Surrogate-assisted global transfer optimization based on adaptive sampling strategy

Surrogate Models have emerged as a useful technique to study system performance in engineering projects, especially engineering optimization. Previous research has focused on developing more efficient surrogate models and their application to practical problems. However, due to the scarcity of training data in the model and the lack of inheritance of similar information, the surrogate model of new projects is usually constructed from scratch, and the optimization effect of engineering design may not be satisfactory. As the need to rapidly design serialized products increases significantly, one potential solution is to transfer prior knowledge of similar models. In this study, a new surrogate-assisted global transfer optimization (SGTO) framework is proposed. The framework consists of three stages: space division, adaptive samples estimation and dynamic transfer allocation. The new promising samples were labeled by the error, predicted value, sample density of the interactive information, and the anti-error deletion strategy was set. In this way, SGTO facilitates information transfer across projects, avoids learning new problems from scratch, and significantly reduces the computational burden. Through 17 benchmark cases and four engineering cases, the average performance of the framework is improved by 12.8%.     

一种基于Kriging模型的天线高维全局优化算法

传统的天线优化设计需要对大量的参数组合进行电磁仿真后才能得到最优结果,使得天线高维优化设计效率普遍较低。针对该问题,使用在参数空间均匀分布的少量样本及其仿真结果构建初始Kriging模型,优化循环中每代种群由高适应度个体和高离散性个体组成,依据Kriging模型预测的个体响应和不确定性,对进化后的下一代种群进行筛选,选择最优个体执行电磁仿真并更新Kriging模型。利用此方法优化一个6变量E形天线的工作频点,相比同类优化算法,所需的电磁仿真次数可减少80%左右。     

A global optimization method for semi-supervised clustering

In this paper, we adapt Tuy’s concave cutting plane method to the semi-supervised clustering. We also give properties of local optimal solutions of the semi-supervised clustering. Numerical examples show that this method can give a better solution than other semi-supervised clustering algorithms do.     

A modified hypervolume based expected improvement for multi-objective efficient global optimization method

The hypervolume indicator has been proved as an outstanding metric for the distribution of Pareto points, and the derived hypervolume based expected improvement (HVEI) has received a particular attention in the multi-objective efficient global optimization (EGO) method. However, the high computational cost has become the bottle neck which limits the application of HVEI on many objective optimization. Aiming at this problem, a modified version of HVEI (MHVEI) is proposed in this paper, which is easier to implement, maintains all the desired properties, and has a much lower computational cost. The theoretical study shows that the new criterion can be considered as a weighted integral form of HVEI, and it prefers the new point with a higher uncertainty compared with HVEI. The numerical tests show that the MHVEI performs similar as HVEI on the lower dimensional problem, and the advantage of MHVEI becomes more obvious as the dimension grows.     

A new unconstrained global optimization method based on clustering and parabolic approximation

A new unconstrained global optimization method based on clustering and parabolic approximation (GOBC-PA) is proposed. Although the proposed method is basically similar to other evolutionary and stochastic methods, it represents a significant advancement of global optimization technology for four important reasons. First, it is orders of magnitude faster than existing optimization methods for global optimization of unconstrained problems. Second, it has significantly better repeatability, numerical stability, and robustness than current methods in dealing with high dimensionally and many local minima functions. Third, it can easily and faster find the local minimums using the parabolic approximation instead of gradient descent or crossover operations. Fourth, it can easily adapted to any theoretical or industrial systems which are using the heuristic methods as an intelligent system, such as neural network and neuro-fuzzy inference system training, packing or allocation of objects, game optimization problems. In this study, we assume that the best cluster center gives the position of the possible global optimum. The usage of clustering and curve fitting techniques brings multi-start and local search properties to the proposed method. The experimental studies, such as performed on benchmark functions, a real world optimization problem and tuning the neural network parameters for classification problems, show that the proposed methodology is simple, faster and, it demonstrates a superior performance when compared with some state of the art methods.     

A global optimization method for nonlinear bilevel programmingproblems

Nonlinear two-level programming deals with optimization problems in which the constraint region is implicitly determined by another optimization problem. Mathematical programs of this type arise in connection with policy problems to which the Stackelberg leader-follower game is applicable. In this paper, the nonlinear bilevel programming problem is restated as a global optimization problem and a new solution method based on this approach is developed. The most important feature of this new method is that it attempts to take full advantage of the structure in the constraints using some recent global optimization techniques.     

基于Powell局部搜索策略的全局优化布谷鸟算法

为了解决布谷鸟搜索算法后期收敛速度慢、求解精度不高、易陷入局部最优等缺陷,提出了一种基于Powell局部搜索策略的全局优化布谷鸟搜索算法.算法将布谷鸟全局搜索能力与Powell方法的局部寻优性能有机地结合,并根据适应度值逐步构建精英种群候选解池在迭代后期牵引Powell搜索的局部优化,在保证求解速度、尽可能找到全局极值点的同时提高算法的求解精度.对52个典型测试函数实验结果表明,该算法相比于传统的布谷鸟搜索算法不仅寻优精度和寻优率有所提高,并且适应能力强、鲁棒性好,与最新提出的其他改进算法相比也具有一定的竞争优势.     

A whale optimization algorithm based on quadratic interpolation for high-dimensional global optimization problems

Whale Optimization Algorithm (WOA), as a new population-based optimization algorithm, performs well in solving optimization problems. However, when tackling high-dimensional global optimization problems, WOA tends to fall into local optimal solutions and has slow convergence rate and low solution accuracy. To address these problems, a whale optimization algorithm based on quadratic interpolation (QIWOA) is presented. On the one hand, a modified exploration process by introducing a new parameter is proposed to efficiently search the regions and deal with the premature convergence problem. On the other hand, quadratic interpolation around the best search agent helps QIWOA to improve the exploitation ability and the solution accuracy. Moreover, the algorithm tries to make a balance between exploitation and exploration. QIWOA is compared with several state-of-the-art algorithms on 30 high-dimensional benchmark functions with dimensions ranging from 100 to 2000. The experimental results show that QIWOA has faster convergence rate and higher solution accuracy than both WOA and other population-based algorithms. For functions with a flat or sharp bottom, QIWOA is difficult to find the global optimum, but it still performs best compared with other algorithms.     

A new filled function method for unconstrained global optimization

Many real world problems can be modelled as optimization problems. However, the traditional algorithms for these problems often encounter the problem of being trapped in local minima. The filled function method is an effective approach to tackle this kind of problems. However the existing filled functions have the disadvantages of discontinuity, non-differentiability or sensitivity to parameters which limit their efficiency. In this paper, we proposed a new filled function which is continuous and differentiable without any parameter to tune. Compared to discontinuous or non-differentiable filled functions, the continuous and differentiable filled function mainly has three advantages: firstly, it is not easier to produce extra local minima, secondly, more efficient local search algorithms using gradient information can be applied and thirdly, a continuous and differentiable filled function can be optimized more easily. Based on the new proposed filled function, a new algorithm was designed for unconstrained global optimization problems. Numerical experiments were conducted and the results show the proposed algorithm was more efficient.     

A 2-Opt based differential evolution for global optimization

Differential evolution (DE) is a simple and effective global optimization algorithm. It has been successfully applied to solve a wide range of real-world optimization problems. However, DE has shown some weaknesses, especially the long computational times because of its stochastic nature. This drawback sometimes limits its application to optimization problems. Therefore we propose the 2-Opt based DE (2-Opt DE) which is inspired by 2-Opt algorithms to accelerate DE. The novel mutation schemes of 2-Opt DE, DE/2-Opt/1 and DE/2-Opt/2 are substituted for mutation schemes of the original DE namely DE/rand/1 and DE/rand/2. We also provide a comparison of 2-Opt DE to DE. A comprehensive set of 19 benchmark functions is employed for experimental verification. The experimental results confirm that 2-Opt DE outperforms the original DE in terms of solution accuracy and convergence speed.     

A new algorithm based on differential transform method for solving multi-point boundary value problems

In this work, an efficient algorithm based on the differential transform method is applied to solve the multi-point boundary value problems. The solution obtained by using the proposed method takes the form of a convergent series with easily computable components. Several numerical examples, both linear and nonlinear, are given to testify the validity and applicability of the proposed method. Comparisons are made between the present method and the other existing methods.     

一种高品质优化的纹理采样滤波方法

提出了从一个Mipmap[1]中通过几种分辨率结合指定数目的纹理来创建高品质采样过滤器的方法。此方法能控制在读取每次采样时的纹理数量,以便扩展品质来匹配GPU的内存。为了找出最好的纹理集合表示一个给定的采样滤波器,采用基数约束最小二乘优化方法,并将优化的编码结果存放到一张表中,让它更容易地存储在GPU上。结果表明,用几个纹理读取能准确地重构滤波器,当使用每样本4个或更多的纹理时,本方法产生的图像质量优于三线性插值。     

Concurrent topology optimization for cellular structures with nonuniform microstructures based on the kriging metamodel

Structural and Multidisciplinary Optimization - This paper proposes a novel multiscale concurrent topology optimization for cellular structures with continuously varying microstructures in space to...     

一种求解非线性约束优化全局最优的新方法

本文提出了一种求解非线性约束优化的全局最优的新方法—它是基于利用非线性互补函数和不断增加新的约束来重复解库恩-塔克条件的非线性方程组的新方法。因为库恩-塔克条件是非线性约束优化的必要条件,得到的解未必是非线性约束优化的全局最优解,为此,本文首次给出了通过利用该优化问题的先验知识,不断地增加约束来限制全局最优解范围的方法,一些仿真例子表明提出的方法和理论有效的,并且可行的。     

An interval arithmetic method for global optimization

An interval arithmetic method is described for finding the global maxima or minima of multivariable functions. The original domain of variables is divided successively, and the lower and the upper bounds of the interval expression of the function are estimated on each subregion. By discarding subregions where the global solution can not exist, one can always find the solution with rigorous error bounds. The convergence can be made fast by Newton's method after subregions are grouped. Further, constrained optimization can be treated using a special transformation or the Lagrange-multiplier technique.     

A global optimization method for Landau gauge fixing in lattice QCD

An algorithm for gauge fixing to the Landau gauge in the fundamental modular region in lattice QCD is described. The method, a combination of an evolutionary algorithm with a steepest descent method, is able to solve the problem of the nonperturbative gauge fixing. The performance of the combined algorithm is investigated on 8⁴, β=5.7, and 16⁴, β=6.0, lattice SU(3) gauge configurations.     

Adaptive infill sampling criterion for multi-fidelity optimization based on Gappy-POD

This paper presents a reformulation of the “Gappy Proper Orthogonal Decomposition” (Gappy-POD) multi-fidelity modeling approach and proposes an enrichment criterion associated with an adaptive infill algorithm. The latter is here applied to the study of the flight domain of the RAE-2822 transonic airfoil at two different levels of accuracy to demonstrate its ability to detect areas in a two-dimensional design space where the surrogate model needs improvement to better drive the optimization process.     

A local adaptive sampling method for reliability-based design optimization using Kriging model

Reliability-based design optimization (RBDO) in practical applications is hindered by its huge computational cost during structure reliability evaluating process. Kriging-model-based RBDO is an effective method to overcome this difficulty. However, the accuracy of Kriging model depends directly on how to select the sample points. In this paper, the local adaptive sampling (LAS) is proposed to enhance the efficiency of constructing Kriging models for RBDO problems. In LAS, after initialization, new samples for probabilistic constraints are mainly selected within the local region around the current design point from each optimization iteration, and in the local sampling region, sample points are first considered to be located on the limit state constraint boundaries. The size of the LAS region is adaptively defined according to the nonlinearity of the performance functions. The computation capability of the proposed method is demonstrated using three mathematical RBDO problems and a honeycomb crash-worthiness design application. The comparison results show that the proposed method is very efficient.