<i>ε</i>-Optimality in Multivalued Optimization

In this paper we apply the directional derivative technique to characterize D-multifunction, quasi D-multifunction and use them to obtain ε-optimality for set valued vector optimization problem with multivalued maps. We introduce the notions of local and partial-ε-minimum (weak) point and study ε-optimality, ε-Lagrangian multiplier theorem and ε-duality results.

Genetic algorithm for λ-optimal translation sequence of rough communication

In rough communication, because each agent has a different language and can not provide precise communication to each other, the concept translated among multi-agents will loss some information, and this results in a less or rougher concept. With different translation sequences the amount of the missed knowledge is varied. The λ-optimal translation sequence of rough communication, which concerns both every agent and the last agent taking part in rough communication to get information as much as he （or she） can, is given. In order to get the λ-optimal translation sequence, a genetic algorithm is used. Analysis and simulation of the algorithm demonstrate the effectiveness of the approach.

ON APPROXIMATE EFFICIENCY FOR NONSMOOTH ROBUST VECTOR OPTIMIZATION PROBLEMS

In this article,we use the robust optimization approach(also called the worst-case approach)for findingε-efficient solutions of the robust multiobjective optimization problem defined as a robust(worst-case)counterpart for the considered nonsmooth multiobjective programming problem with the uncertainty in both the objective and constraint functions.Namely,we establish both necessary and sufficient optimality conditions for a feasible solution to be anε-efficient solution(an approximate efficient solution)of the considered robust multiobjective optimization problem.We also use a scalarizing method in proving these optimality conditions.

改进蚁群算法在带时间窗车辆路径规划问题中的应用

车辆路径规划问题是当下发展和研究的热门问题之一,针对传统蚁群算法容易陷入局部最优的问题提出了3个改进方案。首先,在更新信息素阶段,只更新当前最优路径的信息素,降低信息素在路径上的积累速度,并增加一个奖励值保证前期迭代搜索的质量,同时为信息素的值设置了上下限。其次,随着迭代次数的增加,同时调整信息素挥发因子,逐步增大以适应蚁群搜索的信息素浓度变化。最后,加入了2-opt(2-optimization)算法、顺序交换策略、顺序插入策略来改进蚁群算法优化每次迭代得到的最优路径。将改进的算法应用在带时间窗的车辆路径问题(VRPTW)上,通过在Solomon Benchmark算例上进行实验,对比算法改进前后的路径最优解,从而证明改进后的算法性能更好。

Recoverability analysis of block-sparse representation

Recoverability of block-sparse signals by convex relaxation methods is considered for the underdetermined linear model. In previous works, some explicit but pessimistic recoverability results which were associated with the dictionary were presented. This paper shows the recoverability of block-sparse signals are associated with the block structure when a random dictionary is given. Several probability inequalities are obtained to show how the recoverability changes along with the block structure parameters, such as the number of nonzero blocks, the block length, the dimension of the measurements and the dimension of the block-sparse representation signal. Also, this paper concludes that if the block-sparse structure can be considered, the recoverability of the signals wil be improved. Numerical examples are given to il ustrate the availability of the presented theoretical results.

Design of Poiseuille Flow Controllers Using the Method of Inequalities

This paper investigates the use of the method of inequalities （MoI） to design output-feedback compensators for the problem of the control of instabilities in a laminar plane Poiseuille flow. In common with many flows, the dynamics of streamwise vortices in plane Poiseuille flow are very non-normal. Consequently, small perturbations grow rapidly with a large transient that may trigger nonlinearities and lead to turbulence even though such perturbations would, in a linear flow model, eventually decay. Such a system can be described as a conditionally linear system. The sensitivity is measured using the maximum transient energy growth, which is widely used in the fluid dynamics community. The paper considers two approaches. In the first approach, the MoI is used to design low-order proportional and proportional-integral （PI） controllers. In the second one, the MoI is combined with McFarlane and Glover＇s H∞ loop-shaping design procedure in a mixed-optimization approach.

First Passage Risk Probability Minimization for Piecewise Deterministic Markov Decision Processes

This paper is an attempt to study the minimization problem of the risk probability of piecewise deterministic Markov decision processes(PDMDPs)with unbounded transition rates and Borel spaces.Different from the expected discounted and average criteria in the existing literature,we consider the risk probability that the total rewards produced by a system do not exceed a prescribed goal during a first passage time to some target set,and aim to find a policy that minimizes the risk probability over the class of all history-dependent policies.Under suitable conditions,we derive the optimality equation(OE)for the probability criterion,prove that the value function of the minimization problem is the unique solution to the OE,and establish the existence ofε(≥0)-optimal policies.Finally,we provide two examples to illustrate our results.