On the benefits of populations for noisy optimization

It is known that, in the absence of noise, no improvement in local performance can be gained from retaining candidate solutions other than the best one. Yet, it has been shown experimentally that, in the presence of noise, operating with a non-singular population of candidate solutions can have a marked and positive effect on the local performance of evolution strategies. So as to determine the reasons for the improved performance, we have studied the evolutionary dynamics of the (micro ,lambda)-ES in the presence of noise. Considering a simple, idealized environment, we have developed a moment-based approach that uses recent results involving concomitants of selected order statistics. This approach yields an intuitive explanation for the performance advantage of multi-parent strategies in the presence of noise. It is then shown that the idealized dynamic process considered does bear relevance to optimization problems in high-dimensional search spaces.     

A benchmark of kriging-based infill criteria for noisy optimization

Responses of many real-world problems can only be evaluated perturbed by noise. In order to make an efficient optimization of these problems possible, intelligent optimization strategies successfully coping with noisy evaluations are required. In this article, a comprehensive review of existing kriging-based methods for the optimization of noisy functions is provided. In summary, ten methods for choosing the sequential samples are described using a unified formalism. They are compared on analytical benchmark problems, whereby the usual assumption of homoscedastic Gaussian noise made in the underlying models is meet. Different problem configurations (noise level, maximum number of observations, initial number of observations) and setups (covariance functions, budget, initial sample size) are considered. It is found that the choices of the initial sample size and the covariance function are not critical. The choice of the method, however, can result in significant differences in the performance. In particular, the three most intuitive criteria are found as poor alternatives. Although no criterion is found consistently more efficient than the others, two specialized methods appear more robust on average.     

Fibonacci multi-modal optimization algorithm in noisy environment

Noises are very common in practical optimization problems. It will cause interference on optimization algorithms and thus makes the algorithms difficult to find a true global extreme point and multiple local extreme points. For the problem, this paper proposes a Fibonacci multi-modal optimization (FMO) algorithm. Firstly, the proposed algorithm alternates between global search and local optimization in order not to fall into local optimum points and to retain multiple optimum points. And then, a Fibonacci regional scaling criterion is proposed in the FMO algorithm to alleviate the effects of noise, and the position of optimum point is determined according to its probability distribution under noise interference. In experiments, we evaluate the performance of the proposed FMO algorithm through 35 benchmark functions. The experimental results show that compared with Particle Swarm Optimization (PSO) algorithm, three improved versions of PSO, and Genetic algorithm (GA), the proposed FMO algorithm can gain more accurate location of optimum point and more global and local extreme points under noisy environment. Finally, an example of practical optimization in radio spectrum monitoring is used to show the performance of the FMO algorithm.     

A noisy self-organizing neural network with bifurcation dynamics for combinatorial optimization

The self-organizing neural network (SONN) for solving general "0-1" combinatorial optimization problems (COPs) is studied in this paper, with the aim of overcoming existing limitations in convergence and solution quality. This is achieved by incorporating two main features: an efficient weight normalization process exhibiting bifurcation dynamics, and neurons with additive noise. The SONN is studied both theoretically and experimentally by using the N-queen problem as an example to demonstrate and explain the dependence of optimization performance on annealing schedules and other system parameters. An equilibrium model of the SONN with neuronal weight normalization is derived, which explains observed bands of high feasibility in the normalization parameter space in terms of bifurcation dynamics of the normalization process, and provides insights into the roles of different parameters in the optimization process. Under certain conditions, this dynamical systems view of the SONN reveals cascades of period-doubling bifurcations to chaos occurring in multidimensional space with the annealing temperature as the bifurcation parameter. A strange attractor in the two-dimensional (2-D) case is also presented. Furthermore, by adding random noise to the cost potentials of the network nodes, it is demonstrated that unwanted oscillations between symmetrical and "greedy" nodes can be sufficiently reduced, resulting in higher solution quality and feasibility.     

Efficient multi-criteria optimization on noisy machine learning problems

Recent research revealed that model-assisted parameter tuning can improve the quality of supervised machine learning (ML) models. The tuned models were especially found to generalize better and to be more robust compared to other optimization approaches. However, the advantages of the tuning often came along with high computation times, meaning a real burden for employing tuning algorithms. While the training with a reduced number of patterns can be a solution to this, it is often connected with decreasing model accuracies and increasing instabilities and noise. Hence, we propose a novel approach defined by a two criteria optimization task, where both the runtime and the quality of ML models are optimized. Because the budgets for this optimization task are usually very restricted in ML, the surrogate-assisted Efficient Global Optimization (EGO) algorithm is adapted. In order to cope with noisy experiments, we apply two hypervolume indicator based EGO algorithms with smoothing and re-interpolation of the surrogate models. The techniques do not need replicates. We find that these EGO techniques can outperform traditional approaches such as latin hypercube sampling (LHS), as well as EGO variants with replicates.     

On multiobjective combinatorial optimization and dynamic interim hedging of efficient portfolios

A dynamic portfolio policy is one that periodically rebalances an optimally diversified portfolio to account for time‐varying correlations. In order to sustain target‐level Sharpe performance ratios between rebalancing points, the efficient portfolio must be hedged with an optimal number of contingent claim contracts. This research presents a mixed‐integer nonlinear goal program (MINLGP) that is directed to solve the hierarchical multiple goal portfolio optimization model when the decision maker is faced with a binary hedging decision between portfolio rebalance periods. The MINLGP applied to this problem is formed by extending the separable programming foundation of a lexicographic nonlinear goal program (NLGP) to include branch‐and‐bound constraints. We establish the economic efficiency of applying this normative approach to dynamic portfolio rebalancing by comparing the risk‐adjusted performance measures of a hedged optimal portfolio to those of a naively diversified portfolio. We find that a hedged equally weighted small portfolio and a hedged efficiently diversified small portfolio perform similarly when comparing risk‐adjusted return metrics. However, when percentile risk measures are used to measure performance, the hedged optimally diversified portfolio clearly produces less expected catastrophic loss than does its nonhedged and naively diversified counterpart.     

Swarm algorithms with chaotic jumps applied to noisy optimization problems

In this paper, we investigate the use of some well-known versions of particle swarm optimization (PSO): the canonical PSO with gbest model and lbest model with ring topology, the Bare bones PSO (BBPSO) and the fully informed particle swarm (FIPS) on noisy optimization problems. As far as we know, some of these versions like BBPSO and FIPS had not been previously applied to noisy functions yet. A hybrid approach which consists of the swarm algorithms combined with a jump strategy has been developed for static environments. Here, we focus on investigating the introduction of the jump strategy to the swarm algorithms now applied to noisy optimization problems. The hybrid approach is compared experimentally on different noisy benchmark functions. Simulation results indicate that the addition of the jump strategy to the swarm algorithms is beneficial in terms of robustness.     

Curvature estimation along noisy digital contours by approximate global optimization

In this paper, we introduce a new curvature estimator along digital contours, which we called global min-curvature (GMC) estimator. As opposed to previous curvature estimators, it considers all the possible shapes that are digitized as this contour, and selects the most probable one with a global optimization approach. The GMC estimator exploits the geometric properties of digital contours by using local bounds on tangent directions defined by the maximal digital straight segments. The estimator is then adapted to noisy contours by replacing maximal segments with maximal blurred digital straight segments. Experiments on perfect and damaged digital contours are performed and in both cases, comparisons with other existing methods are presented.     

On the robustness of median sampling in noisy evolutionary optimization

Evolutionary algorithms (EAs) are a sort of nature-inspired metaheuristics,which have wide applications in various practical optimization problems.In these prob...     

强噪声干扰下的对数极坐标空间边缘提取算法

准确提取对数极坐标空间的目标边缘信息是对数极坐标变换视觉不变性获得成功应用的前提和关键。由于传统的边缘提取算法无法满足强噪声干扰下的单像素精度要求,在主动轮廓模型和水平集方法的基础上,设计了一种独特的边缘提取算法。经融合Canny算子的水平集方法全局降噪,利用能量驱动的主动轮廓模型逐次演化逼近,提取可能的边缘曲线,通过改进型跟踪寻迹剔除虚假信息,即可得到最终的目标边缘。实验表明,该算法行之有效,边缘提取特征相似度达96%以上。     

噪声条件下基于粒子群优化的数字稳像方法*

当视频序列中同时存在随机噪声和随机晃动时,传统的数字稳像算法由于受到噪声干扰而无法有效消除视频序列中的随机晃动。为了稳定这种存在随机噪声的视频序列,提出了一种基于粒子群优化的数字稳像方法。首先,定义了衡量寻优结果适应度函数,即输入视频连续若干帧均值图像的能量;然后,算法利用粒子群优化策略来搜索视频序列的最优运动补偿向量;最后,实验分别使用模拟抖动视频和真实拍摄的视频来测试算法的性能。实验结果表明,当测试视频同时存在随机噪声和随机晃动时,该算法不仅能够有效消除视频的随机晃动,并且有效抑制了随机噪声。     

噪声环境下RSSI定位问题及其求解的果蝇优化算法

针对未知节点的定位过度依赖于接收信号强度指示（Received Signal Strength Indicator,RSSI）物理测量的精度问题,将传统RSSI定位模型转化为非约束期望值规划模型,进而设计随机环境下的新型果蝇优化算法寻找未知节点的位置。该算法利用弧形分组将果蝇群均衡划分为子群,对果蝇个体实施混合变异,加速寻优进程,提高收敛速度和寻优精度。比较性的数值实验显示,该算法的收敛速度快,对未知节点的定位精度高,其应用于RSSI定位问题是可行的。     

A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.     

求解供应链优化问题的广义遗传算法

供应链优化研究是供应链管理中的一个重要问题,也是一个难题,针对该问题,提出了一个新型供应链优化模型,并且构造了广义遗传算法对其求解,该算法融入了特殊的演化规则,克服了遗传算法局部收敛的缺陷,提高了全局收敛的能力,实验表明对供应链优化问题的求解,广义遗传算法优于传统的遗传算法和分枝界定法。     

混合多智能体遗传算法

综合多智能体的局部感知能力和遗传算法的强搜索能力,提出了一种混合多智能体遗传算法（HMAGA）。该方法构造了启发式搜索和混合交叉策略完成智能体之间的竞争和合作,综合凸变异和局部搜索体现智能体的自学习特性,通过智能体之间的相互作用来达到信息扩散的目的,最终收敛到全局最优解。在多组不同类型函数上的仿真实验结果表明,该算法具有良好的性能,特别是对于复杂的合成函数。     

Optimality criteria for comparing efficient portfolios

A set of criteria for comparing efficient portfolios is critically reviewed here to show the inadequacy of the standard mean variance criterion used in traditional portfolio theory. These criteria emphasize, among other things, the following: (a) robustness, (b) multivariate distance as a measure of dissimilarity, and (c) diversity as an entropy measure related to information theory.     

基于块分类和字典优化的K-SVD图像去噪研究

基于K-奇异值分解（K-SVD）的图像去噪方法使用K-SVD算法训练得到的过完备字典对图像进行稀疏表示去噪,能够在去除噪声的同时较好地保持原始图像信息。但该方法缺少对图像结构特征的考虑;此外,K-SVD算法训练得到的字典中往往含有噪声原子,从而导致该方法在强噪声下去噪性能欠佳。针对这些局限性,提出一种新的去噪方法：基于块分类和字典优化的K-SVD去噪方法。首先通过图像块的分类训练得到与图像结构相适应的字典,能够更为稀疏地表示图像;然后通过噪声原子检测将字典原子分为噪声原子和非噪声原子,并对噪声原子进行替换,减弱噪声原子对去噪性能的影响,得到优化字典;利用优化字典对图像进行稀疏表示去噪。仿真实验表明,与非局部均值去噪、曲波去噪以及经典K-SVD去噪等算法相比,新方法能够取得更好的去噪结果。     

A robust optimization method for label noisy datasets based on adaptive threshold: Adaptive-k

The use of all samples in the optimization process does not produce robust results in datasets with label noise. Because the gradients calculated according to the losses of the noisy samples cause the optimization process to go in the wrong direction. In this paper, we recommend using samples with loss less than a threshold determined during the optimization, instead of using all samples in the mini-batch. Our proposed method, Adaptive-k, aims to exclude label noise samples from the optimization process and make the process robust. On noisy datasets, we found that using a threshold-based approach, such as Adaptive-k, produces better results than using all samples or a fixed number of low-loss samples in the mini-batch. On the basis of our theoretical analysis and experimental results, we show that the Adaptive-k method is closest to the performance of the Oracle, in which noisy samples are entirely removed from the dataset. Adaptive-k is a simple but effective method. It does not require prior knowledge of the noise ratio of the dataset, does not require additional model training, and does not increase training time significantly. In the experiments, we also show that Adaptive-k is compatible with different optimizers such as SGD, SGDM, and Adam. The code for Adaptive-k is available at GitHub.     

公共自行车调度路径优化算法

针对如何计算出每次派出的最佳运输车数和每辆运输车的最优路线的问题,提出了一种用于求解的数学模型,并提出了一种基于改进的混合智能水滴算法。提出了节约算子、启发式算子、最大最小调制机制、变邻域搜索的融合策略。实验证明:所提出的新算法可以求解所述问题,与其他一些算法相比,求解效率更高。