交通网络建设序列的动态规划方法

交通网络建设序列优化是交通规划中一个重要问题。文章对交通网络设计及其建设序列问题的研究现状进行了分析。按照网络建设中规划者和用户间的关系,以交通网络建设序列下的各阶段系统总费用作为上层规划,以各阶段的交通流用户平衡模型作为下层规划,建立了双层规划模型。并依照问题的特点,采用动态规划的求解方法进行探讨,而下层模型则采用了基于路径搜索的GP算法进行求解。并针对网络规划算例进行了计算,针对固定和变动客流OD两种情况下的结果进行了分析。计算的结果表明,问题的双层规划模型和动态规划求解算法能够为路网规划决策提供支持。     

半无限规划离散化问题一个两阶段序列二次规划算法

本文研究了求解半无限规划离散化问题(P)的一个新的算法.利用序列二次规划(SQP)两阶段方法和约束指标集的修正技术,提出了求解(P)的一个两阶段SQP算法.算法结构简单,搜索方向的计算成本较低.在适当的条件下,证明了算法具有全局收敛性.数值试验结果表明算法是有效的.推广了文献[4]中求解(P)的算法.     

完全分层多目标规划的基线算法

本文采用基线算法求解完全分层多目标规划问题。给出了简单完全分层多目标规划基线算法的求解步骤，并对其进行了修正，从而得到完全分层多目标规划的宽容基线算法。并给出了两个计算实例。     

卫星数传接收规划模型与算法研究

作为对地观测卫星任务执行的两个重要阶段之一,数传接收的规划任务是一个具有多时间窗口、多优化目标和多资源约束的NP-Hard优化问题。中继星的引入为数据全天候近实时传输提供可能,同时也为数传规划提出新的问题。本文主要完成两项工作:第一,建立风险控制的卫星数传接收规划模型;第二,阐述基于遗传禁忌的模型求解方法,进一步采用分布式并行求解策略,改善了求解算法的收敛速度和鲁棒性。最后,通过STK提供基础仿真数据,验证了本文规划模型和求解算法的有效性。     

混合动力公交车能量控制策略的优化模型

针对混合动力公交车在循环工况内功率需求的特点,建立了未来功率需求贝叶斯预测模型;利用2-阶段随机动态规划模型将大规模的随机动态规划问题简化为多个小规模的随机动态规划问题和一个确定型动态规划问题;对于随机动态规划模型的求解,给出了稀疏表示的降维方法,将复杂的泛函极值问题转化为常规的随机动态优化问题,并采用分布估计算法和计算资源最优配置算法的计算机仿真优化算法对随机动态优化问题进行求解;给出了基于查表的在线控制策略,为模型的实际应用进行了有益的探索。     

运筹学中若干离散规划问题的相对差分搜索解法

运筹学中有很多离散规划问题。其中的线性规划通常用分枝定界法或割平面法，还有图上作业法求解。不论哪种方法工作量都不小，而且效率低；至于非线性规划大都是用动态规划法求解，也很麻烦、耗时。对于大规模问题，不论线性或非线性离散规划，现有解法都受到问题规模的限制；还有资源分配和背包问题至今没有见到解决方法。本文就是为了解决这些问题，提出了相对差分搜索算法。通过5个算例和其它文献中的一些算例计算验证了本法简单、快速、有效和精确，尤其不受问题规模的限制是其最大的优点。     

非线性背包问题的动态规划目标水平割算法

提出了求解非线性背包问题的一个动态规划目标水平割算法.通过引入替代约束公式将多约束问题转化为单个替代约束问题,由此结合目标水平割给出了一个收敛的动态规划算法,在解的过程中逐步消除对偶间隙,并确保在有限次迭代步内找到原问题的最优解.数值试验表明该方法的有效性.     

两阶段特殊结构混合0-1规划的分解算法

本文介绍了一种用于求解具有特殊结构的两阶段混合0-1规划问题的原始-对偶分解算法,并以CPLEX软件作为核心求解器将算法实现.该算法将原问题分解成两个相对简单的子问题,较传统分解算法有更平衡的分解结构和收敛性.实验数据表明,该算法在求解较大规模、稀疏度较大、耦合度较大的复杂两阶段下三角结构混合0-1规划问题时,相比CPLEX提供的分枝剪枝法,在时间效率上有明显提高.算法最后通过固定0-1变量的取值可以得到满足管理精度要求的近似最优解.     

多维多目标模糊优选动态规划及其在资源分配中的应用

将目前所研究的一维模糊优选动态规划扩展为多维模糊优选动态规划。在求解多维多阶段问题时,采用遗传算法与模糊动态规划法相结合进行求解,保证了优化变量的全局最优性。在其中权系数的处理中,本文采用了主客观综合评定的方法,保证了数据的合理性及准确性。并且文中用此方法解决了多维多阶段多目标的资源分配问题。     

0-1背包问题的蜂群优化算法

在项目决策与规划、资源分配、货物装载、预算控制等工作中,提出了0-1背包问题.0-1背包问题是组合优化中的典型NP难题,根据群集智能原理,给出一种基于蜂群寻优思想的新算法—蜂群算法,并针对0-1背包问题进行求解.经实验仿真并与蚁群算法计算结果作对比,验证了算法在0-1背包问题求解上的有效性和更快的收敛速度.     

A generalized knapsack problem with variable coefficients

The ordinary knapsack problem is to find the optimal combination of items to be packed in a knapsack under a single constraint on the total allowable resources, where all coefficients in the objective function and in the constraint are constant.In this paper, a generalized knapsack problem with coefficients depending on variable parameters is proposed and discussed. Developing an effective branch and bound algorithm for this problem, the concept of relaxation and the efficiency function introduced here will play important roles. Furthermore, a relation between the algorithm and the dynamic programming approach is discussed, and subsequently it will be shown that the ordinary 0–1 knapsack problem, the linear programming knapsack problem and the single constrained linear programming problem with upper-bounded variables are special cases of the interested problem. Finally, practical applications of the problem and its computational experiences will be shown.     

一种求解分组0-1背包问题的动态规划法

研究了分组0-1背包问题,提出了一种动态规划解决方法,在物品总数为n个和背包承重量为W时,递推过程的复杂度为O(nW),回溯过程的复杂度为O(n).计算实例表明利用该方法易于找到最优解.     

An Efficient Algorithm for Non-Point Source Pollution Management Problems

A dynamic programming (DP) algorithm is proposed for a class of non-point source pollution control problems. The formulation deals with the selection of a spatial distribution of management practices in such a way as to meet a control agency's sediment pollution target. The inherently combinatorial nature of these problems — stemming from the discrete nature of the decision variables, which are production, conservation and mechanical control practices — gives them a special integer programming structure. This paper focuses on the DP formulation and the computer implementation of this algorithm. The approach is shown to be informative, robust and relatively efficient. Furthermore, the paper demonstrates that dynamic programming can be used to generate sensitivity analysis information for multiple-choice knapsack problems.     

A column generation heuristic for the two-dimensional two-staged guillotine cutting stock problem with multiple stock size

We consider a two-dimensional cutting stock problem where stock of different sizes is available, and a set of rectangular items has to be obtained through two-staged guillotine cuts. We propose a heuristic algorithm, based on column generation, which requires as its subproblem the solution of a two-dimensional knapsack problem with two-staged guillotines cuts. A further contribution of the paper consists in the definition of a mixed integer linear programming model for the solution of this knapsack problem, as well as a heuristic procedure based on dynamic programming. Computational experiments show the effectiveness of the proposed approach, which obtains very small optimality gaps and outperforms the heuristic algorithm proposed by Cintra et al. [3].     

Convergent Lagrangian and domain cut method for nonlinear knapsack problems

The nonlinear knapsack problem, which has been widely studied in the OR literature, is a bounded nonlinear integer programming problem that maximizes a separable nondecreasing function subject to separable nondecreasing constraints. In this paper we develop a convergent Lagrangian and domain cut method for solving this kind of problems. The proposed method exploits the special structure of the problem by Lagrangian decomposition and dual search. The domain cut is used to eliminate the duality gap and thus to guarantee the finding of an optimal exact solution to the primal problem. The algorithm is first motivated and developed for singly constrained nonlinear knapsack problems and is then extended to multiply constrained nonlinear knapsack problems. Computational results are presented for a variety of medium- or large-size nonlinear knapsack problems. Comparison results with other existing methods are also reported.     

A dynamic programming algorithm for the bilevel knapsack problem

We propose an efficient dynamic programming algorithm for solving a bilevel program where the leader controls the capacity of a knapsack, and the follower solves the resulting knapsack problem. We propose new recursive rules and show how to solve the problem as a sequence of two standard knapsack problems.     

Budgeting with bounded multiple-choice constraints

We consider a budgeting problem where a specified number of projects from some disjoint classes has to be selected such that the overall gain is largest possible, and such that the costs of the chosen projects do not exceed a fixed upper limit. The problem has several application in government budgeting, planning, and as relaxation from other combinatorial problems. It is demonstrated that the problem can be transformed to an equivalent multiple-choice knapsack problem through dynamic programming. A naive transformation however leads to a drastic increase in the number of variables, thus we propose an algorithm for the continuous problem based on Dantzig–Wolfe decomposition. A master problem solves a continuous multiple-choice knapsack problem knowing only some extreme points in each of the transformed classes. The individual subproblems find extreme points for each given direction, using a median search algorithm. An integer optimal solution is then derived by using the dynamic programming transformation to a multiple-choice knapsack problem for an expanding core. The individual classes are considered in an order given by their gradients, and the transformation to a multiple-choice knapsack problem is performed when needed. In this way, only a dozen of classes need to be transformed for standard instances from the literature. Computational experiments are presented, showing that the developed algorithm is orders of magnitude faster than a general LP/MIP algorithm.     

一个关于二次规划问题的分段线性同伦算法

本文发展了一个关于二次规划问题的分段线性同伦算法。该算法可看作是外点罚函数法的一个变体。凡是符合外点罚函数法收敛条件的二次规划问题用该算法均可经有限次轮回运算得到稳定解。大量的关于随机的凸二次规划问题的数值实验结果表明它的计算效率是高的，在某些条件下可能是多项式时间算法。     

Algorithmic improvements on dynamic programming for the bi-objective {0,1} knapsack problem

This paper presents several methodological and algorithmic improvements over a state-of-the-art dynamic programming algorithm for solving the bi-objective {0,1} knapsack problem. The variants proposed make use of new definitions of lower and upper bounds, which allow a large number of states to be discarded. The computation of these bounds are based on the application of dichotomic search, definition of new bound sets, and bi-objective simplex algorithms to solve the relaxed problem. Although these new techniques are not of a common application for dynamic programming, we show that the best variants tested in this work can lead to an average improvement of 10 to 30 % in CPU-time and significant less memory usage than the original approach in a wide benchmark set of instances, even for the most difficult ones in the literature.