Multi-objective optimization of inverse planning for accurate radiotherapy

The multi-objective optimization of inverse planning based on the Pareto solution set, according to the multi-objective character of inverse planning in accurate radiotherapy, was studied in this paper. Firstly,the clinical requirements of a treatment plan were transformed into a multi-objective optimization problem with multiple constraints. Then, the fast and elitist multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ)was introduced to optimize the problem. A clinical example was tested using this method. The results show that an obtained set of non-dominated solutions were uniformly distributed and the corresponding dose distribution of each solution not only approached the expected dose distribution, but also met the dosevolume constraints. It was indicated that the clinical requirements were better satisfied using the method and the planner could select the optimal treatment plan from the non-dominated solution set.     

Metric inequalities for routings on direct connections with application to line planning

We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the well-known feasibility condition for arc capacities in ordinary multi-commodity flows. The condition can be expressed in terms of a class of metric inequalities for routings on direct connections. We illustrate the concept on the example of the line planning problem in public transport and present an application to large-scale real-world problems.     

MODELING HARVEST SCHEDULING IN MULTIFUNCTIONAL PLANNING OF FORESTS FOR LONGTERM WATER YIELD OPTIMIZATION

In this study, wood production and hydrologic functions of forests were accommodated within a planning procedure for separate working circles (areas dedicated to certain forest functions) that were delineated according to an Ecosystem‐Based Functional Planning approach. Mixed integer goal programming was used as the optimization technique. The timing and scheduling of a maintenance cutting (partial harvest) was the decision variable in the modeling effort, and an original formulation was developed as a multiobjective planning procedure. Four sample planning strategies were developed and model outputs were evaluated according to these strategies. Spatial characteristics of stands were considered, and used to prohibit the regeneration of adjacent stands during the same time period. Because of the positive relationship between qualified water production and standing timber volume in the forest, the model attempts to maximize qualified water production levels by increasing standing volume stocks in the forest through the delay of regeneration activities.     

一类多体系统非完整运动最优规划的拟牛顿算法

研究带有非完整约束的一类多体系统运动规划问题。多体系统中的非完整约束通常是由不可积的速度约束或不可积的守恒律引起。在系统动量和动量矩守恒情况下,动力学方程降阶为非完整形式约束方程,系统的控制问题可转化为无漂移系统的非完整运动规划问题。文中首先导出具有多体开链系统的非完整运动模型。利用最优控制理论和最优化技术,采用输入参数化的方法将连续的最优控制问题转化为离散的最优控制问题,提出一种非完整多体系统运动规划的拟牛顿算法。最后将该方法用于自由漂浮的空间三连杆机构,仿真结果验证了该方法的有效性。     

电热耦合综合能源系统双阶段多目标规划研究

多能耦合系统是未来分布式能源供给方式的重要发展方向。为了实现电热耦合能源供给系统的合理规划、促进能源供给与消费的经济与环保的协调发展,提出一种面向电热耦合能源系统的综合能源系统双阶段规划优化方法。模型的第一阶段是在投资和环境最优的目标下实现电热耦合综合能源系统的合理规划,第二阶段是在考虑设备运行特性的基础上对规划的结果进行运行优化,以获得能源系统的最优运行方案,并从多个指标验证规划方案的合理性。利用NSGA-II算法求得模型进的帕累托解集,使用多准则妥协优化法从帕累托解集中决策出最优配置方案。仿真结果表明,提出的双阶段多目标综合能源规划方法能够实现能源供给系统的经济与环保双优。     

可再生能源系统的不确定性优化模型及求解

结合新提出的满意度方法和混合整数规划方法,给出了多态不确定性环境下可再生能源规划模型.该模型综合描述了多地区、多时期、多品种、多部门之间的可再生能源管理系统的复杂性、系统性、动态性和不确定性.最后的实例求解结果说明该模型能很好地反映能源安全性、系统可靠性与系统成本之间的关系,并能给出不同系统违反水平下的能源配置方式及增容计划,为决策者提供决策参考.     

An evidential approach to SLAM,path planning,and active exploration

Probability theory has become the standard framework in the field of mobile robotics because of the inherent uncertainty associated with sensing and acting. In this paper, we show that the theory of belief functions with its ability to distinguish between different types of uncertainty is able to provide significant advantages over probabilistic approaches in the context of robotics. We do so by presenting solutions to the essential problems of simultaneous localization and mapping (SLAM) and planning based on belief functions. For SLAM, we show how the joint belief function over the map and the robot's poses can be factored and efficiently approximated using a Rao-Blackwellized particle filter, resulting in a generalization of the popular probabilistic FastSLAM algorithm. Our SLAM algorithm produces occupancy grid maps where belief functions explicitly represent additional information about missing and conflicting measurements compared to probabilistic grid maps. The basis for this SLAM algorithm are forward and inverse sensor models, and we present general evidential models for range sensors like sonar and laser scanners. Using the generated evidential grid maps, we show how optimal decisions can be made for path planning and active exploration. To demonstrate the effectiveness of our evidential approach, we apply it to two real-world datasets where a mobile robot has to explore unknown environments and solve different planning problems. Finally, we provide a quantitative evaluation and show that the evidential approach outperforms a probabilistic one both in terms of map quality and navigation performance.     

The snowblower problem

We introduce the snowblower problem (SBP), a new optimization problem that is closely related to milling problems and to some material-handling problems. The objective in the SBP is to compute a short tour for the snowblower to follow to remove all the snow from a domain (driveway, sidewalk, etc.). When a snowblower passes over each region along the tour, it displaces snow into a nearby region. The constraint is that if the snow is piled too high, then the snowblower cannot clear the pile.We give an algorithmic study of the SBP. We show that in general, the problem is NP-complete, and we present polynomial-time approximation algorithms for removing snow under various assumptions about the operation of the snowblower. Most commercially available snowblowers allow the user to control the direction in which the snow is thrown. We differentiate between the cases in which the snow can be thrown in any direction, in any direction except backwards, and only to the right. For all cases, we give constant-factor approximation algorithms; the constants increase as the throw direction becomes more restricted. Our results are also applicable to robotic vacuuming (or lawnmowing) with bounded-capacity dust bin.     

Periodic maintenance and repair rate control in stochastic manufacturing systems

In this paper, we consider a periodic preventive maintenance, repair, and production model of a flexible manufacturing system with failure-prone machines, where the control variables are the repair rate and production rate. We use periodic preventive maintenance to reduce the machine failure rates and improve the productivity of the system. One of the distinct features of the model is that the repair rate is adjustable. Our objective is to choose a control process that minimizes the total cost of inventory/shortage, production, repair, and maintenance. Under suitable conditions, we show that the value function is locally Lipschitz and satisfies an Hamilton-Jacobi-Bellman equation. A sufficient condition for optimal control is obtained. Since analytic solutions are rarely available, we design an algorithm to approximate the optimal control problem. To demonstrate the performance of the numerical method, an example is presented.Research of this author was supported by the Natural Sciences and Engineering Research Council of Canada, Grant OGP0036444.Research of this author was supported in part by the University of Georgia.Research of this author was supported in part by the National Science Foundation, Grant DMS-92-24372.     

A dynamic production planning and scheduling algorithm for two products processed on one line

This paper presents a dynamic production planning and scheduling algorithm for two products processed on one line over a fixed time horizon. Production rates are assumed fixed, and restrictions are placed or inventory levels and production run lengths. The resulting problem is a nonlinear binary program, which is solved using an implicit enumeration strategy. The algorithm focuses on the run changeover period while developing tighter bounds on the length of the upcoming run to improve computational efficiency. About 99% pf 297 randomly generated problems with varying demand patterns are solved in less than 15 seconds of CPU time on a CDC Cyber 172 Computer. A mixed integer programming formulation of the generalized multi-product case under no-backlogging of demand is also given.