一类资源约束的单机成组调度问题

本文讨论具有连续资源的单机成组调度问题.在这一模型中,工件组的安装时间是所消耗资源的非负严格减少连续函数,工件的加工时间是开工时间的严格增加函数.考虑两个问题,第1个问题是在满足资源消耗总量限制条件下,极小化最大完工时间.第2个问题的目标函数是在满足最大完工时间限制条件下,极小化资源消耗总量.分别对两个问题讨论了最优调度的某些特征,分别给出了求解最优资源分配的方法,并通过数值例子进行说明.     

带准备时间的单机调度问题的混合进化算法研究

提出了一种混合进化算法（HEA）用于求解具有序列相关依赖且带准备时间的单机调度问题, 其优化目标为最小化总延迟。该混合进化算法由局部搜索和进化算法框架混合而成。HEA具有一些新的特点, 例如在局部搜索中采用了一种新提出的基于块移动的邻域结构, 这种邻域结构合理地限制了搜索空间, 提高了算法的搜索效率; 在HEA中采用了一种新的组合算子——块顺序交叉算符（BOX）来产生新的子代工作序列。用本算法对当前国际文献中公开的两组共64个算例进行了测试, HEA改进了9个算例在当前文献中的最优解, 表明了所提出的HEA算法的优越性。与之前的国际文献中最好的四个启发式算法进行了详细比较, 表明了HEA算法的优势。     

A bi-criterion single-machine scheduling problem with learning considerations

Conventionally, job processing times are assumed to be constant from the first job to be processed until the last job to be completed. However, recent empirical studies in several industries have verified that unit costs decline as firms produce more of a product and gain knowledge or experience. This phenomenon is known as the learning effect. This paper focuses on a bi-criterion single-machine scheduling problem with a learning effect. The objective is to find a sequence that minimizes a linear combination of the total completion time and the maximum tardiness. A branch-and-bound and a heuristic algorithm are proposed to search for optimal and near-optimal solutions, respectively. Computational results are also provided for the problem.Received: 21 April 2003, Accepted: 9 October 2003, Published online: 16 January 2004     

A branch-and-bound procedure for a single-machine earliness scheduling problem with two agents

This paper addresses a two-agent scheduling problem on a single machine where the objective is to minimize the total weighted earliness cost of all jobs, while keeping the earliness cost of one agent below or at a fixed level Q. A mixed-integer programming (MIP) model is first formulated to find the optimal solution which is useful for small-size problem instances. To solve medium- to large-size problem instances, a branch-and-bound algorithm incorporating with several dominance properties and a lower bound is then provided to derive the optimal solution. A simulated annealing heuristic algorithm incorporating with a heuristic procedure is developed to derive the near-optimal solutions for the problem. A computational experiment is also conducted to evaluate the performance of the proposed algorithms.     

Approximation schemes for single machine scheduling with non-renewable resource constraints

In this paper we discuss exact and approximation algorithms for scheduling a single machine with additional non-renewable resource constraints. Given the initial stock levels of some non-renewable resources (e.g., raw materials, fuel, money), and time points along with replenishment quantities, a set of resource consuming jobs has to be scheduled on the machine such that there are enough resources for starting each job, and the makespan is minimized. We show that the problem admits a pseudo-polynomial time algorithm when the number of replenishments is not part of the input, and also present an FPTAS when there is only a single resource, and it is replenished only once. We also describe a PTAS for the problem with a constant number of replenishments.     

针对资源调度问题的局部优化算法

由于现有局部搜索算法在处理数据量较大的受限资源工程调度问题时效果欠佳,提出了一种与FBI优化相结合的局部搜索方案--FBLS.FBLS利用问题的对称性,以局部搜索的解集为单位,在原问题与对称问题上交替进行优化.通过分析领域中解的合法性以及可能出现的重复情况,削减领域中解的数量,提高搜索效率.在PSPLIB的数据测试中,经FBLS优化所得到的结果已经优于所有非智能甚至大部分智能演化算法.作为一种通过局部搜索进行优化的方法,FBLS可以被灵活诮用于各种已有的智能算法框架求解RCPSP问题.     

A note on a single-machine lot scheduling problem with indivisible orders

In this paper, a lot scheduling problem on a single machine with indivisible orders is studied. The objective is to minimize the total completion time of all orders. We show that the problem is NP-hard in the strong sense. Then, a binary integer programming approach and four simple heuristics are proposed to solve the problem. The binary integer programming approach with running time limit is considered as one heuristic method. As compared to a lower bound, the average performances of the heuristic method are really good and better than those of the four simple heuristics.     

A single-machine bi-criterion learning scheduling problem with release times

The learning effect in scheduling has received considerable attention recently. However, most researchers consider a single criterion with the assumption that jobs are all ready to be processed. The research of bi-criterion problems with learning effect is relatively limited. This paper studies a single-machine learning effect scheduling problem with release times where the objective is to minimize the sum of makespan and total completion time. First, we develop a branch-and-bound algorithm incorporating with several dominance properties and a lower bound to derive the optimal solution. Secondly, we propose a genetic algorithm to obtain near-optimal solutions. Finally, a computational experiment is conducted to evaluate the performance of the branch-and-bound and the genetic algorithms.     

Using a branch-and-bound and a genetic algorithm for a single-machine total late work scheduling problem

Scheduling with learning effects has received a lot of research attention lately. On the other hand, it is commonly seen that time restrictions are usually modeled by due dates or deadlines and the quality of schedules is estimated with reference to these parameters. One of the performance measures involving due dates is the late work criterion, which is relatively unexplored. Thus, we study a single-machine scheduling problem with a position-based learning effect. The objective is to minimize the total late work, where the late work for a job is the amount of processing of this job that is performed after its due date. We attempt to develop a branch-and-bound algorithm incorporating with some dominance rules and a lower bound for the optimal solution. For saving computational time, we also propose three heuristic-based genetic algorithms for the near-optimal solution. Finally, the computational results of proposed algorithms are also provided.     

A two-agent single-machine scheduling problem with truncated sum-of-processing-times-based learning considerations

Scheduling with learning effects has received a lot of research attention lately. By learning effect, we mean that job processing times can be shortened through the repeated processing of similar tasks. On the other hand, different entities (agents) interact to perform their respective tasks, negotiating among one another for the usage of common resources over time. However, research in the multi-agent setting is relatively limited. Meanwhile, the actual processing time of a job under an uncontrolled learning effect will drop to zero precipitously as the number of jobs increases or a job with a long processing time exists. Motivated by these observations, we consider a two-agent scheduling problem in which the actual processing time of a job in a schedule is a function of the sum-of-processing-times-based learning and a control parameter of the learning function. The objective is to minimize the total weighted completion time of the jobs of the first agent with the restriction that no tardy job is allowed for the second agent. We develop a branch-and-bound and three simulated annealing algorithms to solve the problem. Computational results show that the proposed algorithms are efficient in producing near-optimal solutions.     

A dynamic-programming-based exact algorithm for general single-machine scheduling with machine idle time

This paper proposes an efficient exact algorithm for the general single-machine scheduling problem where machine idle time is permitted. The algorithm is an extension of the authors’ previous algorithm for the problem without machine idle time, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. We first extend our previous algorithm to the problem with machine idle time and next propose several improvements. Then, the proposed algorithm is applied to four types of single-machine scheduling problems: the total weighted earliness-tardiness problem with equal (zero) release dates, that with distinct release dates, the total weighted completion time problem with distinct release dates, and the total weighted tardiness problem with distinct release dates. Computational experiments demonstrate that our algorithm outperforms existing exact algorithms and can solve instances of the first three problems with up to 200 jobs and those of the last problem with up to 80 jobs.     

一种多目标资源受限项目调度问题的教学算法

针对多目标资源受限项目调度的特性, 基于结合活动列表和资源列表的编码设计了合理的交叉操作, 提出一种多目标教学算法. 为了在个体间有效交互信息, 在教师阶段非支配个体作为教师与学生执行交叉, 而在学生阶段学生间执行交叉, 同时在每个阶段通过前向-反向改进增强局部搜索能力, 并用Pareto 档案集存储和更新非支配个体.基于标准测试集的数值仿真及与现有最好算法的比较, 验证了所提出算法的有效性.

     

A study of the single-machine two-agent scheduling problem with release times

In many management situations, multiple agents compete on the usage of common processing resources. On the other hand, the importance of the ready times can be shown in Wafer fabrication with the presence of unequal ready times. It is sometimes advantageous to form a non-full batch, while in other situations it is a better strategy to wait for future job arrivals in order to increase the fullness of the batch. However, research on scheduling with two-agent and ready time simultaneously is relatively unexplored. This paper addresses a single-machine two-agent scheduling problem with ready times. The aim is to find an optimal schedule to minimize the total completion time of the jobs of the first agent with the restriction that total completion time is allowed an upper bound for the second agent. To the best of our knowledge, the problem under study has not been considered. Firstly, we show that the proposed problem is strongly NP-hard. Following that, we then develop a branch-and-bound, an ant colony, and four genetic algorithms for an optimal and near-optimal solution, respectively. In addition, the extensive computational experiments are also given.     

Note on a unified approach to the single-machine scheduling problem with a deterioration effect and convex resource allocation

In many resource allocation problems in physical or economic systems, a linear resource consumption function is commonly considered, and job processing times are assumed to be fixed parameters. However, the former assumption fails to reflect the law of diminishing returns, and the latter may be controlled by changing the allocation of resources to jobs. Motivated by these observations, we provide a unified model for solving single-machine scheduling problems in which each job's processing time is a function of its starting time and convex resource allocation. The objective is to find the optimal sequence of jobs subject to a limited resource consumption. We first show how this unified model can be useful in solving scheduling problems under due date assignment considerations. We analyze the problem with four different due date assignment methods, and our objective function includes costs for earliness, tardiness and due date assignments. We also consider scheduling problems without involving due date assignment decisions. The objective function is to minimize the makespan, total completion time, total absolute variation in completion times, and total absolute variation in waiting times. We show that several existing well-known problems can be reduced to a special case of our unified model and solved in O(nlogn) time.     

基于多核系统NOC架构的静态列表调度算法*

在单芯片多核系统中,NoC已成为主流片上通信架构,有效的任务调度是挖掘计算并行性的重要方面。本文在经典静态列表调度基础上,针对HEFT算法中节点排序会得出较多的优先级相同节点的问题,提出一种节点二次排序的调度方法,在边的调度上应用了ALAP原则,改进算法有效提高了调度效果。实验表明：新方法对bl、blcomp、blio等节点优先级算法得出的任务列表均有良好的调度效果,适应性较好;对于2D MESH同构NoC平台,改进算法对三种节点优先级算法有1.15倍的平均加速比,最大可有1.27倍加速比。     

An algorithm for insertion of idle time in the single-machine scheduling problem with convex cost functions

This paper addresses the problem of optimally inserting idle time into a single-machine schedule when the sequence is fixed and the cost of each job is a convex function of its completion time. We propose a pseudo-polynomial time algorithm to find a solution within some tolerance of optimality in the solution space, i.e., each completion time will belong to a small time interval z within which the optimal solution lies. Letting H be the planning horizon and |J| the number of jobs, the proposed algorithm is superior to the current best algorithm in terms of time-complexity when |J|<H/z.     

Ant colony algorithm for satellite control resource scheduling problem

With the increasing number of satellite, the satellite control resource scheduling problem (SCRSP) has been main challenge for satellite networks. SCRSP is a constrained and large scale combinatorial problem. More and more researches focus on how to allocate various measurement and control resources effectively to ensure the normal running of the satellites. However, the sparse solution space of SCRSP leads its complexity especially for traditional optimization algorithms. As the validity of ant colony optimization (ACO) has been shown in many combinatorial optimization problems, a simple ant colony optimization algorithm (SACO) to solve SCRSP is presented in this paper. Firstly, we give a general mathematical model of SCRSP. Then, a optimization model, called conflict construction graph, based on visible arc and working period is introduced to reduce workload of dispatchers. To meet the requirements of TT & C network and make the algorithm more practical, we make the parameters of SACO as constant, which include the bounds, update and initialization of pheromone. The effect of parameters on the algorithm performance is studied by experimental method based on SCRSP. Finally, the performance of SACO is compared with other novel ACO algorithms to show the feasibility and effectiveness of improvements.     

A hybridization of genetic algorithms and fuzzy logic for the single-machine scheduling with flexible maintenance problem under human resource constraints

This work focuses on the problem of scheduling jobs on a single machine that requires flexible maintenance under human resource competence and availability constraints. To solve the problem we developed two fuzzy genetic algorithms that are based on respectively the sequential and total scheduling strategies. The one respecting the sequential strategy consists in two phases. In the first phase, the integrated production and maintenance schedules are generated. In the second one, the human resources are assigned to maintenance activities. The second algorithm respecting a total strategy consists in generating the integrated production and maintenance schedules that explicitly satisfy the human resource constraints. In regard to these two different strategies, we studied then two integrated fuzzy genetic algorithms that use the fuzzy logic framework to deal with the uncertain nature of both production and maintenance data. The proposed genetic algorithms have been implemented and applied to non-standard test problems which integrate production, maintenance and human resource data. The experimental results show that the consideration of human resource constraints and uncertainties allows to get more realistic and applicable solutions. Moreover, the comparison between the two proposed algorithms shows that the one based on the total strategy outperforms the one based on the sequential strategy regarding the objective functions’ optimization. However, this latter is better in terms of computational times.     

A study of single-machine scheduling problem to maximize throughput

We study inherent structural properties of a strongly NP-hard problem of scheduling $n$ jobs with release times and due dates on a single machine to minimize the number of late jobs. Our study leads to two polynomial-time algorithms. The first algorithm with the time complexity $O(n^3\log n)$ solves the problem if during its execution no job with some special property occurs. The second algorithm solves the version of the problem when all jobs have the same length. The time complexity of the latter algorithm is $O(n^2\log n)$ , which is an improvement over the earlier known algorithm with the time complexity $O(n^5)$ .