基于约束规划的岸桥与集卡集成调度

针对进口集装箱卸船的岸桥与集卡集成调度问题,分别提出混合整数规划(MIP)模型和约束规划(CP)模型,目标是使得卸船完工时间最短,该问题是NP难题。通过OPL语言设计约束规划模型,利用其为调度问题提供的特殊构造,如区间变量、序列变量等进行建模,并采用"扩展操作任务"的概念来定义区间变量以提升求解效率。为评价解的质量,设计一个新的下界求解方法。使用不同规模的实例对约束规划模型和MIP模型进行测试,结果表明,在小规模实例中,CP模型求解性能略差于MIP模型,但对于中大规模实例,MIP模型无法在设定时限内找到解,而CP模型则能以较快的收敛速度得到高质量的解,目标距离下界的差距控制在2.19%~8.28%。     

整数规划问题智能求解算法综述*

为了对大规模整数规划问题的求解方法提供参考,对基于智能算法求解整数规划问题的研究进行了分析和评述。鉴于现有算法的缺陷与不足,讨论了应用智能算法求解整数规划问题未来可能的研究方向。     

一种求解整数规划与混合整数规划非线性罚函数方法

证明了任何一个变量有界的整数规划问题（IP）和混合整数规划问题（MIP）都可以转化为一个等价的非整数（或连续化）规划问题（NIP），并给出一个用非线性精确罚函数法来求解该等价NIP的方法，从而达到求解IP或MIP的目的，数值实验表明了算法的可行性。该方法可广泛用于各应用领域里IP和MIP的求解，特别是为非线性IP和MIP问题提供了一条通用 的求解途径，对解决许多实际优化问题具有重要意义。     

利用混合整数规划的卫星操作规划问题研究

对于成像卫星的操作规划,如何高效求解其规划问题模型是一个十分关键的问题。针对基于规划域定义语言(PDDL)表示的成像卫星操作规划问题的求解,采用将基于命题式的PDDL语言描述的模型转化为多值变量模型的方法,建立了基于混合整数规划的问题求解模型,从而可以方便地采用混合整数规划的已有求解器进行求解,提高了问题的求解效率。对关键技术进行了分析,并设计了问题求解流程。仿真实验结果证明该方法是可行和适用的。     

混合云环境中数据敏感工作流调度

混合云环境下调度包含敏感数据的工作流主要考虑在满足数据安全性以及工作流截止时间的前提下,对工作流任务在混合云上进行分配,实现计算资源与任务的映射,并优化调度费用。采用了整数规划来建模求解包含数据敏感性、截止时间和调度费用3种约束条件的混合云工作流调度问题,同时为优化模型求解速度,基于“帕雷托最优”原理对工作流任务在混合云上的分配方案进行筛选以减小模型求解规模。实验表明,优先排除不合理的任务分配方案可有效减小整数规划模型的求解规模,缩短模型计算时间,在产生较小误差的情况下获得较优的调度结果。     

MIP/CP综合考虑的车间作业调度问题研究

作业车间(Job Shop)调度问题是指为具体的任务(工序)安排生产资源(机器)并确定合理的加工顺序,是一个典型的NP-Hard问题,有着广泛的研究.首先简单介绍约束编程(CP)思想及ILOG SOLVER系统并建立Job Shop调度问题的约束编程模型,并对模型的求解进行分析.然后分析混合整数规划(MIP)和约束编程(CP)模型求解的互补优势,建立Job Shop调度问题MIP/CP综合模型,并与CP模型进行比较,证明MIP/CP综合模型求解的效率.     

性能随时间衰减的锅炉蒸汽系统循环调度

针对性能随时间衰减的锅炉蒸汽系统的循环调度问题进行了研究.首先建立了描述该问题的混合整数非线性模型;然后提出了确定各锅炉循环运行状态的时间分段策略以简化问题的求解;最后应用列队竞争算法对该混合整数非线性规划问题进行优化计算.采用某锅炉蒸汽系统循环调度的实例对所提出的方法进行了验证,计算结果表明循环调度优化能够获得比人工随机安排更优的调度方案,节能效果十分明显.     

业务流程管理中的大规模整数规划问题求解

对从企业业务流程管理中抽象出来的大规模整数规划问题的计算机求解方法进行讨论。提出一种内存优化管理方法,能更高效地存储海量数据。同时对求解整数规划问题的经典算法——分枝定界算法进行研究,利用人工智能的搜索思想,给出分枝定界法的改进算法,使其能快速求解大规模整数规划问题。     

多次抢占项目调度问题的混合遗传算法

研究多次抢占式资源受限的项目调度问题，假设任意时间点可作为资源抢占节点且抢占次数不受限制，建立满足多次资源抢占的线性整数规划模型并提出改进遗传算法对其进行求解。为克服遗传算法（GA）局部搜索能力缺陷，在算法中引入禁忌搜索（TS）进一步优化子代。针对性地设计了允许多次抢占的基于工作优先级编码策略以及串行调度方案生成机制。通过测试算例集实验调试算法参数，并以标准算例集（Project Scheduling Problem Library，PSPLIB）对算法进行可行性检验。实验结果表明，资源受限项目调度问题中引入多次抢占机制能有效缩减项目工期，设计的算法对问题求解效果良好。     

最小化全局完成时间的成像卫星任务规划算法

成像侦察卫星任务规划问题是一类典型多约束组合优化问题.最小化全局完成时间是任务规划领域时效性要求较高情况下的一种优化目标.提出一种整合整数规划与约束规划方法,在最小化任务规划方案全局完成时间的目标下,求解成像侦察卫星任务规划问题的组合算法.该算法通过应用Benders分解将原约束整数规划模型划分为主问题与子问题两部分,采用软件MOSEK与GECODE对主、子问题分别求解.根据子问题求解结果生成剪枝约束,返回主问题迭代,直到获得优化解.算法有效性通过仿真实验进行了检验并取得预期效果.     

An advanced start algorithm for all-integer programming

In this paper, we present an all-integer cutting plane technique called the Advanced Start Algorithm (ASA), for solving the all-integer (otherwise linear) programming problem (IP). We develop a good advanced primal-infeasible start based on the optimal solution to the LP relaxation, and use a two-stage dual/primal algorithm to obtain the optimal solution to (IP). We illustrate the operation of the ASA on three small problems, and exhibit computational results on a set of standard test problems.     

Parallel machine scheduling with flexible resources

Parallel machine flexible resource scheduling (PMFRS) problems consider an additional flexible resource (e.g. operators), which can be freely allocated to any jobs and/or any machines and may speed-up the process in proportion to its amount. If job–machine assignment is unspecified, the problem is referred to as unspecified PMFRS (UPMFRS). This paper reviews the mathematical models of both PMFRS and UPMFRS problems in the literature and not only gives some extensions to the model of dynamic PMFRS problem but also presents integer programming (IP) models for static and dynamic UPMFRS problems with the objective of minimizing makespan. To solve large-sized dynamic PMFRS and UPMFRS problems, a relaxed IP based constraint programming (CP) approach is also proposed. All IP models and the proposed IP/CP approach are tested with an extensive computational study. The results of the computational experiments are discussed with respect to the major parameters of the problem and conclusions are drawn.     

Integer programming methods for large-scale practical classroom assignment problems

In this paper we present an integer programming method for solving the Classroom Assignment Problem in University Course Timetabling. We introduce a novel formulation of the problem which generalises existing models and maintains tractability even for large instances. The model is validated through computational results based on our experiences at the University of Auckland, and on instances from the 2007 International Timetabling Competition. We also expand upon existing results into the computational difficulty of room assignment problems.     

On using exterior penalty approaches for solving linear programming problems

In this paper, we investigate three exterior penalty function approaches for solving linear programming problems. These methods are an active set ℓ₂ penalty approach (ASL2), an inequality–equality-based ℓ₂ penalty approach (IEL2), and an augmented Lagrangian approach (ALAG). Particular effective variants are explored for each method, along with comments and experience on alternative algorithmic strategies that were empirically investigated. Our motivation is that heretofore, there has been no empirical evidence on how variants of these exterior point algorithms that have been suitably tuned might perform with respect to solving moderately large-scale linear programming problems. Our experiments using a set of randomly generated problems of varying sizes and density, as well as a set of NETLIB test problems, provide insights into the relative performance of these different approaches derived from the basic ℓ₂ penalty function, and into their viability for solving linear programs. Average rank tests based on the computational results obtained are performed using two different statistics which assess the speed of convergence and the quality or accuracy of the solution. Overall, a particular variant (ALAG2) of ALAG yielded the best performance with respect to the joint criteria of speed of convergence and the quality of the final solution attained. On the other hand, IEL2 invariably achieved the best quality solutions using comparatively designed termination criteria. However, for highly dense linear programming problems, ASL2 appeared to be the best-alternative among the tested algorithms. Moreover, although our implementation was rudimentary in comparison with CPLEX 6.0, a commercial solver, the tested methods were competitive (sometimes favorable) in attaining a final (though only near optimal) solution for the set of large-scale low-density problems.Scope and purposeAlgorithms based on interior point methods for solving linear programming problems have gained popularity due to some recent techniques which eliminate the ill-conditioning that is inherent within barrier function approaches. Yet, there is comparatively less evidence on the performance of exterior penalty function approaches for solving linear programs. This article investigates three exterior penalty function approaches for solving such problems based on the quadratic penalty function, including the augmented Lagrangian function. Several related algorithmic strategies are explored and tested on a set of randomly generated, degenerate problems, as well as on a standard collection of NETLIB problems. We provide insights into the algorithmic performance and suggest avenues for further research in this relatively less explored domain of approaches for solving linear programming problems.     

An implicit enumeration program for zero-one integer programming

This paper describes some techniques to improve the speed of the implicit enumeration method for solving zero-one integer programming problems. Among these techniques, the most powerful is the one of using a column vector which works as a tag for each inequality, indicating whether or not the inequality should be checked for the current partial solution. A new condition for underlining a variable and the concept of pseudo-underlining are also proposed. These techniques were implemented in the computer programil lip (ILLinois Integer Programming code). The computational results for different types of problems are discussed.This work is partly supported by NSF Grant No. GJ-503.     

一类直觉模糊线性规划的求解及其应用

研究一类直觉模糊线性规划及其应用.首先,定义直觉模糊不等式,给出直觉模糊线性规划模型;然后,提出一种基于总精确函数的直觉模糊线性规划求解方法,并给出其求解步骤;最后,建立证劵投资组合的直觉模糊线性规划模型.数值算例表明了所提出理论是合理有效的.     

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.     

面向冗余度机械臂QP问题求解的E47和94LVI数值算法

冗余度机械臂的二次规划(QP)问题同时受制于等式约束、不等式约束和双端约束,且面向冗余度机械臂实时控制的该类QP问题的求解对运算实时性有较高要求。考虑同时受制于上述三种约束的二次规划问题的求解,给出并研究两种数值算法(E47和94LVI算法)。这类带约束的二次规划问题被等价转换为分段线性投影方程。应用E47和94LVI算法求解上述分段线性投影方程,从而得到二次规划问题的最优数值解。同时,通过大量的数值实验,研究两种算法面向冗余度机械臂的QP问题求解性能,并给出E47、94LVI算法与经典有效集算法的对比实验结果。最终证实了E47和94LVI两种算法在求解二次规划问题上的高效性和优越性。     

一类二层规划问题的区间算法

讨论下层规划问题以最优值反应到上层的二层规划问题的数值解法,其中目标函数和约束函数均为Lipschitz连续函数,构造了二层规划问题目标函数的区间扩张和无解区域删除检验原则,建立了求解二层规划问题的区间算法,并进行了数值实验。理论证明和数值实验均表明算法是可靠和有效的。