Antenna-array pattern nulling using a differential evolution algorithm

A new method based on the differential evolution (DE) algorithm is proposed for antenna-array pattern synthesis with prescribed nulls. The array excitation amplitudes are the only controlling parameters, and the objectives are to synthesize array patterns with nulls imposed on directions of interferences while keeping the sidelobe levels (SLLs) below prescribed levels. Many factors such as the excitation dynamic range ratio, null depth level, null width, and SLLs are taken into account in the synthesis. Simulation results of several typical problems are compared with published results to illustrate the effectiveness of the proposed method. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 14: 57–63, 2004.     

Dynamic group-based differential evolution using a self-adaptive strategy for global optimization problems

This paper describes a dynamic group-based differential evolution (GDE) algorithm for global optimization problems. The GDE algorithm provides a generalized evolution process based on two mutation operations to enhance search capability. Initially, all individuals in the population are grouped into a superior group and an inferior group based on their fitness values. The two groups perform different mutation operations. The local mutation model is applied to individuals with better fitness values, i.e., in the superior group, to search for better solutions near the current best position. The global mutation model is applied to the inferior group, which is composed of individuals with lower fitness values, to search for potential solutions. Subsequently, the GDE algorithm employs crossover and selection operations to produce offspring for the next generation. In this paper, an adaptive tuning strategy based on the well-known 1/5th rule is used to dynamically reassign the group size. It is thus helpful to trade off between the exploration ability and the exploitation ability. To validate the performance of the GDE algorithm, 13 numerical benchmark functions are tested. The simulation results indicate that the approach is effective and efficient.     

An extended particle swarm optimization algorithm for pattern synthesis of conformal phased arrays

In this article, an extended particle swarm optimization (EPSO) algorithm is proposed for designing conformal phased arrays. On the basis of traditional particle swarm optimization (PSO), novel velocity updating mechanism, new exceeding boundary control operator, and global best perturbation are introduced in EPSO to overcome the drawbacks of PSO. To validate the efficiency of the proposed algorithm, both the classical test functions and the scenarios concerning a 1 × 9‐element cylindrical conformal phased array and a 3 × 9(27)‐element cylindrical conformal array with flat‐top shaped‐beam pattern are presented. Simulation results show that the proposed method is superior to genetic algorithm (GA) and PSO when applied to both the classical test functions and the practical problems of conformal antenna array synthesis. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.     

Complex weight control of array pattern nulling

An efficient method based on the sequential quadratic programming (SQP) algorithm for the linear antenna arrays pattern synthesis with prescribed nulls in the interference direction and minimum side lobe levels by the complex weights of each array element is presented. In general, the pattern synthesis technique that generates a desired pattern is a greatly nonlinear optimization problem. SQP method is a versatile method to solve the general nonlinear constrained optimization problems and is much simpler to implement. It transforms the nonlinear minimization problem to a sequence of quadratic subproblem that is easier to solve, based on a quadratic approximation of the Lagrangian function. Several numerical results of Chebyshev pattern with the imposed single, multiple, and broad nulls sectors are provided and compared with published results to illustrate the performance of the proposed method. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.     

Bit error rate reduction for circular ultrawideband antenna by dynamic differential evolution

The dynamic differential evolution (DDE) is used to synthesize the radiation pattern of the directional circular arc array to minimize the bit error rate (BER) performance in indoor ultrawideband (UWB) communication system. Using the impulse response of multipath channel, the BER performance of the synthesized antenna pattern on binary pulse amplitude modulation system can be calculated. Based on the topography of the circular antenna array and the BER formula, the array pattern synthesis problem can be reformulated into an optimization problem and solved by the DDE algorithm. The novelties of our approach are not only choosing BER as the object function instead of sidelobe level of the antenna pattern but also considering the antenna feed length effect of each array element. The strong point of the DDE algorithm is that it can find out the solution even if the performance index cannot be formulated by simple equations. Simulation results show that the synthesized antenna array pattern is effective to focus maximum gain to the line of site path which scales as the number of array elements. In other words, the receiver can increase the received signal energy to noise ratio. The synthesized array pattern also can mitigate severe multipath fading in complex propagation environment. As a result, the BER can be reduced substantially in indoor UWB communication system. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.     

Pattern synthesis of time‐modulated conformal arrays by an improved differential evolution algorithm

In this article, an improved differential evolution algorithm (IDE) based on two different colonies is proposed and applied to time‐modulated conformal arrays syntheses. The whole population of IDE is divided into two parts. The one part searches the solution globally while the other searches the neighborhood of the solution provided by the previous one. Benchmark functions are provided to testify IDE. Furthermore, IDE is applied to synthetize sum‐difference patterns with a 1 × 16 elements time‐modulated circular array and low sidelobe level (SLL) patterns with an 8 × 12 elements time‐modulated cone array. After optimization, the sideband level (SBL) of the circular array at the first sideband frequency is ?1.00 dB. The SLL and SBL at the first sideband frequency of the cone array are lower than ?30.00 and ?20.00 dB, respectively. Experiment results verify the superior performance of IDE. Moreover, to accelerate the computation speed, graphics processing unit parallel computing technique is introduced into pattern synthesis and the acceleration ratios of more than 23 times can be achieved. © 2014 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:697–705, 2014.     

Design of multiobjective reconfigurable antenna array with discrete phase shifters using multiobjective differential evolution based on decomposition

The reconfigurable design problem is to find the element that will result in a sector pattern main beam with side lobes. The same excitation amplitudes applied to the array with zero phase should be in a high directivity, low‐side lobe pencil‐shaped main beam. This work presents a multiobjective approach to solve this problem. We consider two design objectives: the minimum value for the dual beam and the dynamic range ratio in qualify the entire array radiation pattern in order to achieve the optimal value between the antenna‐array elements. We use a recently developed and very competitive multiobjective evolutionary algorithm, called MOEA/D. This algorithm uses a decomposition approach to convert the problem of approximation of the Pareto Front into a number of single objective optimization problems. We illustrate that the best solutions obtained by the MOEA/D can outperform stat‐of‐art single objective algorithm: generalized generation‐gap model genetic algorithm (G3‐GA) and differential evolution algorithm (DE). In addition, we compare the results obtained by MOEA/D with those obtained by one of the most widely multiobjective algorithm called NSGA‐II and mutliobjective DE. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22: 675–681, 2012.     

采用二阶锥规划和压缩感知的方向图综合算法

针对常规自适应方向图综合在求解最优权值向量时需经过复杂的广义矩阵求逆运算,计算过程繁琐,占用存储空间大的缺陷,提出一种采用二阶锥规划与压缩感知理论的改进自适应方向图综合算法。改进的算法将传统算法中的误差性能函数通过数学变换转换成标准二阶锥规划形式快速求解。同时应用压缩感知理论将大规模阵列权值稀疏化处理,从而得到最优天线阵列权值向量并减少训练时间。仿真结果表明,采用二阶锥规划与压缩感知的改进算法在大规模阵列天线方向图综合时求解速度快,运算精度高,且在应用压缩感知后形成的方向图有较低旁瓣,干扰方向零陷深,接近满阵时的波束性能。     

基于极大极小距离密度的多目标微分进化算法

微分进化(differential evolution)是一种新的简单而有效的直接全局优化算法,并在许多领域得到了成功应用.提出了基于极大极小距离密度的多目标微分进化算法.新算法定义了极大极小距离密度,给出了基于极大极小距离密度的Pareto候选解集的维护方法,保证了非劣解集的多样性.并根据个体间的Pareto.支配关系和极大极小距离密度改进了微分进化的选择操作,保证了算法的收敛性,实现了利用微分进化算法求解多目标优化问题.通过对5个ZDT测试函数、两个高维测试函数的实验及与其他多目标进化算法的对比和分析,验证了新算法的可行性和有效性.     

Design of a linear array antenna for shaped beam using genetic algorithm

A linear array antenna design with desired radiation pattern has been presented based on genetic algorithm (GA) approach. Examples of cosecant and flat‐topped beam patterns are illustrated to show the flexibility of GA to solve complex antenna synthesis problems by suitably selecting the fitness function, even with a simple GA. The results have been validated by IE3D electromagnetic simulation. The antenna arrays with different element geometries can also be implemented using the proposed technique. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.     

Topology optimization of structures using modified binary differential evolution

Differential evolution (DE) is an efficient population based algorithm used to solve real-valued optimization problems. It has the advantage of incorporating relatively simple and efficient mutation and crossover operators. However, the DE operator is based on floating-point representation only, and is difficult to use when solving combinatorial optimization problems. In this paper, a modified binary differential evolution (MBDE) based on a binary bit-string framework with a simple and new binary mutation mechanism is proposed. Two test functions are applied to verify the MBDE framework with the new binary mutation mechanism, and four structural topology optimization problems are used to study the performance of the proposed MBDE algorithm. The experimental studies show that the proposed MBDE algorithm is not only suitable for structural topology optimization, but also has high viability in terms of solving numerical optimization problems.     

自适应控制参数的通用差异演化算法研究

为提高求解多目标优化问题效率,对通用差异演化(GDE)算法及其自适应参数控制问题进行了研究。首先,分析了GDE3算法的编码、交叉、变异、选择等原理和算法流程;然后,利用个体的适应度作为参数调整的依据,并结合一定的调整概率提出一种新的对缩放因子和交叉概率参数自适应控制策略,提高算法的搜索能力;最后,通过典型的多目标函数对自适应控制参数的通用演化算法(selfGDE3)、GDE3和非劣分层遗传算法2(NS-GA-Ⅱ)的性能进行比较分析,结果表明,selfGDE3算法具有良好的搜索性能。     

Pattern synthesis for opportunistic array radar using least square fitness estimation‐genetic algorithm method

Pattern synthesis in three‐dimensional (3D) opportunistic array radar becomes complex when a multitude of antennas are considered to be randomly distributed in a 3D space. To obtain an optimal pattern, several freedoms must be constrained. A new pattern synthesis approach based on the improved genetic algorithm (GA) using the least square fitness estimation (LSFE) method is proposed. Parameters optimized by this method include antenna locations, stimulus states, and phase weights. The new algorithm demonstrates that the fitness variation tendency of GA can be effectively predicted after several “eras” by the LSFE method. It is shown that by comparing the variation of LSFE curve slope, the GA operator can be adaptively modified to avoid premature convergence of the algorithm. The validity of the algorithm is verified using computer implementation. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

An effective hybrid discrete differential evolution algorithm for the flow shop scheduling with intermediate buffers

In this paper, an effective hybrid discrete differential evolution (HDDE) algorithm is proposed to minimize the maximum completion time (makespan) for a flow shop scheduling problem with intermediate buffers located between two consecutive machines. Different from traditional differential evolution algorithms, the proposed HDDE algorithm adopted job permutation to represent individuals and applies job-permutation-based mutation and crossover operations to generate new candidate solutions. Moreover, a one-to-one selection scheme with probabilistic jumping is used to determine whether the candidates will become members of the target population in next generation. In addition, an efficient local search algorithm based on both insert and swap neighborhood structures is presented and embedded in the HDDE algorithm to enhance the algorithm’s local searching ability. Computational simulations and comparisons based on the well-known benchmark instances are provided. It shows that the proposed HDDE algorithm is not only capable to generate better results than the existing hybrid genetic algorithm and hybrid particle swarm optimization algorithm, but outperforms two recently proposed discrete differential evolution (DDE) algorithms as well. Especially, the HDDE algorithm is able to achieve excellent results for large-scale problems with up to 500 jobs and 20 machines.     

求解大规模优化问题的正交反向混合差分进化算法*

差分进化算法简单高效,然而在求解大规模优化问题时,其求解性能迅速降低。针对该问题,提出一种正交反向差分进化算法。首先,该算法利用正交交叉算子,加强了算法的局部搜索能力。其次,为防止过强的局部搜索使算法陷入早熟收敛,利用反向学习策略调节种群多样性,从而有效地平衡算法的全局和局部搜索能力。利用11个标准测试函数进行实验,并和差分进化算法的4种优秀改进版本进行比较,实验结果表明该算法求解精度高、收敛速率快,是一种求解大规模优化问题的有效算法。     

云环境下求解大规模优化问题的协同差分进化算法

差分进化是一种求解连续优化问题的高效算法。然而差分进化算法求解大规模优化问题时,随着问题维数的增加,算法的性能下降,且搜索时间呈指数上升。针对此问题,本文提出了一种新的基于Spark的合作协同差分进化算法（SparkDECC）。SparkDECC采用分治策略,首先通过随机分组方法将高维优化问题分解成多个低维子问题,然后利用Spark的弹性分布式数据模型,对每个子问题并行求解,最后利用协同机制得到高维问题的完整解。通过在13个高维测试函数上进行的对比实验和分析,实验结果表明算法加速明显且可扩展性好,验证了SparkDECC的有效性和适用性。     

Design of wideband aperiodic linear arrays by constrained differential evolution algorithm

The element placement plays a crucial role in array performance. Especially, aperiodic placement technique is a very effective approach to remove grating lobes and minimize the sidelobe level (SLL) of an array. In this article, a wideband aperiodic array has been designed by a constrained differential evolution algorithm (DE). As a practical application, multiple optimization constraints, such as the given aperture length, the bandwidth, the number of elements and the minimum interelement spacing, are considered. Hence, minimizing SLL for the wideband aperiodic array can be formulated as a constrained optimization problem. Some synthesis examples are solved by the constrained DE. Numerical results demonstrate that the constrained DE is an effective approach for minimize SLL when all the constraint conditions are satisfied. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

A novel modified differential evolution algorithm for constrained optimization problems

A novel modified differential evolution algorithm (NMDE) is proposed to solve constrained optimization problems in this paper. The NMDE algorithm modifies scale factor and crossover rate using an adaptive strategy. For any solution, if it is at a standstill, its own scale factor and crossover rate will be adjusted in terms of the information of all successful solutions. We can obtain satisfactory feasible solutions for constrained optimization problems by combining the NMDE algorithm and a common penalty function method. Experimental results show that the proposed algorithm can yield better solutions than those reported in the literature for most problems, and it can be an efficient alternative to solving constrained optimization problems.     

资源约束项目的改进差分进化参数控制及双向调度算法

针对资源约束项目调度组合优化难题, 提出一种改进的动态差分进化参数控制及双向调度算法.通过参数时变衰减与个体优劣评价, 自适应控制个体进化参数, 提高算法的收敛性能、勘探与开发最优解的能力; 基于动态差分进化(Dynamic differential evolution, DDE), 提出一种双向调度算法, 使用满足任务时序约束的优先数编码、交替正向反向调度, 结合标准化编码调整与精英保留的种群随机重建策略, 建立了一种高效稳健的双向编码调整机制.通过著名的项目调度问题库(Project scheduling problem library, PSPLIB)中实例集测试, 并与其他文献算法比较最优解平均偏差率, 验证了所提算法的有效性与优越性.     

混合模式搜索的分布式memetic差分进化算法

针对差分进化（DE）算法存在的早熟收敛与搜索停滞的问题,提出memetic分布式差分进化（DDE）算法。将memetic算法的思想融入到差分进化算法中,采用分布式的种群结构以及memetic算法中的混合策略,前者将初始种群分为多个子种群,子种群间根据冯·诺依曼拓扑结构周期性地实现信息交流,后者将差分进化算法作为进化的主要框架,模式搜索作为辅助手段,从而平衡算法的探索与开发能力。所提算法充分利用了模式搜索和差分进化算法的优势,建立了有效的搜索机制,增强了算法摆脱局部最优的能力,能够满足搜索过程对种群多样性及收敛速度的需求。将所提算法与几种先进的差分进化算法相比较,对标准测试函数进行优化的实验结果显示：所提算法在解的质量和收敛性能方面,均优于其他几种相比较的先进的差分进化算法。