A double genetic algorithm for the MRCPSP/max

This paper presents a heuristic solution procedure for a very general resource-constrained project scheduling problem. Here, multiple execution modes are available for the individual activities of the project. In addition, minimum as well as maximum time lags between different activities may be given. The objective is to determine a mode and a start time for each activity such that the temporal and resource constraints are met and the project duration is minimised. Project scheduling problems of this type occur e.g. in process industries. The heuristic is a two-phased genetic algorithm with different representation, fitness, crossover operator, etc., in each of them. One of the contributions of the paper is the optimisation in the first phase of a problem dual to the original, the searching for the best modes of the activities. Computational results show that the algorithm outperforms the state-of-the-art algorithms in medium and large instances.     

Reactive scheduling in the multi-mode RCPSP

The multi-mode resource-constrained project scheduling problem (MRCPSP) involves the determination of a baseline schedule of the project activities, which can be executed in multiple modes, satisfying the precedence relations and resource constraints while minimizing the project duration. During the execution of the project, the baseline schedule may become infeasible due to activity duration and resource disruptions. We propose and evaluate a number of dedicated exact reactive scheduling procedures as well as a tabu search heuristic for repairing a disrupted schedule, under the assumption that no activity can be started before its baseline starting time. We report on promising computational results obtained on a set of benchmark problems.     

Heuristic procedures for reactive project scheduling

This paper describes new heuristic reactive project scheduling procedures that may be used to repair resource-constrained project baseline schedules that suffer from multiple activity duration disruptions during project execution. The objective is to minimize the deviations between the baseline schedule and the schedule that is actually realized.We discuss computational results obtained with priority-rule based schedule generation schemes, a sampling approach and a weighted-earliness tardiness heuristic on a set of randomly generated project instances.     

An Optimization-Based Approach for Design Project Scheduling

Concurrent engineering has been widely used in managing design projects to speed up the design process by concurrently performing multiple tasks. Since the progress of a design task often depends on the knowledge about other tasks and requires effective communication, tasks and communication activities need to be properly coordinated to avoid delays caused by waiting for information or the need for rework. This paper presents a novel formulation for design project scheduling with explicit modeling of task dependencies and the associated communication activities. General dependencies are modeled as combinations of three basic types representing sequential, concurrent, and independent processes. Communication activities are also modeled as tasks, and their interactions with design tasks are described by sets of intertask constraints. The objective is to achieve timely project completion with limited resources. To improve algorithm convergence and schedule quality, penalties on the violation of constraints coupling design tasks are added to the objective function. A solution methodology that combines Lagrangian relaxation, dynamic programming, and heuristic is developed to schedule design and communication tasks, and a surrogate optimization framework is used to overcome the “inseperability” caused by nonadditive penalties. A heuristic procedure is then developed to obtain scheduling policies from optimization results and to dynamically construct schedules. Numerical results show that the approach is effective to handle various task dependencies and the associated communication activities to provide high-quality schedules.      

Pareto process optimization of product development project using bi-objective hybrid genetic algorithm

Overlapping and iteration between development activities are the main reasons to cause complexity in product development (PD) process. Overlapping may not only reduce duration of a project but also create rework risk, while iteration increases the project duration and cost. In order to balance the duration and cost, this article presents four types of time models from the angle of time overlapping and activities dependent relationships based on Collaboration Degree Design Structure Matrix (CD-DSM) and builds the cost model considering the negation cost. On basis of the formulated model, a hybridization of the Pareto genetic algorithm (PGA) and variable neighborhood search (VNS) algorithm is proposed to solve the bi-objective process optimization problem of PD project for reducing the project duration and cost. The VNS strategy is implemented after the genetic operation of crossover and mutation to improve the exploitation ability of the algorithm. And then, an industrial example, a LED module PD project in an optoelectronic enterprise, is provided to illustrate the utility of the proposed approach. The optimization model minimizes the project duration and cost associated with overlapping and iteration and yields a Pareto optimal solution of project activity sequence for project managers to make decision following different business purposes. The simulation results of two different problems show that the proposed approach has a good convergence and robustness.     

PSO based approach for scheduling NPD projects including overlapping process

The efficient scheduling of the new product development (NPD) projects is important to reduce the required development time, and to offer the new product faster. Activity overlapping is commonly regarded as the most promising strategy to reduce product development times. However, overlapping must be well-planned by weighting the gain from the activity overlapping against the additional time for rework. The objective of this research was to develop a resource constrained scheduling methodology for NPD projects considering overlapping of activity couples. A particle swarm optimization based approach is used to schedule NPD projects that include overlapping process. The proposed PSO method is developed into a user friendly system so that the practitioners can utilize it. A real-life example of a product development project taken from the literature is used to show the efficiency of the software.     

云计算环境中面向DAG任务的多目标调度算法

为了实现任务执行效率与执行代价的同步优化,提出了一种云计算环境中的DAG任务多目标调度优化算法。算法将多目标最优化问题以满足Pareto最优的均衡最优解集合的形式进行建模,以启发式方式对模型进行求解;同时,为了衡量多目标均衡解的质量,设计了基于hypervolume方法的评估机制,从而可以得到相互冲突目标间的均衡调度解。通过配置云环境与三种人工合成工作流和两种现实科学工作流的仿真实验测试,结果表明,比较同类单目标算法和多目标启发式算法,算法不仅求解质量更高,而且解的均衡度更好,更加符合现实云的资源使用特征与工作流调度模式。     

A two-stage-priority-rule-based algorithm for robust resource-constrained project scheduling

Traditionally, the resource-constrained project scheduling problem (RCPSP) is modeled as a static and deterministic problem and is solved with the objective of makespan minimization. However, many uncertainties, such as unpredictable increases in processing times caused by rework or supplier delays, random transportation and/or setup, may render the proposed solution obsolete. In this paper, we present a two-stage algorithm for robust resource-constrained project scheduling. The first stage of the algorithm solves the RCPSP for minimizing the makespan only using a priority-rule-based heuristic, namely an enhanced multi-pass random-biased serial schedule generation scheme. The problem is then similarly solved for maximizing the schedule robustness while considering the makespan obtained in the first stage as an acceptance threshold. Selection of the best schedule in this phase is based on one out of 12 alternative robustness predictive indicators formulated for the maximization purpose. Extensive simulation testing of the generated schedules provides strong evidence of the benefits of considering robustness of the schedules in addition to their makespans. For illustration purposes, for 10 problems from the well-known standard set J30, both robust and non-robust schedules are executed with a 10% duration increase that is applied to the same randomly picked 20% of the project activities. Over 1000 iterations per instance problem, the robust schedules display a shorter makespan in 55% of the times while the non-robust schedules are shown to be the best performing ones in only 6% of the times.     

An integer programming approach to the multimode resource-constrained multiproject scheduling problem

The project scheduling problem (PSP) is the subject of several studies in computer science, mathematics, and operations research because of the hardness of solving it and its practical importance. This work tackles an extended version of the problem known as the multimode resource-constrained multiproject scheduling problem. A solution to this problem consists of a schedule of jobs from various projects, so that the job allocations do not exceed the stipulated limits of renewable and nonrenewable resources. To accomplish this, a set of execution modes for the jobs must be chosen, as the jobs’ duration and amount of needed resources vary depending on the mode selected. Finally, the schedule must also consider precedence constraints between jobs. This work proposes heuristic methods based on integer programming to solve the PSP considered in the Multidisciplinary International Scheduling Conference: Theory and Applications (MISTA) 2013 Challenge. The developed solver was ranked third in the competition, being able to find feasible and competitive solutions for all instances and improving best known solutions for some problems.     

A branch‐and‐bound algorithm for scheduling of new product development projects

In this paper, we consider scheduling problem in a new product development project. Each research and development project consists of a set of activities in which each activity may be executed in several ways. Each way of execution of an activity is a different technology, called an alternative technology, which may fail due to technical risks. In this work, we focus on alternative technologies for scheduling activities to maximize the expected net present value. We assume that the activity payoff is obtained as soon as any single technology is completed successfully. Therefore, we analyze the problem and develop a two‐phase solution procedure, consisting of a branch‐and‐bound algorithm and a recursive search procedure. The efficiency of the proposed algorithm has been evaluated on a set of randomly generated test instances.     

Computing Completion Time and Optimal Scheduling of Design Activities in Concurrent Product Development Process

This paper proposes a time-computing model and a scheduling method for shortening the completion time of product development under the given rework cost budget. As overlapping and iteration exist between or among design activities in concurrent product development, predictability and efficiency of the process deserve attention. By using the corresponding design structure matrix, the characteristics of information flow are obtained and applied to analysis of the dynamic behavior of the product development process. A time-computing model is set up to estimate the rework cost and completion time of each of the activities, between which both iteration and overlapping are observed. Through sequential quadratic programming, an optimization algorithm is developed for minimizing the development completion time under the constraint of the given rework cost budget. Our application results acquired from our experiments have verified the feasibility and validity of the approach.     

Multi-mode renewable resource-constrained allocation in PERT networks

This paper presents a hybrid metaheuristic algorithm (HMA) for Multi-Mode Resource-Constrained Project Scheduling Problem (MRCPSP) in PERT networks. A PERT-type project, where activities require resources of various types with random duration, is considered. Each activity can be accomplished in one of several execution modes and each execution mode represents an alternative combination of resource requirements of the activity and its duration. The problem is to minimize the regular criterion namely project's makespan by obtaining an optimal schedule and also the amount of different resources assigned to each activity. The resource project scheduling model is strongly NP-hard, therefore a metaheuristic algorithm is suggested namely HMA. In order to validate the performance of new hybrid metaheuristic algorithm, solutions are compared with optimal solutions for small networks. Also the efficiency of the proposed algorithm, for real world problems, in terms of solution quality and CPU time, is compared to one of the well-known metaheuristic algorithms, namely Genetic Algorithm of Hartmann (GAH). The computational results reveal that the proposed method provides appropriate results for small networks and real world problems.     

The contractor time–cost–credit trade‐off problem: integer programming model,heuristic solution,and business insights

Contractors in the construction sector face several trade‐offs between time and cost. The time–cost trade‐off (TCT) is one of these trade‐offs where contractors can reduce a project completion time by assigning more resources to activities, which means spending more money, to shorten the execution times of project activities. On the other hand, contractors who finance their projects through credit lines from banks such that if they reach their credit limits, then the start times of some project activities can be delayed until cash is available again, which might lead to an increase in the project execution time; thus, contractors need to consider the time–credit trade‐off. In this work, we simultaneously consider these two trade‐offs that affect the project completion time and use mixed integer linear programming (MILP) to model the contractor time–cost–credit trade‐off (TCCT) problem. The MILP model minimizes the project execution time given the contractor's budgetary and financial constraints. In addition to the MILP model, we also develop a heuristic solution algorithm to solve the problem. Through a set of benchmark instances, we study the effectiveness of the heuristic algorithm and the computation time of the exact model. It is found that a good upper bound for the MILP results in less computation time. We also study some practical aspects of the problem where we highlight the importance of expediting contractor payments in addition to selecting a financially stable contractor. Finally, we use our MILP model to help a contractor bid for a project.     

Optimal scheduling of cooperative tasks in a distributed systemusing an enumerative method

Preemptive (resume) scheduling of cooperative tasks that have been preassigned to a set of processing nodes in a distributed system, when each task is assumed to consist of several modules is discussed. During the course of their execution, the tasks communicate with each other to collectively accomplish a common goal. Such intertask communications lead to precedence constraints between the modules of different tasks. The objective of this scheduling is to minimize the maximum normalized task response time, called the system hazard. Real-time tasks and the precedence constraints among them are expressed in a PERT/CPM form with activity on arc (AOA), called the task graph (TG), in which the dominance relationship between simultaneously schedulable modules is derived and used to reduce the size of the set of active schedules to be searched for an optimal schedule. Lower-bound costs are estimated, and are used to bound the search. An example of the task scheduling problem and some computational experiences are presented     

基于遗传算法的多模式资源约束项目调度问题研究

为解决多模式资源约束项目调度问题,提出了一种混合遗传算法的求解方法。该算法采用二维编码方法来表示问题的解,基因的值表示任务的优先权和执行模式,每条染色体对应一个满足逻辑关系约束的可行任务排序,根据染色体所对应的任务调度顺序和执行模式序列可以获得一个满足资源约束的项目调度方案。应用该编码方法进行选择、交叉和变异等遗传操作,能够使搜索范围遍及整个问题解空间。实际应用表明,该算法能快速求得问题的最优解或近似最优解。     

网格环境下一种可调目标的启发式调度策略

针对网格环境下不同类型的任务执行时间相差较大的问题,提出了基于任务平均执行时间的忍耐度的概念,重新构造了启发式规则,体现了任务QoS的要求;并将这种服务质量的需求与任务完成时间相结合,给出了一个可调节的局部目标函数,实现了一种基于任务完成时间和任务服务质量的启发式调度算法OA-Sufferage;最后,给出了服务率(service ratio)的概念和定义,定量地衡量任务得到的服务质量.实验结果表明,该策略优先调度那些等待时间相对于执行时间较大的任务,提高了任务的服务率;而且可以通过调节局部目标函数中的偏好因子(preference factor),追求任务完成时间和QoS的不同目标,更加适合开放复杂的网格环境.     

An intelligent search method for project scheduling problems

We develop an approach for implementing a real time admissible heuristic search algorithm for solving project scheduling problems with resource constraints. This algorithm is characterized by the complete heuristic learning process: state selection, heuristic learning, and search path review. The implementation approach is based on the network structure and the activity status of a project; which consists of definition of states, state transition operator, heuristic estimation, and state transition cost. The performance analysis with a benchmark problem shows that, the accumulation of heuristic learning during the search process leads to the re-scheduling of more promising activities, and finds an optimal schedule efficiently.     

Minimum makespan task sequencing with multiple shared resources

In this paper we study the general problem of sequencing multiple jobs, where each job consists of multiple ordered tasks and tasks execution requires simultaneous usage of several resources. In particular, the case of an automatic assembly cell is examined. NP-completeness results are given. A heuristic is designed and evaluated.     

Robust heuristic algorithms for exploiting the common tasks of relational cloud database queries

Cloud computing enables a conventional relational database system's hardware to be adjusted dynamically according to query workload, performance and deadline constraints. One can rent a large amount of resources for a short duration in order to run complex queries efficiently on large-scale data with virtual machine clusters. Complex queries usually contain common subexpressions, either in a single query or among multiple queries that are submitted as a batch. The common subexpressions scan the same relations, compute the same tasks (join, sort, etc.), and/or ship the same data among virtual computers. The total time spent for the queries can be reduced by executing these common tasks only once. In this study, we build and use efficient sets of query execution plans to reduce the total execution time. This is an NP-Hard problem therefore, a set of robust heuristic algorithms, Branch-and-Bound, Genetic, Hill Climbing, and Hybrid Genetic-Hill Climbing, are proposed to find (near-) optimal query execution plans and maximize the benefits. The optimization time of each algorithm for identifying the query execution plans and the quality of these plans are analyzed by extensive experiments.     

A study of combining heuristics for scheduling projects with limited multiple resources

The main objective of this study was to find a simple and quick procedure on the microcomputer for scheduling activities of a constrained multiple resource single project network that would minimize project duration. From this research there are two different types of results presented. First, a combination of simple heuristics which find the average of the minimum project durations for the constrained resource problem is presented. This combination not only supports the previous research on successful simple heuristic methods which set the priorities for constrained resource problems, but also produces results which are significantly better than those obtained by single heuristics. Second, a procedure for determining this combination of heuristics is introduced. A computer algorithm, COMAL, was developed for this study with constrained resource problems, but in the future its use may be expanded into other fields.