求解约束优化的带偏好双目标优化方法

文章提出了一种求解约束优化问题的新方法。它把约束优化问题转化为双目标优化问题,一个目标是原问题的目标,另一目标是由约束条件转化得到。转化得到的双目标优化与一般的双目标优化问题不同在于它偏好那些使约束条件满足的最优解。我们利用动态权值将这一带有偏好的双目标优化转化为无约束的单目标优化,并使其满足偏好特性。我们对四个标准测试函数进行了数据仿真实验,实验结果表明该算法是有效的。     

Multiobjective optimization using an adaptive weighting scheme

A new Pareto front approximation method is proposed for multiobjective optimization problems (MOPs) with bound constraints. The method employs a hybrid optimization approach using two derivative-free direct search techniques, and intends to solve black box simulation-based MOPs where the analytical form of the objectives is not known and/or the evaluation of the objective function(s) is very expensive. A new adaptive weighting scheme is proposed to convert a multiobjective optimization problem to a single objective optimization problem. Another contribution of this paper is the generalization of the star discrepancy-based performance measure for problems with more than two objectives. The method is evaluated using five test problems from the literature, and a realistic engineering problem. Results show that the method achieves an arbitrarily close approximation to the Pareto front with a good collection of well-distributed nondominated points for all six test problems.     

Newton-conjugate gradient （CG） augmented Lagrangian method for path constrained dynamic process optimization

In this paper, a Newton-conjugate gradient (CG) augmented Lagrangian method is proposed for solving the path constrained dynamic process optimization problems. The path constraints are simplified as a single final time constraint by using a novel constraint aggregation function. Then, a control vector parameterization (CVP) approach is applied to convert the constraints simplified dynamic optimization problem into a nonlinear programming (NLP) problem with inequality constraints. By constructing an augmented Lagrangian function, the inequality constraints are introduced into the augmented objective function, and a box constrained NLP problem is generated. Then, a linear search Newton-CG approach, also known as truncated Newton (TN) approach, is applied to solve the problem. By constructing the Hamiltonian functions of objective and constraint functions, two adjoint systems are generated to calculate the gradients which are needed in the process of NLP solution. Simulation examples demonstrate the effectiveness of the algorithm.     

Solving Extremum Problems with Linear Fractional Objective Functions on the Combinatorial Configuration of Permutations Under Multicriteriality

The authors consider the extremum optimization problem with linear fractional objective functions on combinatorial configuration of permutations under multicriteria condition. Solution methods for linear fractional problems are analyzed to choose the approach to problem’s solution. A solution technique based on graph theory is proposed. The algorithm of the modified coordinate method’s subprogram with search optimization is described. It forms a set of points that satisfy additional constraints of the problem. The general solution algorithm without linearization of the objective function and it’s block diagram are proposed. Examples of the algorithm are described.     

Constrained efficient global optimization with support vector machines

This paper presents a methodology for constrained efficient global optimization (EGO) using support vector machines (SVMs). While the objective function is approximated using Kriging, as in the original EGO formulation, the boundary of the feasible domain is approximated explicitly as a function of the design variables using an SVM. Because SVM is a classification approach and does not involve response approximations, this approach alleviates issues due to discontinuous or binary responses. More importantly, several constraints, even correlated, can be represented using one unique SVM, thus considerably simplifying constrained problems. In order to account for constraints, this paper introduces an SVM-based ??probability of feasibility?? using a new Probabilistic SVM model. The proposed optimization scheme is constituted of two levels. In a first stage, a global search for the optimal solution is performed based on the ??expected improvement?? of the objective function and the probability of feasibility. In a second stage, the SVM boundary is locally refined using an adaptive sampling scheme. An unconstrained and a constrained formulation of the optimization problem are presented and compared. Several analytical examples are used to test the formulations. In particular, a problem with 99 constraints and an aeroelasticity problem with binary output are presented. Overall, the results indicate that the constrained formulation is more robust and efficient.     

基于均值改进控制策略的昂贵约束并行代理优化算法

针对具有黑箱特性的昂贵约束优化问题及工程中计算资源利用率不高问题,提出了新的基于均值改进控制策略的并行代理优化算法.该算法为了减少仿真建模计算负担,选取Kriging近似模型对目标函数和约束函数进行近似估计.在Kriging模型基础上,利用均值改进与新增试验样本间的不等关系构建具有距离特性的控制函数.算法的均值改进控制...     

Surrogate‐based methods for black‐box optimization

In this paper, we survey methods that are currently used in black‐box optimization, that is, the kind of problems whose objective functions are very expensive to evaluate and no analytical or derivative information is available. We concentrate on a particular family of methods, in which surrogate (or meta) models are iteratively constructed and used to search for global solutions.     

A hybrid approach to constrained global optimization

In this paper, we propose a novel hybrid global optimization method to solve constrained optimization problems. An exact penalty function is first applied to approximate the original constrained optimization problem by a sequence of optimization problems with bound constraints. To solve each of these box constrained optimization problems, two hybrid methods are introduced, where two different strategies are used to combine limited memory BFGS (L-BFGS) with Greedy Diffusion Search (GDS). The convergence issue of the two hybrid methods is addressed. To evaluate the effectiveness of the proposed algorithm, 18 box constrained and 4 general constrained problems from the literature are tested. Numerical results obtained show that our proposed hybrid algorithm is more effective in obtaining more accurate solutions than those compared to.     

Software prototype for solving multi-objective machining optimization problems: Application in non-conventional machining processes

For an effective and efficient application of machining processes it is often necessary to consider more than one machining performance characteristics for the selection of optimal machining parameters. This implies the need to formulate and solve multi-objective optimization problems. In recent years, there has been an increasing trend of using meta-heuristic algorithms for solving multi-objective machining optimization problems. Although having the ability to efficiently handle highly non-linear, multi-dimensional and multi-modal optimization problems, meta-heuristic algorithms are plagued by numerous limitations as a consequence of their stochastic nature. To overcome some of these limitations in the machining optimization domain, a software prototype for solving multi-objective machining optimization problems was developed. The core of the developed software prototype is an algorithm based on exhaustive iterative search which guarantees the optimality of a determined solution in a given discrete search space. This approach is justified by a continual increase in computing power and memory size in recent years. To analyze the developed software prototype applicability and performance, four case studies dealing with multi-objective optimization problems of non-conventional machining processes were considered. Case studies are selected to cover different formulations of multi-objective optimization problems: optimization of one objective function while all the other are converted into constraints, optimization of a utility function which combines all objective functions and determination of a set of Pareto optimal solutions. In each case study optimization solutions that had been determined by past researchers using meta-heuristic algorithms were improved by using the developed software prototype.     

Direct gradient projection method with transformation of variables technique for structural topology optimization

This paper proposes an efficient and reliable topology optimization method that can obtain a black and white solution with a low objective function value within a few tens of iterations. First of all, a transformation of variables technique is adopted to eliminate the constraints on the design variables. After that, the optimization problem is considered as aiming at the minimum compliance in the space of design variables which is supposed to be solved by iterative method. Based on the idea of the original gradient projection method, the direct gradient projection method (DGP) is proposed. By projecting the negative gradient of objective function directly onto the hypersurface of the constraint, the most promising search direction from the current position is obtained in the vector space spanned by the gradients of objective and constraint functions. In order to get a balance between efficiency and reliability, the step size is constrained in a rational range via a scheme for step size modification. Moreover, a grey elements suppression technique is proposed to lead the optimization to a black and white solution at the end of the process. Finally, the performance of the proposed method is demonstrated by three numerical examples including both 2D and 3D problems in comparison with the typical SIMP method using the optimality criteria algorithm.     

Multidisciplinary design optimization of mechanisms

The optimization of mechanisms is usually done in the field of mechanism itself. As a result the structural safety of the mechanism is neglected. To ensure the safety and improve the dynamic characteristics of mechanisms, a multidisciplinary design optimization procedure is proposed in this paper to synthesize optimum mechanisms. Two disciplines are involved in the multidisciplinary design optimization. They are the mechanism and the structure. The multi-level decomposition approach is chosen to generate optimum mechanisms. The optimized mechanisms not only satisfy mechanism and structural constraints but also have optimum objective function values in the two disciplines. In order to solve general mechanism design problems two widely used commercial softwares MSC/NASTRAN and MSC/ADAMS are integrated in the procedure to do the structural and the mechanism analysis, respectively. When the structural optimization is performed, a compromised approach is introduced to treat multiple configurations of mechanisms during operation. Two mechanism design problems are given to test the proposed method.     

一个基于分枝搜索的函数全局优化方法

本文给出了算法性能的一种度量，并且提出了一种全局优化算法策略，其基本框架（分枝随机搜索）类似于二分搜索，即将搜索区域划分成等测试的两个子区间（也可以多个），通过采样确定最有可能包含全局最优点的子区间，将其保留；去掉另一半，在剩下的区间重复这一过程。尽管这种算法其简单性几近随机算法和络点法，但理论分析和实验结果表明，其效率却高得多。     

Reliability optimization of a series system with multiple-choice and budget constraints using an efficient ant colony approach

This paper deals with a reliability optimization problem for a series system with multiple-choice and budget constraints. The objective is to choose one technology for each subsystem in order to maximize the reliability of the whole system subject to the available budget. This problem is NP-hard and could be formulated as a binary integer programming problem with a nonlinear objective function. In this paper, an efficient ant colony optimization (ACO) approach is developed for the problem. In the approach, a solution is generated by an ant based on both pheromone trails modified by previous ants and heuristic information considered as a fuzzy set. Constructed solutions are not guaranteed to be feasible; consequently, applying an appropriate procedure, an infeasible solution is replaced by a feasible one. Then, feasible solutions are improved by a local search. The proposed approach is compared with the existing metaheuristic available in the literature. Computational results demonstrate that the approach serves to be a better performance for large problems.     

A robust study of reliability-based optimization methods under eigen-frequency

Nowadays, the search in reliability-based design optimization is becoming an important engineering design activity. Traditionally for these problems, the objective function is to minimize a cost function while satisfying the reliability constraints. The reliability constraints are usually formulated as constraints on the probability of failure. This paper focuses on the study of a particular problem with the failure mode on vibration of structure. The difficulty in evaluating reliability constraints comes from the fact that modern reliability analysis methods are themselves formulated as an optimization problem. Solving such nested optimization problems is extremely expensive for large-scale multidisciplinary systems which are likewise computationally intensive. With this in mind research, we propose in this paper a new method to treat reliability-based optimization methods under frequencies constraint. The goal of this development has resolved just one problem of optimization and reduced the cost of computation. Aircraft wing design typically involves multiple disciplines such as aerodynamics and structure; this numerical example demonstrated the different advantages of the proposed method.     

Evolutionary programming techniques for constrained optimizationproblems

Two evolutionary programming (EP) methods are proposed for handling nonlinear constrained optimization problems. The first, a hybrid EP, is useful when addressing heavily constrained optimization problems both in terms of computational efficiency and solution accuracy. But this method offers an exact solution only if both the mathematical form of the objective function to be minimized/maximized and its gradient are known. The second method, a two-phase EP (TPEP) removes these restrictions. The first phase uses the standard EP, while an EP formulation of the augmented Lagrangian method is employed in the second phase. Through the use of Lagrange multipliers and by gradually placing emphasis on violated constraints in the objective function whenever the best solution does not fulfill the constraints, the trial solutions are driven to the optimal point where all constraints are satisfied. Simulations indicate that the TPEP achieves an exact global solution without gradient information, with less computation time than the other optimization methods studied here, for general constrained optimization problems     

基于混合粒子群算法的烧结配料优化

在引入惩罚函数和对目标函数进行适当修改的前提下,充分利用粒子群优化算法的全局搜索能力和约束条件下共轭梯度法的局部搜索能力,设计了烧结配料优化算法．利用惩罚函数方法将约束条件优化问题转化为无约束条件优化问题,然后利用粒子群优化算法进行寻优．当群体最优信息陷入停滞时将目标函数进行适当变化,继续利用共轭梯度法进行寻优．计算结果表明,采用该方法能够在提高混合料中的有用成分、降低有害成分的前提下,更多地降低生产成本．     

Modified harmony search optimization for constrained design problems

Constrained optimization is a major real-world problem. Constrained optimization problems consist of an objective function subjected to both linear and nonlinear constraints. Here a constraint handling procedure based on the fitness priority-based ranking method (FPBRM) is proposed. It is embedded into a harmony search (HS) algorithm that allows it to satisfy constraints. The HS algorithm is conceptualized using the musical process of searching for a perfect state of harmony. Here, the original heuristic HS was improved by combining both improved and global-best methods along with the FPBRM. The resulting modified harmony search (MHS) was then compared with the original HS technique and other optimization methods for several test problems.     

基于差分进化的缺陷样本生成算法

黑盒攻击主要是基于决策的攻击,但普遍存在查询次数多、敏感点难选择的问题,因此提出了基于差分进化的缺陷样本生成算法。算法将黑盒攻击定义为一个无约束优化问题,利用差分进化搜索图像敏感点,并优化基于深度学习模型决策定义的损失函数以及梯度计算方法,实现有效的黑盒攻击。在攻击成功率相同的条件下,在MNIST和CIFAR10数据集上的平均查询次数分别减少了28.3%和14.8%。     

An exact penalty function algorithm for solving general constrained parameter optimization problems

An exact penalty function type of algorithm is proposed to solve a general class of constrained parameter optimization problems. The proposed algorithm has the property that any solution obtained by it will always satisfy the problem constraints, and that it will obtain a solution to the constrained problem, within a given specified tolerance, by solving a single unconstrained problem, i.e. it is not necessary to solve a sequence of unconstrained optimization problems. The algorithm applies a modification of Rosenbrock's (Rosenbrock, 1960) polynomial boundary penalty function, and a negative exponential penalty function with moving parameters, to modify the objective function in the neighborhood of the constrained region; a robust unconstrained algorithm (Davison and Wong, 1975) is then used to solve the resulting unconstrained optimization problem. Some standard test functions are included to show the performance of the algorithhm. Application of the algorithm is then made to solve some computer-aided design problems occurring in the area of control system synthesis.     

A ranking selection-based particle swarm optimizer for engineering design optimization problems

Particle swarm optimization (PSO) algorithms have been proposed to solve optimization problems in engineering design, which are usually constrained (possibly highly constrained) and may require the use of mixed variables such as continuous, integer, and discrete variables. In this paper, a new algorithm called the ranking selection-based PSO (RSPSO) is developed. In RSPSO, the objective function and constraints are handled separately. For discrete variables, they are partitioned into ordinary discrete and categorical ones, and the latter is managed and searched directly without the concept of velocity in the standard PSO. In addition, a new ranking selection scheme is incorporated into PSO to elaborately control the search behavior of a swarm in different search phases and on categorical variables. RSPSO is relatively simple and easy to implement. Experiments on five engineering problems and a benchmark function with equality constraints were conducted. The results indicate that RSPSO is an effective and widely applicable optimizer for optimization problems in engineering design in comparison with the state-of-the-art algorithms in the area.