动态约束多目标演化算法的研究及在天线设计中的应用

发布时间：2018-01-25 12:54

本文关键词： 演化算法多目标优化约束优化动态约束优化天线设计　出处：《中国地质大学》2017年博士论文　论文类型：学位论文

【摘要】：在科学研究及工程应用中,经常遇到约束优化问题。演化算法是一种受自然启发的随机搜索算法,它可以有效的求解最优化问题,过去的几十年中,很多研究者使用演化算法求解约束优化问题。演化多目标优化自上世纪80年代产生至今,得到了长足的发展,形成了很多成熟的算法。使用基于Pareto占优的多目标优化技术处理约束优化问题,取得了良好的效果,是一个重要的研究方向。天线设计是工程实践中一类复杂的约束优化问题,设计要求较多,建立起来的数学模型是一类非线性、多个变量、复杂约束的优化问题。这类优化问题在其它领域里也普遍存在,需要高性能的算法去求解。基于此,本文提出“动态约束多目标演化算法的研究及在天线设计中的应用”课题。所做的主要工作如下:1.设计动态约束“很多”目标演化算法(dynamic constrained many-objective optimization evolutionary algorithm,DCMaOEA)求解约束优化问题。首先将约束优化问题转化为对等的约束“很多”目标优化问题,使用“很多”目标优化技术保持算法搜索的分布性,另外采用动态的处理机制处理约束。算法演化之初,将原始的约束边界进行扩展,使得所有的解都看作可行解;随着演化的进行,慢慢收缩约束边界,让整个搜索过程在一个可行的环境下进行,从而提高了搜索能力;最后,使约束边界收敛到原始边界,输出的解也就是原始问题的解。DCMaOEA用差分算法作为搜索引擎,用基于参考点的非劣排序方法选择个体进入下一代种群。用两套测试问题包60个Benchmark函数对DCMaOEA进行了测试,并和其他先进的同类算法进行了比较。结果说明,设计的算法在求解各种类型的约束优化问题上有着良好的性能。2.基于动态约束技术和多目标比较框架,设计了几种改进算法,分别是混合约束处理机制演化算法、基于计算资源分配的动态约束“很多”目标演化算法和引入参数学习机制的动态约束“很多”目标演化算法。数值实验结果表明,这几种改进算法分别在不同角度不同程度上提高了原算法的性能。3.将设计的动态约束“很多”目标演化算法应用于求解天线设计问题,优化设计了两款天线,分别是低剖面宽波束圆极化天线和S波段中增益天线。用HFSS软件仿真结果表明,本文研究的算法可以有效地求解天线设计这一类复杂约束优化问题。本文的创新点是采用“很多”目标优化算法求解约束优化问题。以前的研究一般把约束优化问题看做两个目标的问题,原始目标和违约目标。将所有的约束条件整合成一个目标,容易忽视各约束条件的区别,丢失一些信息。而采用“很多”目标优化则能分别关注每个约束的满足情况,更适合处理复杂约束的问题。
[Abstract]:In scientific research and engineering applications, constrained optimization problems are often encountered. Evolutionary algorithm is a natural inspired random search algorithm, it can effectively solve the optimization problem, in the past few decades. Many researchers use evolutionary algorithms to solve constrained optimization problems. Evolutionary multi-objective optimization has made great progress since its inception in -20s. Many mature algorithms have been formed. The multi-objective optimization technique based on Pareto is used to deal with constrained optimization problems, and good results are achieved. Antenna design is a kind of complex constrained optimization problem in engineering practice, which requires a lot of design. The established mathematical model is a class of nonlinear and multiple variables. Complex constrained optimization problems. This kind of optimization problems are also common in other fields, and need high performance algorithm to solve them. In this paper, the research of dynamic constraint multi-objective evolutionary algorithm and its application in antenna design are presented. The main work is as follows: 1.Design dynamic constraint "many" target evolution algorithm (. Dynamic constrained many-objective optimization evolutionary. Algorithm. DCMaOEAA is used to solve the constrained optimization problem. Firstly, the constrained optimization problem is transformed into a peer-to-peer constrained "many" goal optimization problem, and the "many" goal optimization techniques are used to maintain the distribution of the algorithm search. In addition, dynamic processing mechanism is used to deal with constraints. At the beginning of the evolution of the algorithm, the original constraint boundary is extended so that all solutions are regarded as feasible solutions. Along with the evolution, the constraint boundary is gradually reduced, and the whole search process is carried out in a feasible environment, which improves the search ability. Finally, the constrained boundary converges to the original boundary, and the output solution is the solution of the original problem. DCMaOEA uses the difference algorithm as the search engine. The non-inferior sorting method based on reference points was used to select individuals to enter the next generation population. 60 Benchmark functions of two sets of test question packets were used to test the DCMaOEA. The results show that the proposed algorithm has good performance in solving various kinds of constrained optimization problems. 2. Based on dynamic constraint technology and multi-objective comparison framework. Several improved algorithms are designed, one is the evolutionary algorithm of hybrid constraint processing mechanism. Dynamic constraint "many" target evolution algorithm based on computational resource allocation and dynamic constraint "many" target evolution algorithm with parameter learning mechanism are introduced. These improved algorithms improve the performance of the original algorithm in different angles and to different degrees. 3. The dynamic constraint "many" target evolution algorithms are applied to solve the antenna design problem. Two antennas are designed, one is low profile wide-beam circular polarization antenna and the other is S-band gain antenna. The simulation results show by HFSS software. The algorithm studied in this paper can effectively solve the complex constrained optimization problems such as antenna design. The objective optimization algorithm is used to solve the constrained optimization problem. Previously, the constrained optimization problem is generally regarded as a two-objective problem. Original objective and default objective. All constraints are integrated into one goal, and the differences of each constraint are easily ignored. Some information is lost, and the "many" objective optimization can focus on the satisfaction of each constraint separately, so it is more suitable to deal with the problem of complex constraints.
【学位授予单位】：中国地质大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TP18;TN820

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