兑换零钱问题的转换求解方法

兑换零钱问题是计算机科学中的一个经典问题。它在自动售货机、生物化学等方面都有着广泛的应用。传统的动态规划算法求解兑换零钱问题的时间和空间复杂度都比较高,与需兑换零钱的金额相关。本文通过将兑换零钱问题转换为一系列子问题的方法,将兑换零钱问题的时间和空间复杂度都大幅降低。最后,本文通过理论和实验验证了算法的高效性。     

伪币问题的动态规划算法

本文在非常一般的情况下,讨论了著名的策略问题伪币问题,设计了解此问题的动态规划算法,并进一步对动态规划算法进行分析,给出了在一般情况下,伪币问题最优值的解析表达式,以及达到最优值的简洁的最优称量算法。     

找钱问题的动态规划解法

动态规划算法对许多实际问题是灵活和有效的。本文首先对一类找钱问题进行了分析和讨论,然后给出了谊问题的一种动态规划解法,最后对所给算法的复杂性进行了分析。实验结果验证了所提出算法的有效性。     

基于动态规划算法的最值问题分析

动态规划法是一种重要的求最优解的计算机程序设计算法,在各类软件设计大赛等各类程序设计大赛中广泛运用。文章通过设计合适的状态转移方程,分别使用两种算法对最值问题进行求解,并通过对求解过程及求解时间效率的对比实验验证了动态规划方法的高效性。     

最大子长方体问题的动态规划算法

动态规划程序设计策略对许多实际应用问题的解决是灵活和有效的。首先对一类最大子长方体问题进行了分析,并给出了该类问题的动态规划解法,最后对所给算法的复杂度进行了分析和讨论。实验结果验证了所提出方法的有效性。     

广义Hanoi塔问题的动态规划算法

基于动态规划算法思想，深入分析了广义Hanoi塔问题动态规划分割点的特征，给出动态规划分割点的简单计算公式，使得动态规划算法转化为一个非常简单的递归算法，由此可以迅速产生广义Hanoi塔问题的最优移动序列，从而彻底解决了广义Hanoi塔问题的最优移动序列问题．     

中国邮递员问题的动态规划算法研究

在动态规划的决策过程思想基础上,针对无向中国邮递员问题,提出了一个新的搜索算法CPDPA(Chinese postman decision process algorithm),首次实现了中国邮递员问题的动态规划求解．针对中国邮递员问题不能直接应用于决策思想,提出了弧点转换算法CEPA(convert edge to Doint algorithm),建立了该问题适用于决策的模型．进而针对这一模型,提出了多阶段决策过程模型转换算法MDPMCA(multistep decision process model convert algorithm),转换所得模型符合多阶段决策过程需求,可用CPDPA算法求解中国邮递员问题．对每一算法都给出了其网络应用实例．对算法的正确性和理论性做出了证明,并对最优性原理在中国邮递员问题上做了一定扩展．     

一类动态规划问题的解法与算法

本文给出了终止段未知的离散动态规划问题的解法和算法，并且结合经济问题的实际应用以及解法。     

实时系统资源分配的动态规划算法

本文提出了一个划分具有决定性的，实时性能的二级存储系统的最优算法。此算法在多项式时间内就能找出这一问题的最优解，并支持存储器资源的在线重新配置。     

方格取数问题的动态规划算法

动态规划算法对很多实际问题的解决是灵活和高效的.首先对方格取数问题进行分析,通过一条路径和两条路径选择的对比分析,得出了该问题的动态规划算法,并对该算法关键部分加以代码实现,最后对该算法的时间和空间复杂度进行分析和讨论,并对复杂度进行优化.试验的结果说明了该算法对于解决该类问题在时间效率上要明显优于贪心算法等一些算法.     

A dynamic programming algorithm for tree-like weighted set packing problem

In hierarchical organizations, hierarchical structures naturally correspond to nested sets. That is, we have a collection of sets such that for any two sets, either one of them is a subset of the other, or they are disjoint. In other words, a nested set system forms a hierarchy in the form of a tree structure. The task assignment problem on such hierarchical organizations is a real life problem. In this paper, we introduce the tree-like weighted set packing problem, which is a weighted set packing problem restricted to sets forming tree-like hierarchical structure. We propose a dynamic programming algorithm with cubic time complexity.     

An approximate dynamic programming approach to solving a dynamic, stochastic multiple knapsack problem

We model a multiperiod, single resource capacity reservation problem as a dynamic, stochastic, multiple knapsack problem with stochastic dynamic programming. As the state space grows exponentially in the number of knapsacks and the decision set grows exponentially in the number of order arrivals per period, the recursion is computationally intractable for large-scale problems, including those with long horizons. Our goal is to ensure optimal, or near optimal, decisions at time zero when maximizing the net present value of returns from accepted orders, but solving problems with short horizons introduces end-of-study effects which may prohibit finding good solutions at time zero. Thus, we propose an approximation approach which utilizes simulation and deterministic dynamic programming in order to allow for the solution of longer horizon problems and ensure good time zero decisions. Our computational results illustrate the effectiveness of the approximation scheme.     

Solving dynamic double row layout problem via combining simulated annealing and mathematical programming

Double row layout problem (DRLP) is to allocate facilities on two rows separated by a straight aisle. Aiming at the dynamic environment of product processing in practice, we propose a dynamic double-row layout problem (DDRLP) where material flows change over time in different processing periods. A mixed-integer programming model is established for this problem. A methodology combining an improved simulated annealing (ISA) with mathematical programming (MP) is proposed to resolve it. Firstly, a mixed coding scheme is designed to represent both of sequence of facilities and their exact locations. Secondly, an improved simulated annealing algorithm is suggested to produce a solution to DDRLP. Finally, MP is used to improve this solution by determining the optimal exact location for each facility. Experiments show that this methodology is able to obtain the optimal solutions for small size problems and outperforms an exact approach (CPLEX) for problems of realistic size.     

Improved dynamic programming and approximation results for the knapsack problem with setups

In this paper, we consider the 0–1 knapsack problem with setups. Items are grouped into families and if any items of a family are packed, this induces a setup cost as well as a setup resource consumption. We introduce a new dynamic programming algorithm that performs much better than a previous dynamic program and turns out to be also a valid alternative to an exact approach based on the use of an Integer Linear Programming (ILP) solver. Then we present a general inapproximability result. Furthermore, we investigate several relevant special cases that still permit fully polynomial‐time approximation schemes and others where the problem remains hard to approximate.     

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.     

基于两阶段求解算法的动态车辆调度问题研究

在分析需求动态变化的基础上,根据需求信息的提出顺序,将动态配送问题转换成不同时刻的静态车辆调度问题,建立基于时间轴的动态车辆调度模型;利用量子理论改进遗传算法,设计量子遗传算法;针对动态车辆调度问题实时性强的特点,设计＂初始优化阶段＋实时优化阶段＂的两阶段求解策略,通过信息更新插入动态需求客户,并对已产生的计划路径进行局部优化调整.通过仿真计算,验证了模型和算法的有效性.     

基于动态规划算法的矢量压缩方法研究与改进

将动态规划算法应用于矢量数据压缩是一种非常有效的优化压缩方法,可以得到压缩误差最小的压缩曲线,但是会导致局部失真明显。针对该缺点提出一种改进算法,通过在动态规划算法执行过程中设定阈值限制最大位移来防止局部失真,同时对A. KOLESNIKOV等提出的原动态规划算法公式的错误进行了纠正。实验表明,改进算法在保持原算法优势的同时,可以较好地解决压缩曲线局部失真问题。     

An approximate dynamic programming approach to convex quadratic knapsack problems

Quadratic knapsack problem (QKP) has a central role in integer and combinatorial optimization, while efficient algorithms to general QKPs are currently very limited. We present an approximate dynamic programming (ADP) approach for solving convex QKPs where variables may take any integer value and all coefficients are real numbers. We approximate the function value using (a) continuous quadratic programming relaxation (CQPR), and (b) the integral parts of the solutions to CQPR. We propose a new heuristic which adaptively fixes the variables according to the solution of CQPR. We report computational results for QKPs with up to 200 integer variables. Our numerical results illustrate that the new heuristic produces high-quality solutions to large-scale QKPs fast and robustly.     

动态规划-粒子群算法在水库优化调度中的应用

水库优化调度是一个典型的具有多约束条件的、动态的、非线性的优化问题。针对这些问题,利用动态规划-粒子群(DP-PSO)算法加以求解。利用动态规划中的多阶段最优策略原理,将水库优化调度问题转化为多阶段决策子问题,各个子问题采用粒子群算法优化求解。数值实验表明,在计算时段较多时,DP-PSO算法计算的可靠性明显优于一般的动态规划(DP)算法,在计算时间上,DP-PSO算法用时较动态规划-遗传算法(DP-GA)少。     

利用CPDH和动态规划算法的形状检索

用形状轮廓上点的坐标位置相对于形状重心位置的分布关系描述形状,提出一种极坐标下形状轮廓点分布直方图描述符(contour points distribution histogram),该描述符不仅符合人眼的视觉直观感受、计算简单,而且其本质上具有缩放和平移不变性。用动态规划算法(dynamic programming algorithm)来度量轮廓点分布直方图之间的距离,部分解决了轮廓点分布直方图对于旋转不变性的要求。在多个形状图像数据库中的实验结果表明,该方法在单目标封闭轮廓的形状图像检索中取得了良好效果。