A GLOBALLY AND SUPERLINEARLY CONVERGENT TRUST REGION METHOD FOR LC^1 OPTIMIZATION PROBLEMS

A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.

Homotopy Continuous Method for Weak Efficient Solution of Multiobjective Optimization Problem with Feasible Set Unbounded Condition

In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.

RECURRENT NEURAL NETWORK MODEL BASED ON PROJECTIVE OPERATOR AND ITS APPLICATION TO OPTIMIZATION PROBLEMS

The recurrent neural network （RNN） model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.

Dual-Stage Hybrid Learning Particle Swarm Optimization Algorithm for Global Optimization Problems

Particle swarm optimization(PSO)is a type of swarm intelligence algorithm that is frequently used to resolve specific global optimization problems due to its rapid convergence and ease of operation.However,PSO still has certain deficiencies,such as a poor trade-off between exploration and exploitation and premature convergence.Hence,this paper proposes a dual-stage hybrid learning particle swarm optimization(DHLPSO).In the algorithm,the iterative process is partitioned into two stages.The learning strategy used at each stage emphasizes exploration and exploitation,respectively.In the first stage,to increase population variety,a Manhattan distance based learning strategy is proposed.In this strategy,each particle chooses the furthest Manhattan distance particle and a better particle for learning.In the second stage,an excellent example learning strategy is adopted to perform local optimization operations on the population,in which each particle learns from the global optimal particle and a better particle.Utilizing the Gaussian mutation strategy,the algorithm’s searchability in particular multimodal functions is significantly enhanced.On benchmark functions from CEC 2013,DHLPSO is evaluated alongside other PSO variants already in existence.The comparison results clearly demonstrate that,compared to other cutting-edge PSO variations,DHLPSO implements highly competitive performance in handling global optimization problems.

GLOBAL OPTIMIZATION OF PUMP CONFIGURATION PROBLEM USING EXTENDED CROWDING GENETIC ALGORITHM

An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective function contained several local optima and globaloptimality could not be ensured by all the traditional MINLP optimization method. The concepts ofspecies conserving and composite encoding are introduced to crowding genetic algorithm (CGA) formaintain the diversity of population more effectively and coping with the continuous and/or discretevariables in MINLP problem. The solution of three-levels pump configuration got from DICOPT++software (OA algorithm) is also given. By comparing with the solutions obtained from DICOPT++, ECPmethod, and MIN-MIN method, the ECGA algorithm proved to be very effective in finding the globaloptimal solution of multi-levels pump configuration via using the problem-specific information.

CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS

In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem using the existing algorithms about them.

Global Optimization for Solving Linear Non-Quadratic Optimal Control Problems

This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.

A NEW NONMONOTONE TRUST REGION ALGORITHM FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS

Based on the nonmonotone line search technique proposed by Gu and Mo （Appl. Math. Comput. 55, （2008） pp. 2158-2172）, a new nonmonotone trust region algorithm is proposed for solving unconstrained optimization problems in this paper. The new algorithm is developed by resetting the ratio ρk for evaluating the trial step dk whenever acceptable. The global and superlinear convergence of the algorithm are proved under suitable conditions. Numerical results show that the new algorithm is effective for solving unconstrained optimization problems.

Hybridizing grey wolf optimization with differential evolution for global optimization and test scheduling for 3D stacked SoC

A new meta-heuristic method is proposed to enhance current meta-heuristic methods for global optimization and test scheduling for three-dimensional （3D） stacked system-on-chip （SoC） by hybridizing grey wolf optimization with differential evo- lution （HGWO）. Because basic grey wolf optimization （GWO） is easy to fall into stagnation when it carries out the operation of at- tacking prey, and differential evolution （DE） is integrated into GWO to update the previous best position of grey wolf Alpha, Beta and Delta, in order to force GWO to jump out of the stagnation with DE＇s strong searching ability. The proposed algorithm can accele- rate the convergence speed of GWO and improve its performance. Twenty-three well-known benchmark functions and an NP hard problem of test scheduling for 3D SoC are employed to verify the performance of the proposed algorithm. Experimental results show the superior performance of the proposed algorithm for exploiting the optimum and it has advantages in terms of exploration.

A Filled Function with Adjustable Parameters for Unconstrained Global Optimization

A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two adjustable parameters. We will discuss the properties of the proposed filled function. Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.

GLOBAL CONVERGENCE OF TRUST REGION ALGORITHM FOR EQUALITY AND BOUND CONSTRAINED NONLINEAR OPTIMIZATION

This paper presents a trust region two phase model algorithm for solving the equality and bound constrained nonlinear optimization problem. A concept of substationary point is given. Under suitable assumptions,the global convergence of this algorithm is proved without assuming the linear independence of the gradient of active constraints. A numerical example is also presented.

Numerical Approach of Network Problems in Optimal Mass Transportation

In this paper, we focus on the theoretical and numerical aspects of network problems. For an illustration, we consider the urban traffic problems. And our effort is concentrated on the numerical questions to locate the optimal network in a given domain (for example a town). Mainly, our aim is to find the network so as the distance between the population position and the network is minimized. Another problem that we are interested is to give an numerical approach of the Monge and Kantorovitch problems. In the literature, many formulations (see for example [1-4]) have not yet practical applications which deal with the permutation of points. Let us mention interesting numerical works due to E. Oudet begun since at least in 2002. He used genetic algorithms to identify optimal network (see [5]). In this paper we introduce a new reformulation of the problem by introducing permutations . And some examples, based on realistic scenarios, are solved.

带隐藏约束昂贵黑箱问题的自适应代理优化方法

针对带隐藏约束的昂贵黑箱全局优化问题,提出采用自适应转换搜索策略的代理优化方法。在转换搜索子步中采用与已估值点个数相关的标准差在当前最优点附近通过随机扰动生成候选点,以更好地平衡局部搜索和全局搜索。为更好地近似真实黑箱目标函数,采用了自适应组合目标代理模型。在50个测试问题上进行了数值实验,计算结果说明了所提算法的有效性。

二维矩形Strip Packing问题的算法研究与改进

二维矩形Strip Packing问题的约束条件及目标函数与基本型二维矩形Packing问题类似,都是在有限的矩形容器中,有效地摆放各个矩形块,以最大化容器利用率为目标。为了解决这一NP-hard问题,该文在邓见凯、王磊提出的拟人型全局优化算法的基础上进行了深入的算法研究与改进。针对Strip Packing问题特点,提出了QHG(Quasi-Human Group)算法,其核心改进涵盖了多个方面,包括扩充初始点集合、删除和替换评价标准以及扩大邻域空间搜索范围。和单个局部极小值点的迭代相比,对局部极小值点集合进行迭代所生成布局优度更高,跳坑策略用于跳出局部极小值点,将搜索引向有希望的区域,优美度枚举有望进一步提高布局优度。通过这些措施,QHG算法更好地模拟人类决策过程,提高了全局搜索的效率。为评估QHG算法性能,对8组标准问题实例(C组、N组、NT组、CX组、NP组、ZDF组、2sp组、bwmv组)进行了大量实验。实验结果表明,QHG算法生成的布局优度优于当前国际文献中的几种较先进算法,展现了其在Strip Packing问题上的卓越性能。

SEMI-PROXIMAL POINT METHOD FOR NONSMOOTH CONVEX-CONCAVE MINIMAX OPTIMIZATION

Minimax optimization problems are an important class of optimization problems arising from modern machine learning and traditional research areas.While there have been many numerical algorithms for solving smooth convex-concave minimax problems,numerical algorithms for nonsmooth convex-concave minimax problems are rare.This paper aims to develop an efficient numerical algorithm for a structured nonsmooth convex-concave minimax problem.A semi-proximal point method(SPP)is proposed,in which a quadratic convex-concave function is adopted for approximating the smooth part of the objective function and semi-proximal terms are added in each subproblem.This construction enables the subproblems at each iteration are solvable and even easily solved when the semiproximal terms are cleverly chosen.We prove the global convergence of our algorithm under mild assumptions,without requiring strong convexity-concavity condition.Under the locally metrical subregularity of the solution mapping,we prove that our algorithm has the linear rate of convergence.Preliminary numerical results are reported to verify the efficiency of our algorithm.

具约束向量拟均衡问题的Global有效解的最优条件

向量均衡问题是运筹学的重要组成部分,其研究的主要内容包含各种解的存在性、稳定性、连续性、连通性、适定性、最优条件。向量均衡问题的解主要有有效解、弱有效解、强有效解、Global有效解、Henig有效解、超有效解。研究向量均衡问题各种有效解的最优条件是向量均衡问题的一个重要课题。首先,在实Hausdorff拓扑线性空间中引入具约束条件的向量拟均衡问题及其Global有效解的概念;其次,在实拓扑线性空间中分析了锥-凸、几乎锥-类凸与几乎锥-次类凸3种广义凸性的内在关系;最后,在3种广义凸性条件下借助于凸集分离定理给出了具约束条件的向量拟均衡问题Global有效解的充要条件。

全局求解线性比式和问题的迭代算法

本文针对一类线性比式和问题(SLR)提出一种迭代算法.首先将问题(SLR)转化为等价问题,然后通过提出的松弛技术将等价问题松弛为线性规划问题,并利用区域缩减技术加速算法的迭代.最后给出算法的收敛性以及复杂度,数值实验表明了算法的有效性.

带有延迟步长的循环BB梯度法

梯度法是求解大规模无约束优化问题的常用方法。将求解二次函数极小化问题的步长推广至一般无约束优化问题,通过使用延迟一步以及循环梯度法的思想,提出了循环Barzilai-Borwein梯度法(BB梯度法),并结合Zhang-Hager非单调线搜索技术,给出了求解一般无约束优化问题的循环BB梯度算法—CBBGM算法。在适当的假设下,CBBGM算法是全局收敛的,且目标函数为强凸函数时,该算法具有线性收敛速度。数值试验表明,与现有的方法相比,所提出的方法在计算上更高效。