多目标量子编码遗传算法

如何使算法快速收敛到真正的Pareto前沿,并保持解集在前沿分布的均匀性是多目标优化算法重点研究解决的问题。该文提出一种基于量子遗传算法的多目标优化算法,利用量子遗传算法的高效全局搜索能力,在整个解空间内快速搜索多目标函数的Pareto最优解,利用量子遗传算法维持解集多样性的特点,使搜索到的Pareto最优解在前沿均匀分布。通过求解带约束的多目标函数优化问题,对该文算法的多目标优化性能进行了考察,并与NSGAII,PAES,MOPSO和Ray-Tai-Seows算法等知名多目标优化算法进行比较,结果证明了该文算法的有效性和先进性。     

多目标优化问题的遗传算法改进研究

基于Nash均衡的思想在NSGA所求得的Pareto最优解基础上,探讨一种能对多目标优化问题进行求解的遗传算法。采用Nash均衡的思想在多目标优化的遗传算法,结合NSGA算法,提出一种能得到多个Pareto最优解的多目标优化算法。通过目标函数线性加权法、NSGA对函数进行了试验分析,对部分自变量进行固定,对其他的自变量进行优化,对Pareto最优解进行持续优化,进而实现加速算法的收敛,从实验中得出了这种算法具有较快的收敛性,但是其运行时间和NSGA相比没有多少改善。     

基于多目标遗传算法的星载天线干扰抑制算法

提出了一种基于多目标遗传算法的星载天线干扰抑制算法，该算法在射频端通过调节权系数进行输出功率判决从而实现波束形成。文中引入多目标优化问题Pareto最优解的概念，采用了无支配性排序遗传算法（NSGA-Ⅱ）来搜索干扰调零权值的Pareto最优解集，充分发挥这种先进多目标遗传算法的高内在并行性、强鲁棒性以及能够不断优化最优解集的优势，较好地兼顾了星载天线干扰抑制时干扰抑制深度与主波束保形这一对矛盾问题。最后提出了归一化双目标函数加权选择最优调零权的方法从Pareto最优解集中选择一组符合决策者偏好的最优调零权。计算机仿真实验证明，文中所提出的算法具有较好的干扰抑制能力和主波束保形效果。     

基于余弦距离的多目标粒子群优化算法

针对粒子群优化算法具有的个体分布不均匀以及重复个体较多等缺陷,提出了一种基于余弦距离的多目标粒子群优化算法,该算法根据外部精英存储策略,利用余弦距离排挤机制来选取最分散的粒子,扩大 Pareto最优解集的收敛性和多样性,增强算法的全局寻优能力。通过采用标准多目标优化问题ZDTl～ZDT3进行仿真实验与粒子群算法、混沌粒子群算法、基于拥挤距离的多目标优化算法对比表明,该算法在Pareto前沿的收敛性和多样性方面均优于基于拥挤距离排挤机制,并具有较高的效率     

多宇宙并行量子遗传算法

提出了一种多宇宙并行量子遗传算法,并从理论上证明了算法的全局收敛性.算法中将所有的个体按照一定的拓扑结构分成一个个独立的子群体,称为宇宙;采用多状态基因量子比特编码方式来表达宇宙中的个体;采用通用的量子旋转门策略和动态调整旋转角机制对个体进行演化;采用量子非门实现量子变异以阻止早熟收敛;各宇宙独立演化,宇宙之间采用最佳移民和量子交叉操作来交换信息,提高算法的执行效率.将该算法与独立分量分析算法相结合,提出一种盲源分离新方法.仿真结果表明:新方法比采用常规遗传算法和量子遗传算法的盲源分离方法具有明显的高效性.     

基于DE和NSGA-Ⅱ的集装箱多式联运的路径优化算法

考虑集装箱多式联运过程中时间参数的不确定性,引入三角模糊数用于表示在途时间和中转时间,同时考虑班期产生的等待时间,将碳排放纳入考量范畴,建立基于时间、成本和碳排放量的多目标模型。提出基于DE和NSGA-Ⅱ的DE-NSGAⅡ多目标优化算法,该算法通过差分方法模拟NSGA-Ⅱ的交叉和变异算子及自适应控制策略调整交叉因子和缩放因子来提高算法搜索能力。实例表明,在求解组合优化问题时,DE-NSGAⅡ算法的Pareto最优解集分布更均匀,收敛速度更快,证明了DE-NSGAⅡ算法的可行性和优越性。     

基于自适应截断策略的约束多目标优化算法

为提高约束多目标优化问题所求解集的分布性和收敛性,该文提出基于自适应截断策略的约束多目标优化算法。首先,自适应截断选择策略能够保留Pareto最优解和约束违反度及目标函数值均较优的不可行解,不仅提高了种群多样性,而且能够较好地兼顾多样性和收敛性;其次,为增强算法的局部开发能力,在变异操作和交叉操作之后进行指数变异;最后,改进的拥挤密度估计方式只选择一部分Pareto最优解和距离较近的个体参与计算,不仅更加准确地反映解集的分布性,而且降低了计算量。通过在标准测试问题(CTP系列)上与其他4种优秀算法的对比结果可以得出,该算法所求解集的分布性和收敛性均得到一定提高,而且相较于对比算法在求解性能上具备一定的优势。     

基于IMOPSO算法的多目标多聚焦图像融合

目前的多聚焦图像融合方法对于融合模型的建立主要依赖于经验,其参数配置存在主观性.提出了一种基于IMOPSO算法的多目标多聚焦图像融合方法,简化了多聚焦图像融合模型,克服了参数配置对经验的依赖性.首先给出了多聚焦图像融合有效的评价指标,然后构造了统一的小波域多聚焦图像融合模型,最后以模型参数作为决策变量,采用IMOPSO算法进行多目标优化搜索.IMOPSO算法不但引入变异算子以避免早熟,而且引入拥挤算子,使Pareto优解尽可能均匀分布于Pareto前端,并采用一种新的自适应惯性权重提高寻优能力.实验结果表明,IMOPSO算法具有更快的收敛速度和更好的寻优能力,同时基于该算法的融合方法也实现了Pareto最优多聚焦图像融合.     

关于如何用角度信息引入决策者偏好的研究

在实际的多目标优化中,决策者通常只对少部分的Pareto最优解感兴趣。然而,传统多目标优化算法关注整个Pareto最优面上的解集,这不仅需要花费大量计算时间在无用解的搜索上,同时决策者也很难从众多解中选出符合自己偏好的解（特别是问题目标个数大于3时）。为此,本文提出了一种利用个体间的角度关系的偏好多目标进化算法。该方法通过重新定义个体间的支配关系和聚集距离使那些离决策者偏好区域越近的个体优先被保留下来,从而引导种群趋近于决策者的偏好区域。     

一种非均匀分布问题分布性维护方法

 几乎所有多目标进化算法(multi-objective optimization evolutionary algorithm,MOEA)都是针对Pareto最优面为均匀分布问题而言.然而现实中很多问题Pareto最优面是非均匀分布的,决策者希望得到一个与Pareto最优面分布类似的解集.现存算法并不能有效解决该问题.对此,提出一种针对于非均匀分布多目标优化问题的维护方法(non-uniformly diversity maintenance method,NUDMM).该方法定义一个反映个体分布"规则"程度的指标——杂乱度,并设计一种降低种群杂乱度的方法,在未知Pareto最优面分布规律情况下有效剔除造成种群混乱的个体.通过与NSGA-II和SPEA2在不同维数下8个非均匀函数上对比实验,表明NUDMM在有效保持问题真实分布的同时,具有良好的收敛性.     

Shape optimization of corrugated coatings under grazing incidence using a genetic algorithm

We report on the use of a genetic algorithm (GA) to design optimal shapes for a corrugated coating under near-grazing incidence. A full-wave electromagnetic solver based on the boundary integral formulation is employed to predict the performance of the coating shape. In our GA implementation, we encode each shape of the coating into a binary chromosome. A two-point crossover scheme involving three chromosomes and a geometrical filter are implemented to achieve efficient optimization. A standard magnetic radar absorbing material (MAGRAM) is used for the absorber coating. We present the optimized coating shapes depending on different polarizations. A physical interpretation for the optimized structure is discussed and the resulting shape is compared to conventional planar and triangular shaped designs. Next, we extend this problem from single to multiobjective optimization by using a Pareto GA. The optimization results with two different objectives, viz. height (or weight) of the coating versus absorbing performance, are presented.     

Multiobjective optimization design of Yagi-Uda antenna

An optimization method, such as the steepest gradient methods, could not easily obtain globally optimum solutions for devising antenna design parameters that allow the antenna to simultaneously improve multiple performances such as gain, sidelobe level, and input impedance. The genetic algorithm (GA) is suitable for empirically solving optimization problems and is effective in designing an antenna. In particular, this method can solve the multiobjective optimization problem using various Pareto-optimal solutions in an extremely efficient manner. In this paper, the Pareto GA, by which various Pareto-optimal solutions for each objective function (performance) can be obtained in a single trial of a numerical simulation and which enables the selection of parameters in accordance with the design requirement, is applied to the multiobjective optimization design of the Yagi-Uda antenna. The effectiveness of the Pareto GA was demonstrated by comparing the performances obtained by the Pareto GA with those of the previously reported values, which were obtained by the conventional GA, and with the values of the design benchmark reference.     

Design of electrically small wire antennas using a pareto genetic algorithm

We report on the use of a genetic algorithm (GA) in the design optimization of electrically small wire antennas, taking into account of bandwidth, efficiency and antenna size. For the antenna configuration, we employ a multisegment wire structure. The Numerical Electromagnetics Code (NEC) is used to predict the performance of each wire structure. To efficiently map out this multiobjective problem, we implement a Pareto GA with the concept of divided range optimization. In our GA implementation, each wire shape is encoded into a binary chromosome. A two-point crossover scheme involving three chromosomes and a geometrical filter are implemented to achieve efficient optimization. An optimal set of designs, trading off bandwidth, efficiency, and antenna size, is generated. Several GA designs are built, measured and compared to the simulation. Physical interpretations of the GA-optimized structures are provided and the results are compared against the well-known fundamental limit for small antennas. Further improvements using other geometrical design freedoms are discussed.     

Grid Implementation of a Parallel Multiobjective Genetic Algorithm for Optimized Allocation of Chlorination Stations in Drinking Water Distribution Systems: Chojnice Case Study

Solving multiobjective optimization problems requires suitable algorithms to find a satisfactory approximation of a globally optimal Pareto front. Furthermore, it is a computationally demanding task. In this paper, the grid implementation of a distributed multiobjective genetic algorithm is presented. The distributed version of the algorithm is based on the island algorithm with forgetting island elitism used instead of a genetic data exchange. The algorithm is applied to the allocation of booster stations in a drinking water distribution system. First, a multiobjective formulation of the allocation problem is further enhanced in order to handle multiple water demand scenarios and to integrate controller design into the allocation problem formulation. Next, the new grid-based algorithm is applied to a case study system. The results are compared with a nondistributed version of the algorithm.     

Multiobjective genetic optimization of diagnostic classifiers withimplications for generating receiver operating characteristiccurves

It is well understood that binary classifiers have two implicit objective functions (sensitivity and specificity) describing their performance. Traditional methods of classifier training attempt to combine these two objective functions (or two analogous class performance measures) into one so that conventional scalar optimization techniques can be utilized. This involves incorporating a priori information into the aggregation method so that the resulting performance of the classifier is satisfactory for the task at hand. We have investigated the use of a niched Pareto multiobjective genetic algorithm (GA) for classifier optimization. With niched Pareto GA's, an objective vector is optimized instead of a scalar function, eliminating the need to aggregate classification objective functions. The niched Pareto GA returns a set of optimal solutions that are equivalent in the absence of any information regarding the preferences of the objectives. The a priori knowledge that was used for aggregating the objective functions in conventional classifier training can instead be applied post-optimization to select from one of the series of solutions returned from the multiobjective genetic optimization. We have applied this technique to train a linear classifier and an artificial neural network (ANN), using simulated datasets. The performances of the solutions returned from the multiobjective genetic optimization represent a series of optimal (sensitivity, specificity) pairs, which can be thought of as operating points on a receiver operating characteristic (ROC) curve. All possible ROC curves for a given dataset and classifier are less than or equal to the ROC curve generated by the niched Pareto genetic optimization.     

Sidelobe reduction in array-pattern synthesis using geneticalgorithm

A simple and flexible genetic algorithm (GA) for pattern synthesis of antenna array with arbitrary geometric configuration is presented. Unlike conventional GA using binary coding and binary crossover, this approach directly represents the array excitation weighting vectors as complex number chromosomes and uses decimal linear crossover without a crossover site. Compared with conventional GAs, this approach has a few advantages: giving a clearer and simpler representation of the problem, simplifying chromosome construction, and totally avoiding binary encoding and decoding so as to simplify software programming and to reduce CPU time. This method also allows us to impose constraints on phases and magnitudes of complex excitation coefficients for preferable implementation in practice using digital phase shifters and digital attenuators. Successful applications show that the approach can be used as a general tool for pattern synthesis of arbitrary arrays     

Multiobjective programming using uniform design and genetic algorithm

The notion of Pareto-optimality is one of the major approaches to multiobjective programming. While it is desirable to find more Pareto-optimal solutions, it is also desirable to find the ones scattered uniformly over the Pareto frontier in order to provide a variety of compromise solutions to the decision maker. We design a genetic algorithm for this purpose. We compose multiple fitness functions to guide the search, where each fitness function is equal to a weighted sum of the normalized objective functions and we apply an experimental design method called uniform design to select the weights. As a result, the search directions guided by these fitness functions are scattered uniformly toward the Pareto frontier in the objective space. With multiple fitness functions, we design a selection scheme to maintain a good and diverse population. In addition, we apply the uniform design to generate a good initial population and design a new crossover operator for searching the Pareto-optimal solutions. The numerical results demonstrate that the proposed algorithm can find the Pareto-optimal solutions scattered uniformly over the Pareto frontier.     

基于极坐标变换的改进NSGA-II算法

在实际工程中存在着大量的多目标优化问题,而由于大部分多目标优化问题有无穷多个最优解,且传统的数学方法如梯度下降法和牛顿法,无法求解一些不可微或表达式过于复杂的多目标优化问题。为避免以上局限,NSGA-II作为求解多目标优化问题的代表算法被提出,但NSGA-II算法仍存在着一些不足,如变异算子功能过于简单,降低了Pareto最优解的多样性。为增加Pareto最优解的多样性,文中设计了一种基于极坐标变换的改进NSGA-II算法,该算法可使得Pareto最优解分布更加均匀,并最终通过标准的测试函数验证了算法的有效性。     

An Improved Genetic Algorithm with Quasi-Gradient Crossover

The convergence of genetic algorithm is mainly determined by its core operation crossover operation. When the objective function is a multiple hump function, traditional genetic algorithms are easily trapped into local optimum, which is called premature conver- gence. In this paper, we propose a new genetic algorithm with improved arithmetic crossover operation based on gradient method. This crossover operation can generate offspring along quasi-gradient direction which is the Steepest descent direction of the value of objective function. The selection operator is also simplified, every individual in the population is given an opportunity to get evolution to avoid complicated selection algorithm. The adaptive mutation operator and the elitist strategy are also applied in this algorithm. The case 4 indicates this algorithm can faster converge to the global optimum and is more stable than the conventional genetic algorithms.