多目标最优化的交互投影梯度算法

本文借助拓广的投影梯度法的基本思想，利用由决策者提供的权衡比信息，构造了一个求解多目标最优化问题的交互规划算法，根据拓广的投影梯度法的原理，此法在约束条件退化情况下依然适用。     

多目标非线性规划的可行方向交互算法

本文提出一个求解多目标非线性规划问题的交互规划算法．在每一轮迭代中,此法仅要求决策者提供目标间权衡比的局部信息．算法中的可行方向是基于求解非线性规划问题的Topkis－Veinott法构千的．我们证明,在一定条件下,此算法收敛于问题的有效解．     

一个求解多目标群体决策问题的交互规划方法

本文引进决策个体偏爱强度函数和决策群体偏爱强度函数概念,分别给出了决策个体和决策群体的偏爱排序规则.由此,借助于各决策个体提供的权衡比信息,构造了一个求解多目标群体决策问题的交互规划方法.1.引言群体决策,就是联结决策群体中各决策个体的偏爱结构,对供选方案集作出群体偏爱结构判断,进行选优或偏爱排序的过程.     

求解约束优化问题的记忆梯度Goldstein-Lavintin-Polyak投影算法

给求解无约束规划问题的记忆梯度算法中的参数一个特殊取法,得到目标函数的记忆梯度G o ldste in-L av in tin-Po lyak投影下降方向,从而对凸约束的非线性规划问题构造了一个记忆梯度G o ldste in-L av in tin-Po lyak投影算法,并在一维精确步长搜索和去掉迭代点列有界的条件下,分析了算法的全局收敛性,得到了一些较为深刻的收敛性结果.同时给出了结合FR,PR,HS共轭梯度算法的记忆梯度G o ldste in-L av in tin-Po lyak投影算法,从而将经典共轭梯度算法推广用于求解凸约束的非线性规划问题.数值例子表明新算法比梯度投影算法有效.     

求解变分不等式问题的一类新算法

变分不等式问题(简称VIP)通过广义D-gap函数可以转化成无约束优化问题.在找到使优化问题目标函数达到最大的y值后,直接构造了一类下降方向,使算法避免了求解梯度问题.最后证明了这种算法具有全局收敛性.     

一种改进粒子群优化算法及其在投资规划中的应用

粒子群优化算法(PSO)是模拟生物群体智能的优化算法,具有良好的优化性能.但是群体收缩过快和群体多样性降低导致早熟收敛.本文引入了多样性指标和收敛因子模型来改进PSO算法,形成多样性收敛因子PSO算法(DCPSO),并且对现代资产投资的多目标规划问题进行了优化,简化了多目标规划的问题,并且表现出了比传统PSO算法更好性能.     

线性比式和规划问题的输出空间分支定界算法

本文旨在针对线性比式和规划这一NP-Hard非线性规划问题提出新的全局优化算法.首先,通过引入p个辅助变量把原问题等价的转化为一个非线性规划问题,这个非线性规划问题的目标函数是乘积和的形式并给原问题增加了p个新的非线性约束,再通过构造凸凹包络的技巧对等价问题的目标函数和约束条件进行相应的线性放缩,构成等价问题的一个下界线性松弛规划问题,从而提出了一个求解原问题的分支定界算法,并证明了算法的收敛性.最后,通过数值结果比较表明所提出的算法是可行有效的.     

数学规划与约束规划整合下的多目标分组排序问题研究

分组排序问题属于NP-难题, 单纯的数学规划模型或约束规划模型都无法在有效时间内解决相当规模的此类问题. 控制成本、缩短工期和减少任务延迟是排序问题的三个基本目标, 在实际工作中决策者通常需要兼顾三者, 并在 三者之间进行权衡. 多目标分组排序问题 的研究增强了排序问题的实际应用价值, 有利于帮助决策者处理复杂的多目标环境. 然而, 多目标的引入也增加了问题求解难度, 针对数学规划擅长寻找最优, 约束规划擅长排序的特点, 将两类方法整合起来, 提出一个基于Benders分解算法, 极大提高了此类问题的求解 效率.     

一类新的非线性比式和问题的分枝定界算法(英文)

对一类新的非线性比式和问题(SNR)提出分枝定界算法,该问题的研究还很少.首先,通过两层线性化技术,构造一个松弛线性规划,求解该线性规划问题,得到问题(SNR)最优值的下界.其次,介绍新的下界更新技术,证明所给算法的收敛性.数值试验显示了算法的可行性和有效性     

全局最优化问题的一个无参数的填充函数算法

本文研究了全局最优化问题.利用构造填充函数的方法,提出了一个新的无参数填充函数,它是目标函数的一个明确表达式.得到了一个新的无参数填充函数算法,数值试验结果表明该填充函数算法是有效的,从而推广了填充函数算法在求解全局最优化问题方面的应用.     

A modified objective function method for solving nonlinear multiobjective fractional programming problems

A new method is used for solving nonlinear multiobjective fractional programming problems having V-invex objective and constraint functions with respect to the same function η. In this approach, an equivalent vector programming problem is constructed by a modification of the objective fractional function in the original nonlinear multiobjective fractional problem. Furthermore, a modified Lagrange function is introduced for a constructed vector optimization problem. By the help of the modified Lagrange function, saddle point results are presented for the original nonlinear fractional programming problem with several ratios. Finally, a Mond-Weir type dual is associated, and weak, strong and converse duality results are established by using the introduced method with a modified function. To obtain these duality results between the original multiobjective fractional programming problem and its original Mond-Weir duals, a modified Mond-Weir vector dual problem with a modified objective function is constructed.     

SUBJECTIVE RADE-OFF RATE METHOD OF MULTIOBJECTIVE DECISION-MAKING

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Preference modelling by estimating local utility functions for multiobjective optimization

This paper is intended to design goal programming models for capturing the decision maker's (DM's) preference information and for supporting the search for the best compromise solutions in multiobjective optimization. At first, a linear goal programming model is built to estimate piecewise linear local utility functions based on pairwise comparisons of efficient solutions as well as objectives. The interactive step trade-off method (ISTM) is employed to generate a typical subset of efficient solutions of a multiobjective problem. Another general goal programming model is then constructed to embed the estimated utility functions in the original multiobjective problem for utility optimization using ordinary nonlinear programming algorithms. This technique, consisting of the ISTM method and the newly investigated search process, facilitates the identification and elimination of possible inconsistent information which may exist in the DM's preferences. It also provides various ways to carry out post-optimality analysis to test the robustness of the obtained best solutions. A modified nonlinear multiobjective management problem is taken as example to demonstrate the technique.     

AnUV-algorithm for semi-infinite multiobjective programming

In this paper, we give an application ofUV-decomposition method of convex programming to multiobjective programming, and offer a new algorithm for solving semi-infinite multiobjective programming. Finally, the superlinear convergence of the algorithm is proved.     

An interactive dynamic approach based on hybrid swarm optimization for solving multiobjective programming problem with fuzzy parameters

Real engineering design problems are generally characterized by the presence of many often conflicting and incommensurable objectives. Naturally, these objectives involve many parameters whose possible values may be assigned by the experts. The aim of this paper is to introduce a hybrid approach combining three optimization techniques, dynamic programming (DP), genetic algorithms and particle swarm optimization (PSO). Our approach integrates the merits of both DP and artificial optimization techniques and it has two characteristic features. Firstly, the proposed algorithm converts fuzzy multiobjective optimization problem to a sequence of a crisp nonlinear programming problems. Secondly, the proposed algorithm uses H-SOA for solving nonlinear programming problem. In which, any complex problem under certain structure can be solved and there is no need for the existence of some properties rather than traditional methods that need some features of the problem such as differentiability and continuity. Finally, with different degree of α we get different α-Pareto optimal solution of the problem. A numerical example is given to illustrate the results developed in this paper.     

Gradient projection and local region search for multiobjective optimisation

This paper presents a new method for multiobjective optimisation based on gradient projection and local region search. The gradient projection is conducted through the identification of normal vectors of an efficient frontier. The projection of the gradient of a nonlinear utility function onto the tangent plane of the efficient frontier at a given efficient solution leads to the definition of a feasible local region in a neighbourhood of the solution. Within this local region, a better efficient solution may be sought. To implement such a gradient-based local region search scheme, a new auxiliary problem is developed. If the utility function is given explicitly, this search scheme results in an iterative optimisation algorithm capable of general nonseparable multiobjective optimisation. Otherwise, an interactive decision making algorithm is developed where the decision maker (DM) is expected to provide local preference information in order to determine trade-off directions and step sizes. Optimality conditions for the algorithms are established and the convergence of the algorithms is proven. A multiobjective linear programming (MOLP) problem is taken for example to demonstrate this method both graphically and analytically. A nonlinear multiobjective water quality management problem is finally examined to show the potential application of the method to real world decision problems.     

Solving Convex MINLP Optimization Problems Using a Sequential Cutting Plane Algorithm

In this article we look at a new algorithm for solving convex mixed integer nonlinear programming problems. The algorithm uses an integrated approach, where a branch and bound strategy is mixed with solving nonlinear programming problems at each node of the tree. The nonlinear programming problems, at each node, are not solved to optimality, rather one iteration step is taken at each node and then branching is applied. A Sequential Cutting Plane (SCP) algorithm is used for solving the nonlinear programming problems by solving a sequence of linear programming problems. The proposed algorithm generates explicit lower bounds for the nodes in the branch and bound tree, which is a significant improvement over previous algorithms based on QP techniques. Initial numerical results indicate that the described algorithm is a competitive alternative to other existing algorithms for these types of problems.     

The linearization method: Principal concepts and perspective directions

The linearization method, for solving the general problem of nonlinear programming and its various modifications, is considered. On the basic ideas of the linearization method, the algorithms for solving the various problems of mathematical programming are constructed for (a) solving systems of equalities and inequalities, (b) multiobjective programming and (c) complementary problem.     

非线性比式和问题的全局优化算法

In this paper,a global optimization algorithm is proposed for nonlinear sum of ratios problem(P).The algorithm works by globally solving problem(P1) that is equivalent to problem(P),by utilizing linearization technique a linear relaxation programming of the (P1) is then obtained.The proposed algorithm is convergent to the global minimum of(P1) through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming.Nume...