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91.
Robert-Paul Berretty Mark H. Overmars A. Frank van der Stappen 《Computational Geometry》1998,11(3-4):157-173
A fundamental task for an autonomous robot is to plan its own motions. Exact approaches to the solution of this motion planning problem suffer from high worst-case running times. The weak and realistic low obstacle density (L.O.D.) assumption results in linear complexity in the number of obstacles of the free space (Van der Stappen et al., 1997). In this paper we address the dynamic version of the motion planning problem in which a robot moves among polygonal obstacles which move along polylines. The obstacles are assumed to move along constant complexity polylines, and to respect the low density property at any given time. We will show that in this situation a cell decomposition of the free space of size O(n2(n) log2 n) can be computed in O(n2(n) log2 n) time. The dynamic motion planning problem is then solved in O(n2(n) log3 n) time. We also show that these results are close to optimal. 相似文献
92.
Summary Linear Porgramming models for stochastic planning problems and a methodology for solving them are proposed. A production planning
problem with uncertainty in demand is used as a test case, but the methodology presented here is applicable to other types
of problems as well. In these models, uncertainty in demand is characterized via scenarios. Solutions are obtained for each
scenario and then these individual scenario solutions are aggregated to yield an implementable non-anticipative policy. Such
an approach makes it possible to model correlated and nonstationary demand as well as a variety of recourse decision types.
For computational purposes, two alternative representations are proposed. A compact approach that is suitable for the Simplex
method and a splitting variable approach that is suitable for the Interior Point Methods. A crash procedure that generates
an advanced starting solution for the Simplex method is developed. Computational results are reported with both the representations.
Although some of the models presented here are very large (over 25000 constraints and 75000 variables), our computational
experience with these problems is quite encouraging. 相似文献
93.
We consider a location problem where the distribution of the existing facilities is described by a probability distribution
and the transportation cost is given by a combination of transportation cost in a network and continuous distance. The motivation
is that in many cases transportation cost is partly given by the cost of travel in a transportation network whereas the access
to the network and the travel from the exit of the network to the new facility is given by a continuous distance.
相似文献
94.
对 2 0 0 1年全国大学生数学建模竞赛的 B题——公交车调度问题进行了分析 ,建立了调度的目标规划模型及 0— 1规划模型 .在假设各站上、下车人数服从均匀分布的条件下 ,通过对模型的求解 ,求出了公交公司的最小运行车辆数 5 2辆 ,并给出了发车时刻表 ,其中上行方向运行 2 2 5班次 ,下行方向运行 2 2 0班次 .该模型简单 ,求解容易 ,能较好地考虑各方利益 相似文献
95.
Helene Gunnarsson Mikael Rönnqvist Dick Carlsson 《Journal of Mathematical Modelling and Algorithms》2007,6(1):25-45
In this paper we consider integrated planning of transportation of raw material, production and distribution of products of the supply chain at Södra Cell AB, a major European pulp mill company. The strategic planning period is one year. Decisions included in the planning are transportation of raw materials from harvest areas to pulp mills, production mix and contents at pulp mills, distribution of pulp products from mills to customer via terminals or directly and selection of potential orders and their levels at customers. Distribution is carried out by three different transportation modes; vessels, trains and trucks. We propose a mathematical model for the entire supply chain which includes a large number of continuous variables and a set of binary variables to reflect decisions about product mix and order selection at customers. Five different alternatives regarding production mix in a case study carried out at Södra Cell are analyzed and evaluated. Each alternative describes which products will be produced at which pulp mills. 相似文献
96.
Water resources planning based on complex system dynamics: A case study of Tianjin city 总被引:4,自引:0,他引:4
X.H. Zhang H.W. Zhang B. Chen G.Q. Chen X.H. Zhao 《Communications in Nonlinear Science & Numerical Simulation》2008,13(10):2328-2336
A complex system dynamic (SD) model focusing on water resources, termed as TianjinSD, is developed for the integrated and scientific management of the water resources of Tianjin, which contains information feedback that governs interactions in the system and is capable of synthesizing component-level knowledge into system behavior simulation at an integrated level, thus presenting reasonable predictive results for policy-making on water resources allocation and management. As for the Tianjin city, interactions among 96 components for 12 years are explored and four planning alternatives are chosen, one of which is based on the conventional mode assuming that the existing pattern of human activities will be prevailed, while the others are alternative planning designs based on the interaction of local authorities and planning researchers. Optimal mode is therefore obtained according to different scenarios when compared the simulation results for evaluation of different decisions and dynamic consequences. 相似文献
97.
关于圆形和方形城市工作区道路交通面积的解析与比较 总被引:1,自引:1,他引:0
对于城市规划来讲,事先预测其工作区内所需道路面积,以尽量避免实际交通网络中发生拥挤阻塞,具有重要意义,在本文,我们通过考虑一个城市通勤高峰时期的车辆交通情况,并通过利用走行中的车辆占用道路面积这一概念,基于一个相对现实的模型,从理论上对圆形方形城市工作区推导了所需的道路面积,并将两者加以比较,以发现与其交通网络结构相关的工作区的相对有效形状。 相似文献
98.
Unless procedures for the economic evaluation of flexible manufacturing technology are revamped, much of U.S. industry could repeat the experience of American automobile and steel companies from the recent past. The dynamic character of flexible manufacturing technology in terms of associated developments in microelectronics, a trend toward equipment modularity, and the increasing diversity of relevant markets make flexible manufacturing especially vulnerable to the weaknesses of conventional procedures for the justification of capital expenditures. Building on the work of V. Smith, M.I. Kamien and N.L. Schwartz, this paper presents optimization models from which economically reasonable plans can be derived for the implementation of flexible manufacturing technology. Although the assumptions of these models are not focused on the situation of a specific plant, model implications and the overall perspectives here on the economic evaluation of flexible system options should provide general guidance for manufacturing planners. 相似文献
99.
S. Shekhar 《Journal of Nonlinear Science》1996,6(2):105-138
Summary An application in robotics motivates us to characterize the evolution of a subset in state space due to a compact neighborhood
of an arbitrary dynamical system—an instance of a differential inclusion. Earlier results of Blagodat·skikh and Filippov (1986)
and Butkovskii (1982) characterize the boundary of theattainable set and theforward projection operator of a state. Our first result is a local characterization of the boundary of the forward projection ofa compact regular subset of the state space.
Let the collection of states such that the differential inclusion contains an equilibrium point be called asingular invariant set. We show that the fields at the boundary of the forward projection of a singular invariant set are degenerate under some
regularity assumptions when the state-wise boundary of the differential inclusion is smooth. Consider instead those differential
inclusions such that the state-wise boundary of the problem is a regular convex polytope—a piecewise smooth boundary rather
than smooth. Our second result gives conditions for theuniqueness andexistence of the boundary of the forward projection of a singular invariant set. They characterize the bundle of unstable and stable
manifolds of such a differential inclusion. 相似文献
100.
Cost minimization multi-product production problems with static production resource usage and internal product flow requirements have been solved by linear programming (LP) with input/output analysis. If the problem is complicated by interval resource estimates, interval linear programming (ILP) can be used. The solution of realistic problems by the above method is cumbersome. This paper suggests that linear goal programming (LGP) can be used to model a multi-product production system. LGP's unique modeling capabilities are used to solve a production planning problem with variable resource parameters. Input/output analysis is used to determine the technological coefficients for the goal constraints and is also used to derive an information sub-model that is used to reduce the number of variable resource goal constraints. Preliminary findings suggest that the LGP approach is more cost-efficient (in terms of CPU time) and in addition provides valuable information for aggregate planning. 相似文献