改进的MOCS算法相较于当前主流的NSGA-Ⅱ算法拥有更快的收敛速度和更高的收敛精度。以RAE2822双目标升阻比优化设计为例,将改进的MOCS算法应用于多目标气动优化中,改进的MOCS算法共获得64个Pareto解,优化后的翼型气动性能有明显的提升,设计者可以根据自己的偏好选取不同的Pareto解。对于气动优化问题,改进的MOCS算法与目前主流的NSGA-Ⅱ相比,收敛速度更快。
Cuckoo Search(CS)algorithm is a newly proposed meta-heuristic optimization algorithm inspired by natural phenomena.It received wide attention due to its powerful global searching capability and fast convergence speed.The MultiObjective Cuckoo Search(MOCS)algorithm is a multi-objective optimization algorithm developed on the basis of the singleobjective cuckoo search which can directly obtain a set of Pareto solutions.Aiming at alleviating the shortcomings of the original MOCS algorithm,a series of methodologies are introduced to improve the convergence accuracy,convergence speed,and distribution of the solutions:the fast non-dominated sorting and crowding distance are introduced to improve the fitness evaluation of solutions,a random walk strategy is modified to improve local search ability,an adaptive abandon probability strategy is used to improve the convergence speed,and an archive management mechanism is added to improve the uniformity of the distribution of the Pareto set.The results of the benchmark analytical multi-objective tests show that the improved MOCS algorithm has a faster convergence speed and higher convergence accuracy than the original MOCS as well as the NSGA-II algorithm.Finally,taking the RAE2822 two-point lift-to-drag ratio maximization design as an example,the improved MOCS algorithm is applied to a multi-objective aerodynamic optimization problem.The results show that the improved MOCS algorithm can obtain 64 Pareto solutions.The aerodynamic performances of the optimized airfoils are significantly improved,and the designers can choose different Pareto solutions based on their own requirements.For the aerodynamic optimization problem,the convergence speed of improved MOCS algorithm is faster than MOCS and NSGA-II algorithms.
Cuckoo Search(CS)algorithm is a newly proposed meta-heuristic optimization algorithm inspired by natural phenomena.It received wide attention due to its powerful global searching capability and fast convergence speed.The MultiObjective Cuckoo Search(MOCS)algorithm is a multi-objective optimization algorithm developed on the basis of the singleobjective cuckoo search which can directly obtain a set of Pareto solutions.Aiming at alleviating the shortcomings of the original MOCS algorithm,a series of methodologies are introduced to improve the convergence accuracy,convergence speed,and distribution of the solutions:the fast non-dominated sorting and crowding distance are introduced to improve the fitness evaluation of solutions,a random walk strategy is modified to improve local search ability,an adaptive abandon probability strategy is used to improve the convergence speed,and an archive management mechanism is added to improve the uniformity of the distribution of the Pareto set.The results of the benchmark analytical multi-objective tests show that the improved MOCS algorithm has a faster convergence speed and higher convergence accuracy than the original MOCS as well as the NSGA-II algorithm.Finally,taking the RAE2822 two-point lift-to-drag ratio maximization design as an example,the improved MOCS algorithm is applied to a multi-objective aerodynamic optimization problem.The results show that the improved MOCS algorithm can obtain 64 Pareto solutions.The aerodynamic performances of the optimized airfoils are significantly improved,and the designers can choose different Pareto solutions based on their own requirements.For the aerodynamic optimization problem,the convergence speed of improved MOCS algorithm is faster than MOCS and NSGA-II algorithms.
引文
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[2]田旭,李杰.一种改进的果蝇优化算法及其在气动优化设计中的应用[J].航空学报,2017,38(4):55-65.TIAN X,LI J.An improved fruit fly optimization algorithm and its application in aerodynamic optimization design[J].Acta Aeronautica et Astronautica Sinica,2017,38(4):55-65(in Chinese).
[3]黄江涛,高正红,余婧,等.大型民用飞机气动外形典型综合设计方法分析[J].航空学报,2019,40(1):522369.HUANG J T,GAO Z H,YU J,et al.The analysis of a typical integrated design method for large civil aircraft aerodynamic op-timization[J].Acta Aeronautica et Astronautica Sinica,2019,40(1):522369(in Chinese).
[4] KIRKPATRICK S,GELATT C D,VECCHI M P.Optimization by simulated annealing[J].Science,1983,220(4598):671-680.
[5] POLI R,KENNEDY J,BLACKWELL T.Particle swarm optimization[J].Swarm Intelligence,2007,1(1):33-57.
[6] DORIGO M,MANIEZZO V,COLORNI A.Ant system:optimization by a colony of cooperating agents[J].IEEE Transactions on Systems,Man,and Cybernetics,Part B(Cybernetics),1996,26(1):29-41.
[7] GOLDBERG D E.Genetic algorithm in search optimization and machine learning[J].Addison Wesley,1989,13(7):2104-2116.
[8] YANG X S,DEB S.Engineering optimisation by cuckoo search[J].International Journal of Mathematical Modelling&Numerical Optimisation,2010,1(4):330-343.
[9]兰少峰,刘升.布谷鸟搜索算法研究综述[J].计算机工程与设计,2015,36(4):1063-1067.LAN S F,LIU S.Overview of research on Cuckoo search algorithm[J].Computer Engineering and Design,2015,36(4):1063-1067(in Chinese).
[10]高述涛.CS算法优化BP神经网络的短时交通流量预测[J].计算机工程与应用,2013,49(9):106-109.GAO S T.Short time traffic flow prediction model based on neural network and cuckoo search algorithm[J].Computer Engineering and Applications,2013,49(9):106-109(in Chinese).
[11] TIWARI V.Face recognition based on cuckoo search algorithm[J].Indian Journal of Computer Science and Engineering,2012,7(8):401-405.
[12]吴炅,周健勇.整数规划的布谷鸟算法[J].数学理论与应用,2013,33(3):99-106.WU J,ZHOU J Y.Cuckoo search algorithm for solving integer programming[J].Mathematical Theory and Applications,2013,33(3):99-106(in Chinese).
[13] YANG X S,DEB S.Multiobjective cuckoo search for design optimization[J].Computers&Operations Research,2013,40(6):1616-1624.
[14] YANG X S.Engineering optimization:an introduction with metaheuristic applications[M].New York:John Wiley&Sons,2010.
[15] YANG X S,SUASH D.Cuckoo search:recent advances and applications[J].Neural Computing and Applications,2014,24(1):169-174.
[16] DEB K,AGRAWAL S,PRATAP A,et al.A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization:NSGA-II[C]∥International Conference on Parallel Problem Solving From Nature.Springer,2000:849-858.
[17] ZHANG M,WANG H,CUI Z,et al.Hybrid multi-objective cuckoo search with dynamical local search[J].Memetic Computing,2018,10(2):199-208.
[18] HE X S,LI N,YANG X S.Non-dominated sorting cuckoo search for multiobjective optimization[C]∥IEEE SSCI2014 Symposium Series on Computational Intelligence,2015:27-33.
[19] ZITZLER E,DEB K,THIELE L.Comparison of multiobjective evolutionary algorithms:empirical results[J].Evolutionary Computation,2000,8(2):173-195.
[20] STRAATHOF M H,TOOREN M J L V.Extension to the class-shape-transformation method based on B-splines[J].AIAA Journal,2011,49(4):780-790.
[21] HICKS R M,HENNE P A.Wing design by numerical optimization[J].Journal of Aircraft,1978,15(7):407-412.
[22] HAJEK J.Parameterization of airfoils and its application in aerodynamic optimization[C]∥WDS Proceedings of Contributed Papers.2007,7:233-240.
[23]马晓永,范召林,吴文华,等.基于NURBS方法的机翼气动外形优化[J].航空学报,2011,32(9):1616-1621.MA X Y,FAN Z L,WU W H,et al.Aerodynamic shape optimization for wing based on NURBS[J].Acta Aeronautica et Astronautica Sinica,2011,32(9):1616-1621(in Chinese).
[24] PRAUTZSCH H,BOEHM W,PALUSZNY M.Bezier and B-spline techniques[M].New York:Springer-Verlag,2002.
[25] SAMAREH J.Aerodynamic shape optimization based on free-form deformation[C]∥10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference.Reston,VA:AIAA,2004.
[26]刘俊.基于代理模型的高效气动优化设计方法及应用[D].西安:西北工业大学,2015.LIU J.Efficient surrogate-based optimization method and its application in aerodynamic design[D].Xi’an:Northwestern Polytechnical University,2015(in Chinese).
[27] COOK P H,MCDONALD M A,FIRMIN M C P.Aerofoil RAE 2822-pressure distributions,and boundary layer and wake measurements:AGARD Report AR 138[R].Paris:AGARD,1979.