摘 要
粒子群優(yōu)化算法(Particle Swarm Optimization，PSO)是近十幾年新出現(xiàn)的一種基于群迭代的模擬群體生物相互協(xié)同尋優(yōu)的啟發(fā)式優(yōu)化算法，因其收斂速度快和易于實現(xiàn)等特點，已經(jīng)成為計算智能領(lǐng)域新的研究熱點。自2002年J. Robinson首次使用PSO算法設(shè)計了賦形波紋喇叭天線，此后，粒子群優(yōu)化算法在天線設(shè)計，特別是陣列天線設(shè)計問題中得到了大量廣泛的應(yīng)用。由于粒子群算法理論基礎(chǔ)還不完備，并存在早熟收斂的問題，因此，對算法進行深入的理論分析及改進是研究者們的工作重點之一?；谶@種情況，本文對標(biāo)準(zhǔn)粒子群算法的邊界條件進行了分析，為了提高算法的全局搜索能力及收斂速度分別提出了二進制粒子群（Binary Particle Swarm Optimization，BPSO）和量子粒子群（Quantum Particle Swarm Optimization，QPSO）的改進算法，并將改進后的算法用于天線陣列綜合問題。本文主要研究內(nèi)容如下：
1. 研究了標(biāo)準(zhǔn)粒子群算法的邊界條件設(shè)置，基于前人研究的基礎(chǔ)，提出了一組新的受限制的邊界條件，即，將出界粒子隨機置于搜索空間內(nèi)。除此之外，還將吸收的優(yōu)點引入到現(xiàn)有的無形邊界條件中，組合成無形/吸收的邊界條件。由仿真結(jié)果對比分析，新提出的隨機重置的邊界條件的性能明顯優(yōu)于置于邊界的情況，無形/吸收的邊界條件也稍微優(yōu)于其他不受限制的邊界條件。
2. 為了提高算法的收斂速度和全局搜索能力，本文提出了兩種二進制粒子群的改進算法，分別通過引入全局次優(yōu)活躍點和鯰魚擾動機制，并對改進算法進行參數(shù)設(shè)置，通過典型測試函數(shù)驗證，改進算法和參數(shù)設(shè)置方法的可行性和有效性。
3. 研究了Sun等人提出的量子粒子群算法，為了克服算法早熟收斂，從收斂速度和收斂精度兩個方面提出了隨機搜索和反向?qū)W習(xí)機制兩種改進思路，綜合兩種改進方法，提出多種組合的QPSO改進算法，通過測試函數(shù)驗證，改進算法加快了算法收斂速度并提高了算法的收斂精度。
4. 利用改進的量子粒子群算法綜合直線陣列，給出具體通信要求的天線陣實例，綜合結(jié)果優(yōu)于現(xiàn)有文獻結(jié)果。
5. 研究了改進算法綜合平面陣，包括矩形面陣和圓陣的陣元幅度優(yōu)化和稀疏陣問題，討論了陣元數(shù)目、圓環(huán)半徑等參數(shù)的選取對單層圓環(huán)和多層同心圓環(huán)的方向圖的影響。
6. 最后研究了共形陣綜合，同樣分析陣元行間距、圓環(huán)半徑等參數(shù)對陣列方向圖的影響，并研究適應(yīng)度函數(shù)的選取對方向圖的影響，最后簡單研究了圓錐陣的綜合。
關(guān)鍵字 粒子群算法，二進制粒子群，量子粒子群，天線陣，方向圖綜合

Abstract
Particle Swarm Optimization (PSO) algorithm is a kind of heuristic optimization algorithm based on swarm iteration. It has become a new hotspot in the area of computation intelligence for the rapid convergence and simple implementation. Since it is recently introduced to design the corrugated horn antenna first by Robinson and Rahmat-Samii in 2002, after that, PSO algorithm get a lot of wide used in antenna design, especially antenna array design. Due to the theoretical basic of PSO algorithm is not complete, and it also has a problem of premature convergence, deep theoretical analysis and improvements of algorithm is one of the most important work of researchers. Based on this situation, the boundary conditions of standard PSO are analyzed in order to improve the global search ability and the algorithm convergence speed, the improvements of Binary Particle Swarm Optimization (BPSO) and Quantum Particle Swarm Optimization (QPSO) are presented, and the improved algorithms are used in antenna array synthesis. The main research works are discussed as follows:
1. The set of standard PSO boundary conditions are studied. Based on the basis of previous studies, a group of new boundary conditions are put forward, namely, errant particles are relocated in the solution space randomly. In addition, an invisible/absorbing boundary condition is proposed in which the favorable characteristic of the absorbing boundary condition is introduced into the existing invisible boundary condition. The simulation results show that the new boundary conditions which relocate errant particles randomly offer superior performance than relocate errant particles on the boundary of solution space. The invisible/absorbing boundary condition edges out other unrestricted boundary conditions.
2. In order to improve the algorithm convergence speed and the global search ability, two kinds of improved BPSOs are put forward, respectively. By introducing global subprime active point and catfish perturbation mechanism, the parameters set of improved algorithms are researched. Through the typical functions’ test and verify, the improved algorithms and the methods of parameters setting are feasible and effective.
3. QPSO algorithm proposed by Sun and others is studied. In order to overcome algorithm premature convergence, random search and reverse learning mechanism are put forward separately in convergence speed and the accuracy of convergence. Considering these two improvement ideas comprehensively, several combination improved algorithms are suggested. The simulation results of test functions show that the improved algorithms can speed up the convergence rate and improve the algorithm convergence precision.
4. The improved QPSO is used to synthesis linear array, the examples of specific communication requirements are given, its results are better than the existing literatures’ results.
5. The plane array synthesis using improved algorit..