多阶段双层目标分配问题的精确算法

针对所有工作必须分阶段依次完成,但同一个阶段的工作可以同时进行的情况下,如何分配现有人员来承担这些工作,才能使得完成所有工作的工期最短,并在此前提下使花费的总用时最少的分配问题,通过引入立方检测矩阵,给出了一种单调下降的迭代算法。该算法不但能获取精确最优解,而且有很好的计算效率。     

针对经典排序问题的一种新算法的近似比分析

给定m台平行机(同型机),n个工件,寻找一种分配方案,使得把这n个工件分配到m台机器后,整体完工时间尽可能短,这个NP-难问题被称为经典排序问题。如果每个工件的加工时间满足一定的条件,则有望能在多项式时间内有效地得到最优的分配方案。Yue等对加工时间满足整除性质的经典排序问题考虑了一种新的算法,该算法总是能得到这种特殊情况的最优分配。该算法在多项式时间内能够得到最优分配,是对于一般的经典排序问题的近似算法。文章在此基础上,考虑该新算法在一般问题上的近似比。文中考虑了这个新算法的两种版本,分别得到了3/2和2-1/2 ^q(q∈Z⁺)的近似比。紧例子表明,文中对算法的两个版本的分析都是最优的。     

Markov控制过程基于性能势的平均代价最优策略

研究了一类离散时间Markov控制过程平均代价性能最优控制决策问题.应用 Markov性能势的基本性质,在很一般性的假设条件下,直接导出了无限时间平均代价模型在紧 致行动集上的最优性方程及其解的存在性定理.提出了求解最优平稳控制策略的迭代算法,并 讨论了这种算法的收敛性问题.最后通过分析一个实例来说明这种算法的应用.     

时间依赖代价函数下的最优路径查询问题研究

作者研究了时间依赖图下,具有时间限制的费用代价最优路径的查询问题.目前有关时间依赖图上的最短路径查询的研究工作解决的是最短旅行时间问题(TDSP),这些工作都利用了以下性质:到达某个顶点的最早时刻可以通过到达其邻居的最早时刻计算得出.然而,在计算具有时间限制的费用代价最优路径时,该性质并不成立.因此,目前解决TDSP问题的方法均不能解决文中面对的问题.对此作者提出一个新的算法用于计算时间依赖图模型上的满足时间限制的费用代价最优路径.该算法适用于有向图和无向图.作者证明了算法的时间复杂度和空间复杂度分别为O(knlogn+mk2logk)和O((n+m)k).最后,作者通过真实数据集上的实验,验证了该算法的有效性.     

基于前向预测策略的块正交匹配追踪算法研究

在块正交匹配追踪算法中,候选集匹配原子块的选择策略对信号重建具有重要作用,但是该算法在迭代选择原子块的过程中,每次选择当次最优迭代的原子块,并不能保证最终迭代性能是最优的。为此,提出一个基于前向预测的最优匹配原子块选择策略的块正交匹配追踪算法,通过预测原子块在未来迭代过程中的性能选择最优匹配的原子块。实验结果表明,与块正交匹配追踪算法相比,该算法的重建误差随前向预测参数的增大而减小。     

多车场满载车辆路径优化算法

针对多车场满载车辆路径问题(MDVRPFL),结合节约法提出了一种依次对车场、配送中心、用户进行循环调整直到最优的迭代算法.该算法具有使总费用随迭代次数逐渐降低的特点,其运算结果能同时得到最优车辆分配方案和车辆行驶路径.最后用该算法对不同规模的算例进行试验.试验结果表明,该算法对多车场车辆路径问题有效适用.     

认知无线电网络基于QoS的监听时间与资源联合分配

以最大化所有认知无线电用户(CRU)的吞吐量为目标,同时保证每个CRU的服务质量(QoS)约束,研究了联合最优监听时间和资源分配问题,并基于此提出了一种监听时间与资源联合分配算法.在多信道认知无线电网络中,频谱监听和资源分配都会影响网络的吞吐量.兼顾二者的联合优化问题可以被分解为两个子问题:固定监听时间的资源分配问题, 以及固定资源分配策略的最优监听时间一维穷举搜索问题.提出的算法可以通过穷举搜索获得最优监听时间,并通过次梯度算法获得最优资源分配策略.仿真结果表明,提出的最优监听时间与资源分配算法可以最大化认知无线网络的吞吐量; 此外,各认知用户的QoS需求也能得到保证.     

模拟生物理想自由分布模型的粒子群算法

在分析生物觅食行为中资源斑块选择理想自由分布模型的基础上,提出一种新型的粒子群算法——理想自由分布粒子群优化算法（IFDPSO）．该算法将所有粒子中3个不重叠的个体最优位置的适应度视为资源斑块的食物质量,根据理想自由分布模型随机分配相应数量的粒予到各资源斑块中．为保证群体的多样性,各资源斑块的群体最优位置保持随迭代次数增加而线性递减的距离．在间隔一定的迭代次数后,将各资源斑块的粒子重新组合．标准测试函数的仿真结果表明了IFDPSO算法的有效性．     

基于最优虚拟截止日期多处理器混合时序调度

为提高混合临界系统实时调度有效性,提出基于最优虚拟截止日期的多处理器混合时序调度算法.将现有非抢占最早截止时间可调度性测试算法推广到混合临界多处理器系统,引入时序保证技术,确保系统在两个不同临界值间过渡;将所提可调度性测试扩展到混合临界系统,利用系统级截止期缩减参数控制,设计最优虚拟截止日期分配策略.仿真结果表明,采用最优虚拟截止时间分配策略可调度性测试可发现大量额外可调度任务集,实现混合临界多处理器非抢占调度性能提升.     

模拟退火蚁群算法求解二次分配问题

提出了一种求解二次分配问题的模拟退火蚁群算法。将模拟退火机制引入蚁群算法,在算法中设定随迭代变化的温度,将蚁群根据信息素矩阵搜索得到的解集作为候选集,根据当前温度按照模拟退火机制由候选集生成更新集,利用更新集更新信息素矩阵,并利用当前最优解对信息素矩阵进行强化。当算法出现停滞对信息素矩阵进行重置。实验表明,该算法有着高的稳定性与收敛速度。     

Modified rate-monotonic algorithm for scheduling periodic jobs withdeferred deadlines

The deadline of a request is the time instant at which its execution must complete. The deadline of the request in any period of a job with deferred deadline is some time instant after the end of the period. The authors describe a semi-static priority-driven algorithm for scheduling periodic jobs with deferred deadlines: each job is assigned two priorities, the higher one for old requests and the lower one for the current request. This algorithm is called the modified rate-monotonic algorithm and is based on the well-known rate-monotonic algorithm. It is shown that the modified rate-monotonic algorithm is optimal when the deadline of every job is deferred by max (1, γ-1) periods or more, where γ is the ratio between the longest period and the shortest period. When the deadline of each job is deferred by one period of the job, any set of n independent jobs whose total utilization is equal to or less than [1+n(2¹n/-1)]/2 can be feasibly scheduled by this algorithm. This bound approaches 0.845 when n approaches infinity     

非确定型指派问题的求解算法

考虑了一类非确定型指派问题,每人所承担的工作数不确定,按每人至少承担一项工作,每项工作只允许一人承担的指派原则,针对人员无工作数限制和有工作数限制两种情况加以讨论和分析,借鉴Floyd算法的负回路思想,提出了一种迭代算法,并给出了应用此算法求解的具体实例。实验表明：与其他求解算法相比,该算法求解规模小,效率高,应用简便,易于编程实现。     

人数少于任务数的全指派问题的迭代算法

针对人数少于任务数的情况,按每人至少承担一项任务,至多承担L项任务,但每项任务只允许一人承担的指派原则,给出了一种求解这种指派问题的迭代算法,该算法操作简便、易于用计算机运行。构建该算法的方法,用于某些其它指派问题,可以使相应的算法更加便捷。     

Preemptive scheduling on uniformly related machines: minimizing the sum of the largest pair of job completion times

We revisit the classic problem of preemptive scheduling on m uniformly related machines. In this problem, jobs can be arbitrarily split into parts, under the constraint that every job is processed completely, and that the parts of a job are not assigned to run in parallel on different machines. We study a new objective which is motivated by fairness, where the goal is to minimize the sum of the two maximal job completion times. We design a polynomial time algorithm for computing an optimal solution. The algorithm can act on any set of machine speeds and any set of input jobs. The algorithm has several cases, many of which are very different from algorithms for makespan minimization (algorithms that minimize the maximum completion time of any job), and from algorithms that minimize the total completion time of all jobs.     

一种双匹配动态调度算法

提出了适于异构环境独立任务调度的双匹配动态调度算法（BM算法）．BM算法将任务与处理机实现双匹配，使大部分任务在执行时间最短而且完成时间最早的处理机上执行．对于无法实现双匹配的任务，采用最早完成时间最小者优先的策略进行调度．BM算法可以同时满足负载均衡和高吞吐率两个目标．BM算法与通常用作评测基准的Min-min算法的比较结果表明，BM算法的运行时间远少于Min-min算法，其调度跨度比Min-min算法减少约9％．     

Parallel machine scheduling problem to minimize the earliness/tardiness costs with learning effect and deteriorating jobs

The focus of this work is to analyze parallel machine earliness/tardiness (ET) scheduling problem with simultaneous effects of learning and linear deterioration, sequence-dependent setups, and a common due-date for all jobs. By the effects of learning and linear deterioration, we mean that the processing time of a job is defined by an increasing function of its starting time and a decreasing function of the position in the sequence. We develop a mixed integer programming formulation for the problem and show that the optimal sequence is V-shaped: all jobs scheduled before the shortest jobs and all jobs scheduled after the shortest job are in a non-increasing and non-decreasing order of processing times, respectively. The developed model allows sequence-dependent setups and sequence-dependent early/tardy penalties. The illustrative example with 11 jobs for 2 machines and 3 machines shows that the model can easily provide the optimal solution, which is V-shaped, for problem.     

A branch and bound algorithm for minimizing makespan on a single machine with unequal release times under learning effect and deteriorating jobs

We present a single-machine problem with the unequal release times under learning effect and deteriorating jobs when the objective is minimizing the makespan. In this study, we introduced a scheduling model with unequal release times in which both job deterioration and learning exist simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 30 jobs, and the average error percentage of the proposed heuristic is less than 0.16%.     

A group priority earliest deadline first scheduling algorithm

In most priority scheduling algorithms, the number of priority levels is assumed to be unlimited. However, if a task set requires more priority levels than the system can support, several jobs must in practice be assigned the same priority level. To solve this problem, a novel group priority earliest deadline first (GPEDF) scheduling algorithm is presented. In this algorithm, a schedulability test is given to form a job group, in which the jobs can arbitrarily change their order without reducing the schedulability. We consider jobs in the group having the same priority level and use shortest job first (SJF) to schedule the jobs in the group to improve the performance of the system. Compared with earliest deadline first (EDF), best effort (BE), and group-EDF (gEDF), simulation results show that the new algorithm exhibits the least switching, the shortest average response time, and the fewest required priority levels. It also has a higher success ratio than both EDF and gEDF.     

A three-stage approach for the resource-constrained shortest path as a sub-problem in column generation

This paper focuses on the common scenario in which the resource-constrained shortest path problem (RCSP) on an acyclic graph is a sub-problem in the context of column generation. It proposes a pseudo-polynomial time, three-stage solution approach. Stages 1 (preprocessing) and 2 (setup) are implemented one time to transform RCSP into a shortest path problem, which is solved by stage 3 (iterative solution) at each column generation iteration, each time with different arc costs. This paper analyzes certain properties related to each stage as well as algorithm complexity. Computational tests compare the performances of this method, a state-of-the-art label-setting algorithm, and CPLEX optimization software on four classes of instances, each of which involves either one or multiple resources, and show that the new method is effective. The new method outperforms the label-setting algorithm when resource limitations are tight—as can be expected in practice, and outperforms CPLEX for all tested instances. The label-setting algorithm outperforms CPLEX for all single-resource RCSP instances and almost all multiple-resource RCSP instances.     

A Truncated Sum of Processing‐Times–Based Learning Model for a Two‐Machine Flowshop Scheduling Problem

Scheduling with learning effects has gained increasing attention in recent years. A well‐known learning model is called “sum‐of‐processing‐times‐based learning” in which the actual processing time of a job is a nonincreasing function of the jobs already processed. However, the actual processing time of a given job drops to zero precipitously when the normal job processing times are large. Moreover, the concept of learning process is relatively unexplored in a flowshop environment. Motivated by these observations, this article addresses a two‐machine flowshop problem with a truncated learning effect. The objective is to find an optimal schedule to minimize the total completion time. First, a branch‐and‐bound algorithm incorporating with a dominance property and four lower bounds is developed to derive the optimal solution. Then three simulated annealing algorithms are also proposed for near‐optimal solution. The experimental results indicated that the branch‐and‐bound algorithm can solve instances up to 18 jobs, and the proposed simulated annealing algorithm performs well in item of CPU time and error percentage. © 2011 Wiley Periodicals, Inc.