查询词典 constrained optimization

The center coordinates of the n circles can then be obtained. The problem is reduced to a nonlinear constrained optimization problem of finding the minimum circumscribed circle for the n central points through regional optimization.

为求这平面点列的最小包容圆，将问题转化为非线性约束最优化问题，通过分区优化搜索算法求解目标。

In addition, we introduce the application of this algorithm in function optimization, constrained optimization and parameter optimization.

并介绍了这种新算法在函数优化、约束优化和参数优化问题中的具体应用。

This is the optimization method in a way, is a condition for constrained optimization.

详细说明：这个是优化方法中的一种方法，，是一种用于带约束条件的优化。

A theorem of the alternative for the generalized subconvexlike set-valued maps is established using the separation theorem of convex sets in a Banach spaces, the concept of weak Benson proper efficient elements for a vector optimization problem is introduced, and the optimality necessary and sufficient Lagrange conditions for a vector set-valued map constrained optimization problem with the weak Benson proper efficiency is developed, with which the optimality Lagrange conditions for a nonconvex vector top-base constrained optimization of set-valued maps with the Benson proper efficiency are obtained.

刘莹 ，刘三阳，盛宝怀运用凸集分离定理对广义锥次类凸集值映射建立了一种择一性定理。引入向量优化弱Benson真有效元的概念，对带约束的非凸向量集值优化问题建立了在弱Benson真有效意义下有效元应满足Lagrange乘子型的必要及充分条件，并用这一结果建立了多目标主从非凸向量集值优化在弱Benson真有效意义下最优解的Lagrange乘子型充要条件。

The uniformity degree and rank of the population are given to measure the distribution and quality of the solutions in the population based on the characteristic. Using the uniform degree of the population as objective function and the rank as the constrained condition, the bi-objective optimization problem is transformed into a single objective constrained optimization problem. The computational equations of the charge and force exerted on the particles are presented.

针对这一特点，定义了种群的均匀度和序值，来度量种群中解的分布和质量，将双目标优化问题转化为以均匀度为目标函数，序值为约束条件的单目标优化问题；设计了双目标优化问题粒子的电荷和受力的计算公式，提出了一种新的类电磁算法求解问题。

The experiment results on 13 well-known benchmark problems show that the proposed algorithm is capable of improving the search performance significantly in convergent speed and precision with respect to four techniques representative of the state-of-the-art in constrained optimization such as evolutionary algorithm based on homomorphous maps, artificial immune response constrained evolutionary strategy, constraint handling differential evolution, and evolutionary strategies based on stochastic ranking.

对13个标准测试问题的测试结果表明：与动态惩罚函数的进化算法、人工免疫响应约束进化策略、可行性规则的差分进化算法以及采用随机排序的进化策略相比，新算法在收敛速度和求解精度上均具有一定的优势。关键词：人工智能；差分进化算法；约束优化；随机排序

The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming.

这门课程的主题包括：无约束最优化方法，约束最优化方法，凸分析，拉格朗日松弛法，不可微函数最优化，以及在整数规划上的应用。

The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming.

这门课程的主题包括：无限制最适化方法，限制最适化方法，凸分析，拉格朗日松弛法，不可微分函数最适化，以及在整数规划上的应用。

This paper proposes an Improved Particle Swarm Optimization algorithm.IPSO adopts a new mutation operator and a new method that congregates some neighboring individuals to form multiple sub-populations in order to lead particles to explore new search space.Additionally,this algorithm incorporates a mechanism with a simple and easy penalty function to handle constraint.Thus,this algorithm has strong global exploratory capability and efficiency while being applied to solve nonlinear constrained optimization problems.

提出了一种改进的粒子群算法（Improved Particle Swarm Optimization，IPSO），使用了一种新型的变异策略，并在搜索过程中将部分邻近的个体聚集成核，从而形成多子群引导粒子探测新的搜索区域，采用了简单易行的罚函数约束处理机制，使算法在求解较难的非线性约束优化问题时具有很强的全局搜索能力与效率。

Firstly, on the basis of defining the characteristics of project and reviewing the mathematical models for RCPSP, we constructed the mathematical model for RCPSP under the condition that there is non-fixed duration and splittable tasks in project; In order to solve above model, we emphatically discussed the basic principle of the swarm intelligence algorithm--the particle swarm optimization algorithm as well as improvement research for current algorithm, and then proposed a new improved particle swarm optimization algorithm and analyzed its application process in the resource-constrained project scheduling problem; Lastly, in order to confirm the validity of the model and the algorithm, we took an experiment based on 108 instances that produced by problem instance generator which was developed by our team.

首先，在对RCPSP项目特征进行界定以及对项目进度优化模型回顾的基础之上，构建了基于活动工期不固定、任务可拆分特征的RCPSP的数学模型；为了求解上述模型，本文详细阐述粒子群优化算法(Particle Swarm Optimization，PSO)的基本原理以及当前对其改进的研究成果，提出了一种新的改进PSO算法，并对其在RCPSP的应用过程进行了设计；最后，为了检验模型的有效性及算法的优越性，基于梯队内部开发的案例生成器生成的108个算例，进行了仿真试验。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。