超大规模集成电路布局的优化模型与算法

布局确定集成电路单元在芯片中的具体位置,在单元互不重叠的基础上优化一些性能指标。该问题是NP困难的组合优化问题,是超大规模集成电路物理设计的核心问题之一,对集成电路的性能指标,如线网可布通性、时延、功耗、电路可靠性等有重大影响。在现代的集成电路设计中,布局问题通常包含数百万个集成电路单元,以及大小相异的异质性模块,和各种复杂的布局约束。目前的超大规模集成电路布局算法通常分解为总体布局、布局合法化和详细布局三个步骤。根据近年来集成电路布局算法的研究进展,综述并分析集成电路的总体布局、布局合法化和详细布局的相关优化模型和算法,并展望进一步的研究方向。     

在VLSI布局中的Boole方法

用Boole方法,讨论那些与VLSI布局有关的图的嵌入,主要是在图的平面性一般理论、可定向性以及纵横布局等方面,似有异曲同工之妙.     

开关布局中本质不同的开关线路计算

通过对开关布局问题的研究，来解决一类象开关线路一样比较特殊，比较复杂的布局优化问题。从而寻找出这类问题的全局优化算法。本应用对称群对集合的作用，轨道，不动点等讨论了开关布局问题，给出了本质不同的开关线路个数的计算公式。     

结构布局几何可调的优化设计

对于结构优化设计问题其中X是设计变量;K是刚度矩阵;U是结构位移;F是外荷载;σ是应力.如果X分量含有结构布局的几何参数(如杆的长度、钣的面积、梁的长度等),则称为结构布局几何可调的优化设计问题.在上述问题中,h(X)=0是含有结构布局几何参数的等式关系.对于结构进行布局可调的优化设计,通常可以取得更为合理和良好的效果,然而为达到     

卫星舱内长方体群布局的优化模型及全局优化算法

本文研究了卫星舱内长方体群优化问题,建立了一个三维布局优化模型,并用图论,群论等工具克服了布局优化问题时断时续性质带来的困难,在此基础上构造了一个全局收敛的优化算法,文中所用的方法可用于求解类似问题。     

配送中心订单分拣系统中的拣货路径选择研究

订单分拣是订单履行流程中一项重要活动,分拣成本是配送中心成本的主要组成部分之一。订单分拣系统的设计需要考虑订单类型、产品特点、分拣策略、分拣区域的布局、分拣路径和储位选择等因素。本文主要评价各种拣货路径方法,作者利用方差分析中的最小显著性差异法.1602640178otmail.com对仿真结果进行多重比较。本文的研究结果显示,当订单规模较小时,单区布局下的最优启发式路径方法是最大间隙法;双区布局下的最优启发式路径是组合方法;而且双区布局下的各种路径方法更能节省分拣行走距离。这些结论有助于配送中心管理人员通过分析订单规模来改变分拣路径和布局,进而提高配送中心分拣效率。     

关于可靠性设施布局问题的近似算法

设施布局问题的研究始于20世纪60年代,主要研究选择修建设施的位置和数量,以及与需要得到服务的城市之间的分配关系,使得设施的修建费用和设施与城市之间的连接费用之和达到最小.现实生活中, 受自然灾害、工人罢工、恐怖袭击等因素的影响,修建的设施可能会出现故障, 故连接到它的城市无法得到供应,这就直接影响到了整个系统的可靠性.针对如何以相对较小的代价换取设施布局可靠性的提升,研究人员提出了可靠性设施布局问题.参考经典设施布局问题的贪婪算法、原始对偶算法和容错性问题中分阶段分层次处理的思想,设计了可靠性设施布局问题的一个组合算法.该算法不仅在理论上具有很好的常数近似度,而且还具有运算复杂性低的优点.这对于之前的可靠性设施布局问题只有数值实验算法, 是一个很大的进步.     

主通道位置不固定的设施布局问题多目标优化模型及算法

以物流中心设施布局问题为对象,提出了考虑出入口及主通道位置不固定情况下的设施布局问题的多目标优化模型并设计了其改进的遗传算法。首先,以物料搬运成本最小、活动关系密切度最大和面积利用率最大为目标,构建了考虑出入口位置不固定条件下的具有I型主通道的设施布局多目标优化数学模型。然后,设计了一种改进的遗传算法,包括:改进的编码、解码方法,追加了解码修正操作,基于惩罚函数策略的适应度函数等。实例测试表明,本算法的执行效率高而且结果稳定,优化效果好,布局结果紧凑适用。     

探井布局问题的遗传算法

首先建立探井布局问题的数学模型 .其次基于所建立的数学模型 ,给出了求解探井布局问题的遗传算法 ,并就一个具体问题进行了计算 .计算结果表明 ,用遗传算法求解探井布局问题耗时少 ,适应性好 ,且对于处理大规模的探井布局问题十分有效 .     

基于结构熵权法和HFWGHM算子的海上救援航空应急资源布局评价方法研究

研究海上救援航空应急资源的布局评价方法,构建了四阶段的资源布局评价模型.在评价结果分类的基础上,利用鱼骨图和专家法分析了影响布局效果的主要因素,构建了布局评价指标体系,并利用结构熵权法完成了指标的赋权;在评估中,综合考虑指标的权重和评价的模糊性,利用HFWGHM算子对指标分层集成.模型可以同时评估资源布局的总体效果和各细分指标的表现.     

带性能约束的矩形图元布局优化模型及不干涉性算法

本文讨论了以航天卫星仪器舱布局优化设计为背景的、带性能约束的矩形图元布局优化模型及不干涉性判别算法,主要讨论了模型的性质,并将这一模型转化为带反凸约束的凸规划问题。应用文献(4)给出的最优性条件及定界锥分拆算法,可求得带性能约束的矩形图元布局优化问题的全局最优解。     

A new mixed integer programming formulation for facility layout design using flexible bays

This paper presents a mixed-integer programming formulation to find optimal solutions for the block layout problem with unequal departmental areas arranged in flexible bays. The nonlinear department area constraints are modeled in a continuous plane without using any surrogate constraints. The formulation is extensively tested on problems from the literature.     

卫星舱三维布局优化模型及判断不干涉性算法

本以人造卫星仪器舱布局问题为背景。建立了在抛物圆柱体空间中带性能约束的长方体群的布局优化模型。分析模型中不干涉性约束的性质，利用凸集分离定理给出了等价的显式表达式，并构造了判断不干涉性的算法。     

Exact multiplicity results for variational inequalities involving pointwise constraints on the derivatives

This paper concerns a class of nonlinear variational problems involving pointwise constraints on the second derivatives. Our aim is to describe the set of data for which these problems have solutions and to analyse the structure of the set of solutions under suitable assumptions on the asymptotic behaviour of the nonlinear term. In particular, if this term is assumed to be convex, then we can specify the number of solutions and obtain exact multiplicity results.The existence, nonexistence and multiplicity results we obtain show that the presence of constraints of this kind produces some phenomena which are typical of nonlinear elliptic equations with “jumping” nonlinearities.     

Optimal cargo allocation on board a plane: a sequential linear programming approach

We examine a case study of an airline company whose problem is to plan cargo allocations on board a plane. Given the volume, weight, and structural constraints, the problem of finding the optimal load layout is formulated as a fractional programming problem. An algorithm is suggested to solve the linearized problem as a sequence of linear programming problems whose optimal solutions converge to the optimum (with a predetermined level of tolerance).     

Intelligent gradient search in linear programming

The simplex algorithm is still the best known and most frequently used way to solve LP problems. Khachian has suggested a method to solve these problems in polynomial time. The average behaviour of his method, however, is still inferior to the modern simplex based LP codes. A new gradient based approach which also has polynomial worst-case behaviour has been suggested by Karmarkar. This method was modified, programmed and compared with other available LP codes. It is shown that the numerical efficiency of Karmarkar's method compares favourably with other LP codes, particularly for problems with high numbers of variables and few constraints.     

On the unboundedness of facility layout problems

Facility layout problems involve the location of facilities in a planar arrangement such that facilities that are strongly connected to one another are close to each other and facilities that are not connected may be far from one another. Pairs of facilities that have a negative connection should be far from one another. Most solution procedures assume that the optimal arrangement is bounded and thus do not incorporate constraints on the location of facilities. However, especially when some of the coefficients are negative, it is possible that the optimal configuration is unbounded. In this paper we investigate whether the solution to the facility layout problem is bounded or not. The main Theorem is a necessary and sufficient condition for boundedness. Sufficient conditions that prove boundedness or unboundedness are also given.     

On stability in multiobjective programming — A stochastic approach

In this paper we assume that a deterministic multiobjective programming problem is approximated by surrogate problems based on estimations for the objective functions and the constraints. Making use of a large deviations approach, we investigate the behaviour of the constraint sets, the sets of efficient points and the solution sets if the size of the underlying sample tends to infinity. The results are illustrated by applying them to stochastic programming with chance constraints, where (i) the distribution function of the random variable is estimated by the empirical distribution function, (ii) certain parameters have to be estimated.     

Quadratic 0/1 optimization and a decomposition approach for the placement of electronic circuits

The placement problem in the layout design of electronic circuits consists of finding a nonoverlapping assignment of rectangular cells to positions on the chip so that wireability is guaranteed and certain technical constraints are met. This problem can be modelled as a quadratic 0/1-program subject to linear constraints. We will present a decomposition approach to the placement problem and give results above NP-hardness and the existence of-approximative algorithms for the involved optimization problems. A graph theoretic formulation of these problems will enable us to develop approximative algorithms. Finally we will present details of the implementation of our approach and compare it to industrial state of the art placement routines.     

Prices stabilization for inexact unit-commitment problems

A widespread and successful approach to tackle unit-commitment problems is constraint decomposition: by dualizing the linking constraints, the large-scale nonconvex problem decomposes into smaller independent subproblems. The dual problem consists then in finding the best Lagrangian multiplier (the optimal “price”); it is solved by a convex nonsmooth optimization method. Realistic modeling of technical production constraints makes the subproblems themselves difficult to solve exactly. Nonsmooth optimization algorithms can cope with inexact solutions of the subproblems. In this case however, we observe that the computed dual solutions show a noisy and unstable behaviour, that could prevent their use as price indicators. In this paper, we present a simple and easy-to-implement way to stabilize dual optimal solutions, by penalizing the noisy behaviour of the prices in the dual objective. After studying the impact of a general stabilization term on the model and the resolution scheme, we focus on the penalization by discrete total variation, showing the consistency of the approach. We illustrate our stabilization on a synthetic example, and real-life problems from EDF (the French Electricity Board).