Explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming

This work presents a new algorithm for solving the explicit/multi-parametric model predictive control (or mp-MPC) problem for linear, time-invariant discrete-time systems, based on dynamic programming and multi-parametric programming techniques. The algorithm features two key steps: (i) a dynamic programming step, in which the mp-MPC problem is decomposed into a set of smaller subproblems in which only the current control, state variables, and constraints are considered, and (ii) a multi-parametric programming step, in which each subproblem is solved as a convex multi-parametric programming problem, to derive the control variables as an explicit function of the states. The key feature of the proposed method is that it overcomes potential limitations of previous methods for solving multi-parametric programming problems with dynamic programming, such as the need for global optimization for each subproblem of the dynamic programming step.     

离散时间最优控制—–评论动态规划

阐述离散时间最优控制的特点.对比3种求解离散时间最优控制的解法,即:1)用非线性规划求解离散时间最优控制;2)用无约束优化求解离散时间最优控制;3)动态规划及其数值解.1)和2)都适用于多维静态优化,计算效率较高,是高级方法.在名义上,3)为动态优化.实际上,3)为一维分段无约束静态优化,计算效率较低,是初级方法.本文并用数字实例进一步阐明动态规划及其数值解在求解方面较差,故动态规划及其数值解已失去实用价值.在求解离散时间最优控制问题方面,无法与非线性规划求解相匹敌.     

Algorithms for solving the single-sink fixed-charge transportation problem

The single-sink fixed-charge transportation problem is an important subproblem of the fixed-charge transportation problem. Just a few methods have been proposed in the literature to solve this problem. In this paper, solution approaches based on dynamic programming and implicit enumeration are revisited. It is shown how the problem size as well as the search space of a recently published dynamic programming method can be reduced by exploiting reduced cost information. Additionally, a further implicit enumeration approach relying on solution concepts for the binary knapsack problem is introduced. The performance of the various solution methods is compared in a series of computational experiments.     

Algorithmic and Computational Aspects of Composite Concave Programming

In this paper we discuss the algorithmic and computational aspects of the parametric nonlinear optimization method c-programming. Our objective in looking at the method from this vantage point is twofold. First, to explain more clearly where c-programming sits in optimization theory. Second, to throw more light on the details of the collaboration that it forges with other optimization methods. The first objective is accomplished through an analysis of c-programming'ys genealogy. The latter is achieved by an examination of the basic structure of c-programming algorithms, and by reporting on extensive numerical experiments conducted with c-programming algorithms in collaboration with linear programming and dynamic programming techniques. These experiments very convincingly show that c-programming has the ability to significantly expand the scope of linear programming, dynamic programming, and possibly other optimization methods.     

Remarks on the application of dynamic programming to the optimal path timing of robot manipulators

In this paper, we investigate the use of the dynamic programming approach in the solution of the optimal path timing problem in robotics. This problem is computationally feasible because the path constraint reduces the dimension of the state in the problem to two. The Hamilton–Jacobi–Bellman equation of dynamic programming, a nonlinear first order partial differential equation, is presented and is solved approximately using finite difference methods. Numerical solution of this results in the optimal policy which can then be used to define the optimal path timing by numerical integration. Issues relating to the convergence of the numerical schemes are discussed, and the results are applied to an experimental SCARA manipulator. © 1998 John Wiley & Sons, Ltd.     

Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness

In this paper, we address a new Lagrangian relaxation (LR) method for solving the hybrid flowshop scheduling problem to minimize the total weighted tardiness. For the conventional LR, the problem relaxing machine capacity constraints can be decomposed into individual job-level subproblems which can be solved by dynamic programming. The Lagrangian dual problem is solved by the subgradient method. In this paper, a Lagrangian relaxation with cut generation is proposed to improve the Lagrangian bounds for the conventional LR. The lower bound is strengthened by imposing additional constraints for the relaxed problem. The state space reductions for dynamic programming for subproblems are also incorporated. Computational results demonstrate that the proposed method outperforms the conventional LR method without significantly increasing the total computing time.     

A dynamic programming method with lists for the knapsack sharing problem

In this paper, we propose a method to solve exactly the knapsack sharing problem (KSP) by using dynamic programming. The original problem (KSP) is decomposed into a set of knapsack problems. Our method is tested on correlated and uncorrelated instances from the literature. Computational results show that our method is able to find an optimal solution of large instances within reasonable computing time and low memory occupancy.     

基于数据的自学习优化控制:研究进展与展望

自适应动态规划(Adaptive dynamic programming, ADP)方法可以解决传统动态规划中的"维数灾"问题, 已经成为控制理论和计算智能领域最新的研究热点. ADP方法采用函数近似结构来估计系统性能指标函数, 然后依据最优性原理来获得近优的控制策略. ADP是一种具有学习和优化能力的智能控制方法, 在求解复杂非线性系统的最优控制问题中具有极大的潜力. 本文对ADP的理论研究、算法实现、相关应用等方面进行了全面的梳理, 涵盖了最新的研究进展, 并对ADP的未来发展趋势进行了分析和展望.     

移动AdHoc网络中基于动态规划法的OoS路由研究

在移动AdHoc网络中,为不同的多媒体应用需求提供QoS保证已经成为一个热点问题。目前,大多数的研究者都将研究点关注于QoS路由的度量选择上,而忽视了移动AdHoc网络自身的能量局限性的问题,而能量又是影响AdHoc网络一个极其关键的因素。因此,在本文中我们使用一种动态规划算法来解决AdHoc网络的电池约束。首先,我们构建了一个基于动态规划法的QoS路由模型,然后分析了该算法的时间复杂度,最后通过仿真验证了本文提出的改进算法的优越性。     

Methods based on discrete optimization for finding road network rehabilitation strategies

We study a dynamic optimization problem arising in the (long-term) planning of road rehabilitation activities. In this area one seeks a pavement resurfacing plan for a road network under budget constraints. Our main approach is to model this as an integer programming problem with underlying dynamic programming structure. We investigate properties of this model and propose a solution method based on Lagrangian relaxation where one gets subproblems that are shortest path problems. Some computational experiences based on realistic data are reported.     

一种基于衍生类的动态类修改方法

在面向对象语言的动态程序设计环境中,动态修改一个类时,会导致该类已经存在的那些活动对象难以处理的情况.本文提出了一种基于衍生类来实现类的动态修改的方法,并与其它方法进行了比较.     

递阶动态规划在大规模火力规划中的应用

在基本火力规划模型的基础上,建立了一种大规模火力规划问题的递阶模型,并运用大系统的递阶优化算法和动态规划优化算法,提出了一种新的求解该模型的递阶动态规划算法。该方法层次清晰,降低了计算复杂程度,并且适合并行计算,能迅速找到火力规划问题的最优火力分配方案和最优解。仿真算例表明了该方法的实用性。     

基于动态规划的商品装载问题及JAVA实现

如何装载商品使经济利益最大化是物流配载装箱问题中划分出的子问题。该子问题被抽象为0-1背包问题,根据动态规划算法建立数学模型,分析其优点,并用JAVA语言得以实现。最后给出测试实例,得出动态规划法具有高效性的特点,该算法可以广泛使用于物流领域。     

可重入混合流水车间调度的拉格朗日松弛算法

为了有效提升多重入车间的生产效率,考虑了实际生产中检查和修复过程对于逐层制造的可重入生产系统的重要性,提出了基于拉格朗日松弛算法的可重入混合流水车间的调度方法.首先进行了问题域的描述,并在此基础上以最小化加权完成时间为调度目标,建立数学规划模型.针对该调度问题提出了基于松弛机器能力约束的拉格朗日松弛算法,使松弛问题分解成工件级子问题,并使用动态规划方法建立递归公式,求解工件级子问题.随后,使用次梯度算法求解拉格朗日对偶问题.最后,对各种不同问题规模进行了仿真实验,结果表明,所提出的调度算法能够在合理的时间内获得满意的近优解.     

Solving efficiently the 0–1 multi-objective knapsack problem

In this paper, we present an approach, based on dynamic programming, for solving the 0–1 multi-objective knapsack problem. The main idea of the approach relies on the use of several complementary dominance relations to discard partial solutions that cannot lead to new non-dominated criterion vectors. This way, we obtain an efficient method that outperforms the existing methods both in terms of CPU time and size of solved instances.     

基于动态规划和遗传算法的混合算法研究

动态规划法和遗传算法是目前在水电站厂内经济运行中广泛应用的两种优化算法，文章提出了一种基于动态规划法和遗传算法的混合优化算法来分别解决大规模机组组合问题中空间最优化和时间最优化的计算机求解问题。避免了遗传算法计算速度缓慢的问题，又避免了动态规划法的“维数灾”问题。最后使用清江隔河岩水电站的4台机组的运行数据进行了仿真研究，并和完全使用动态规划法的结果进行了比较，获得了良好的效果，说明该混合优化算法对于厂内经济运行是一种可行的算法。     

Probabilistic dual heuristic programming-based adaptive critic

Adaptive critic (AC) methods have common roots as generalisations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, non-linear and non-stationary environments. In this study, a novel probabilistic dual heuristic programming (DHP)-based AC controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) AC method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterised by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the probabilistic critic network is then calculated and shown to be equal to the analytically derived correct value. Full derivation of the Riccati solution for this non-standard stochastic linear quadratic control problem is also provided. Moreover, the performance of the proposed probabilistic controller is demonstrated on linear and non-linear control examples.     

背包问题的算法设计与分析研究

背包问题是算法设计分析中的经典问题,本文采用贪婪法、动态规划法及递归法三种方法分别对背包问题、0-1背包问题及简单0-1背包问题进行算法设计和时间复杂度分析,给出具体算法设计和实现过程,并以具体实例详细描述不同方法求解问题解时算法基本思想,总结三种方法实现的优缺点并得出结论。     

背包问题的算法设计与分析研究

背包问题是算法设计分析中的经典问题,本文采用贪婪法、动态规划法及递归法三种方法分别对背包问题、0-1背包问题及简单0-1背包问题进行算法设计和时间复杂度分析,给出具体算法设计和实现过程,并以具体实例详细描述不同方法求解问题解时算法基本思想,总结三种方法实现的优缺点并得出结论。     

基于LINGO的优化问题动态规划法求解

介绍了LINGO优化软件的使用,指出LINGO在求解动态规划问题时可以不需要目标函数。基于LINGO分别对最短路问题和生产批量计划问题使用动态规划法进行了求解,给出了相应的LINGO求解代码,增强了学生对动态规划法的理解同时提高了使用优化软件编程解决问题的能力。