求解多目标优化问题的邻近牛顿法

针对一类特殊的多目标优化问题,其每个目标函数为一个二阶连续可微凸函数与一个真凸但不必可微函数之和,提出了邻近牛顿法.我们引入了带线搜索的邻近牛顿法和不带线搜索的邻近牛顿法.在适当的条件下,我们证明了由这两类算法产生的序列的每个聚点是多目标优化问题的Pareto平稳点.此外,我们给出了它们在约束多目标优化和鲁棒多目标优化...     

非光滑非凸多目标优化不动点方法

本文首次讨论了用不动点刻划的不可微多目标优化的最优性必要条件和充分条件，并研究了不动点算法求解此问题的方法及大范围收敛性．为不可微多目标优化研究提供了另一条新的途径．     

多目标优化正则条件的一个注记

给出带不等式约束的非光滑多目标优化问题正则条件的一个例子.通过该例,指出最近由Burachik和Rizvi利用线性化锥提出的可微多目标优化问题的正则条件不能利用Clarke导数推广到非光滑情形.     

LC^1类优化问题的Broyden算法的收敛性分析

本文讨论了利用Ｂｒｏｙｄｅｎ算法求解ＬＣ＾１类优化问题。所谓ＬＣ＾１类优化问题是指目标函数一阶连续可微，且它的导函数Ｌｉｐｓｃｈｉｔｚ连续。若假设目标函数是强凸的，讨论了该算法的全局收敛性；若假设目标函数是半光滑的，还给出了该算法的超线性收敛性分析。     

多目标装配线平衡的优化算法

在生产制造系统中，装配线的平衡需要针对多个目标，传统的装配线平衡问题，优化单一目标，忽略了目标之间的联系。优化一个目标的同时，劣化了另外一个目标。章研究了多目标装配线平衡问题，探讨了这些目标之间的联系，设计了禁忌搜索算法求解多目标装配线的平衡问题。章从生产管理系统的角度优化多目标装配线平衡，与单一目标相比，具有显的改进。     

一种改进的GDF多目标优化算法

本文提出一种交互式非线性多目标优化算法，该算法是ＧＤＦ多目标优化算法的改进，具有这样的特点：算法采用了既约设计空间策略，具有良好的收敛性；算法生成的迭代点是有效解；算法具有多种一维搜索准则；对于线性多目标问题，算法只需一次交互迭代即可示出多目标问题的最优解。     

一类广义凸多目标规划问题研究

首先引入了涉及高阶强Pre-invex函数的多目标优化问题m阶严格局部极小元的定义,在此基础上讨论了多目标优化问题的优化条件,最后研究了变分不等式的解与多目标优化问题高阶严格极小元之间的关系,其变分不等式的解正是多目标优化问题的高阶严格极小元,这些研究内容推广了Guneer-Bhatia给出的相关结论.     

不可微多目标优化非控解的最优性条件与对偶

本文对由一类局部Ｌｉｐｓｃｈｉｔｚ的ρ－ｉｎｖｅｘ函数所构成的不可微多目标优化问题进行了讨论；给出了最优性条件。并且对Ｗｏｌｆｅ、Ｗｅｉｒ－Ｍｏｎｄ和Ｃｒａｖｅｎ型对偶问题进行了研究，得到了相应的对偶定理。     

城市交通信号实时控制问题

以车辆平均延误时间最小为目标,建立单交叉口和线状区域的多交叉口信号实时配置的优化模型,结合外点罚函数法和模式搜索法求解,解决函数的不可微问题,算法简单可行.     

不确定条件下工程项目的多目标模糊均衡优化

在工程项目多目标优化问题研究基础上,研究不确定环境下工程项目多目标均衡优化问题.利用模糊数表示费用变化率和质量变化率,考虑模糊集的不同可能性水平,建立工程项目多目标模糊均衡优化模型,给出模型的求解方法和步骤,得到不同可能性水平下多目标优化问题的最优折衷解变化范围.优化方法使决策者能够根据决策风险的大小进行最优目标值的确定.     

A novel elitist multiobjective optimization algorithm: Multiobjective extremal optimization

Recently, a general-purpose local-search heuristic method called extremal optimization (EO) has been successfully applied to some NP-hard combinatorial optimization problems. This paper presents an investigation on EO with its application in numerical multiobjective optimization and proposes a new novel elitist (1 + λ) multiobjective algorithm, called multiobjective extremal optimization (MOEO). In order to extend EO to solve the multiobjective optimization problems, the Pareto dominance strategy is introduced to the fitness assignment of the proposed approach. We also present a new hybrid mutation operator that enhances the exploratory capabilities of our algorithm. The proposed approach is validated using five popular benchmark functions. The simulation results indicate that the proposed approach is highly competitive with the state-of-the-art multiobjective evolutionary algorithms. Thus MOEO can be considered a good alternative to solve numerical multiobjective optimization problems.     

Robustness to uncertain optimization using scalarization techniques and relations to multiobjective optimization

In this paper, we propose two kinds of robustness concepts by virtue of the scalarization techniques (Benson’s method and elastic constraint method) in multiobjective optimization, which can be characterized as special cases of a general non-linear scalarizing approach. Moreover, we introduce both constrained and unconstrained multiobjective optimization problems and discuss their relations to scalar robust optimization problems. Particularly, optimal solutions of scalar robust optimization problems are weakly efficient solutions for the unconstrained multiobjective optimization problem, and these solutions are efficient under uniqueness assumptions. Two examples are employed to illustrate those results. Finally, the connections between robustness concepts and risk measures in investment decision problems are also revealed.     

Vector Ordinal Optimization

Ordinal optimization is a tool to reduce the computational burden in simulation-based optimization problems. So far, the major effort in this field focuses on single-objective optimization. In this paper, we extend this to multiobjective optimization and develop vector ordinal optimization, which is different from the one introduced in Ref. 1. Alignment probability and ordered performance curve (OPC) are redefined for multiobjective optimization. Our results lead to quantifiable subset selection sizes in the multiobjective case, which supplies guidance in solving practical problems, as demonstrated by the examples in this paper.This paper was supported in part by Army Contract DAAD19-01-1-0610, AFOSR Contract F49620-01-1-0288, and a contract with United Technology Research Center (UTRC). The first author received additional funding from NSF of China Grants 60074012 and 60274011, Ministry of Education (China), and a Tsinghua University (Beijing, China) Fundamental Research Funding Grant, and the NCET program of China.The authors are grateful to and benefited from two rounds of reviews from three anonymous referees.     

Hard uncertainties in multiobjective layout optimization of photovoltaic power plants

This paper describes how to treat hard uncertainties defined by so-called uncertainty maps in multiobjective optimization problems. For the uncertainty map being set-valued, a Taylor formula is shown under appropriate assumptions. The hard uncertainties are modeled using parametric set optimization problems for which a scalarization result is given. The presented new approach for the solution of multiobjective optimization problems with hard uncertainties is then applied to the layout optimization of photovoltaic power plants. Since good weather forecasts are difficult to obtain for future years, weather data are really hard uncertainties arising in the planning process. Numerical results are presented for a real-world problem on the Galapagos island Isabela.     

Multiobjective GRASP with Path Relinking

In this paper we review and propose different adaptations of the GRASP metaheuristic to solve multiobjective combinatorial optimization problems. In particular, we describe several alternatives to specialize the construction and improvement components of GRASP when two or more objectives are considered. GRASP has been successfully coupled with Path Relinking for single-objective optimization. Moreover, we propose different hybridizations of GRASP and Path Relinking for multiobjective optimization. We apply the proposed GRASP with Path Relinking variants to two combinatorial optimization problems, the biobjective orienteering problem and the biobjective path dissimilarity problem. We report on empirical tests with 70 instances and 30 algorithms, that show that the proposed heuristics are competitive with the state-of-the-art methods for these problems.     

大规模系统的全局优化

本文讨论了可分非凸大规模系统的全局优化控制问题 .提出了一种 3级递阶优化算法 .该算法首先把原问题转化为可分的多目标优化问题 ,然后凸化非劣前沿 ,再从非劣解集中挑出原问题的全局最优解 .建立了算法的理论基础 ,证明了算法的收敛性 .仿真结果表明算法是有效的 .     

Multiobjective Search Algorithm with Subdivision Technique

This paper presents a multiobjective search algorithm with subdivision technique (MOSAST) for the global solution of multiobjective constrained optimization problems with possibly noncontinuous objective or constraint functions. This method is based on a random search method and a new version of the Graef-Younes algorithm and it uses a subdivision technique. Numerical results are given for bicriterial test problems.     

D-η-半预不变真拟凸多目标优化的最优性刻画

首先,举例验证了三种D-η-半预不变真拟凸映射的存在性;然后,在D-η-半严格(严格)半预不变真拟凸性下,得出了多目标优化问题的局部有效解为全局有效解,局部弱有效解为全局弱有效解,并举例验证了所得结果;最后,在D-η-严格半预不变真拟凸性下,建立了多目标优化问题的全局弱有效解和局部弱有效解的唯一性的刻画。     

D-η-半预不变真拟凸多目标优化的最优性刻画

首先,举例验证了三种D-η-半预不变真拟凸映射的存在性;然后,在D-η-半严格(严格)半预不变真拟凸性下,得出了多目标优化问题的局部有效解为全局有效解,局部弱有效解为全局弱有效解,并举例验证了所得结果;最后,在D-η-严格半预不变真拟凸性下,建立了多目标优化问题的全局弱有效解和局部弱有效解的唯一性的刻画。