Multi‐mode resource‐constrained project scheduling using modified variable neighborhood search heuristic

This paper aims at providing a fast near‐optimum solution to the multi‐mode resource‐constrained project scheduling problems (MRCPSPs), for projects with activities that have known deterministic renewable and nonrenewable resource requirements. The MRCPSP is known to be nondeterministic polynomial‐time hard and has been solved using various exact, heuristic, and meta‐heuristic procedures. In this paper, a modified variable neighborhood search heuristic algorithm is used as an advanced optimization technique that suits scheduling problems. For the experimental study, we have considered a standard set of 3929 multi‐mode benchmark instances from the project scheduling library with a range of projects comprising 10–30 activities. Moreover, for a better comparison, this research also considers a standard set of 4320 newly developed multi‐mode instances from MMLIB50, MMLIB100, and MMLIB+ datasets. With the limit of 50,000 schedules on these datasets, our proposed algorithm provides better makespan for 106, 34, and 1601 instances, respectively, which justifies the efficiency of the proposed algorithm, particularly for projects with a larger number of activities. The results reported in this paper can be used as a benchmark for other researchers to compare and improve.     

An extended Akers graphical method with a biased random‐key genetic algorithm for job‐shop scheduling

This paper presents a local search, based on a new neighborhood for the job‐shop scheduling problem, and its application within a biased random‐key genetic algorithm. Schedules are constructed by decoding the chromosome supplied by the genetic algorithm with a procedure that generates active schedules. After an initial schedule is obtained, a local search heuristic, based on an extension of the 1956 graphical method of Akers, is applied to improve the solution. The new heuristic is tested on a set of 205 standard instances taken from the job‐shop scheduling literature and compared with results obtained by other approaches. The new algorithm improved the best‐known solution values for 57 instances.     

自适应混合蚁群算法在MRCPSP中的应用

以多模式资源受限项目调度问题(Multi-mode Resource Constrained Project Scheduling Problem,MRCPSP)为背景,针对蚁群算法收敛速度和解的多样性之间的平衡问题,提出一种改进的自适应混合蚁群算法.该算法中参数的取值范围和变化幅度能够随算法的运行同步自适应调整,蚂蚁...     

Using an enhanced scatter search algorithm for a resource-constrained project scheduling problem

The resource-constrained project scheduling problem is one of the classical problems in the field of operations research. There are many criteria to efficiently determine the desired schedule of a project. In this paper, a well-known criterion namely project’s makespan is considered. Due to the complexity of the problem, it is very difficult to obtain optimum solution for this kind of problems by means of traditional methods. Therefore, an enhanced scatter search, based on a new path relinking and two prominent permutation-based and crossover operators, is devised to solve the problem. In order to validate the performance of the proposed algorithm, in terms of solution quality, the algorithm is applied to various test problems available on the literature and the reliability of it, is compared with well-reported benchmark algorithms. The computational results reveal that the proposed algorithm has appropriate results in comparison with the existing benchmark algorithms.     

求解工件车间调度问题的一种新的邻域搜索算法

该文提出了一种新的求解工件车间调度(job shop scheduling)问题的邻域搜索算法．问题的目标是：在满足约束条件的前提下使得调度的makespan尽可能地小．定义了一种新的优先分配规则以生成初始解;定义了一种新的邻域结构;将邻域搜索跟单机调度结合在一起;提出了跳坑策略以跳出局部最优解并且将搜索引向有希望的方向．计算了当前国际文献中的一组共58个benchmark问题实例,算法的优度高于当前国外学者提出的两种著名的先进算法．其中对18个10工件10机器的实例,包括最著名的难解实例ft10,在可接受的时间内都找到了最优解．这些实例是当前文献中报导的所有规模为10工件10机器的实例．     

Iterated greedy algorithms for the blocking flowshop scheduling problem with makespan criterion

Recently, iterated greedy algorithms have been successfully applied to solve a variety of combinatorial optimization problems. This paper presents iterated greedy algorithms for solving the blocking flowshop scheduling problem (BFSP) with the makespan criterion. Main contributions of this paper can be summed up as follows. We propose a constructive heuristic to generate an initial solution. The constructive heuristic generates better results than those currently in the literature. We employ and adopt well-known speed-up methods from the literature for both insertion and swap neighborhood structures. In addition, an iteration jumping probability is proposed to change the neighborhood structure from insertion neighborhood to swap neighborhood. Generally speaking, the insertion neighborhood is much more effective than the swap neighborhood for the permutation flowshop scheduling problems. Instead of considering the use of these neighborhood structures in a framework of the variable neighborhood search algorithm, two powerful local search algorithms are designed in such a way that the search process is guided by an iteration jumping probability determining which neighborhood structure will be employed. By doing so, it is shown that some additional enhancements can be achieved by employing the swap neighborhood structure with a speed-up method without jeopardizing the effectiveness of the insertion neighborhood. We also show that the performance of the iterated greedy algorithm significantly depends on the speed-up method employed. The parameters of the proposed iterated greedy algorithms are tuned through a design of experiments on randomly generated benchmark instances. Extensive computational results on Taillard’s well-known benchmark suite show that the iterated greedy algorithms with speed-up methods are equivalent or superior to the best performing algorithms from the literature. Ultimately, 85 out of 120 problem instances are further improved with substantial margins.     

考虑资源置信度的跨企业项目鲁棒性调度算法

资源不确定性高和调度鲁棒性要求高是跨企业项目调度问题的重要特征,本文采用资源置信度度量资源的不确定性,建立了考虑资源置信度约束的跨企业项目鲁棒性优化调度模型,设计了路径重连求解算法.算法以路径重连机制搜索解空间,以嵌入 的启发式时间缓冲插入算法快速生成鲁棒性调度,并可通过局部增强搜索算法进一步优化调度的鲁棒性.本文应用项目调度标准问题 库PSPLIB中大量问题实例进行了仿真实验,同两个当前具有代表性的鲁棒性项目调度算法进行了比较,实验结果表明了文中算法的有 效性与优势.     

New strategies for stochastic resource-constrained project scheduling

We study the stochastic resource-constrained project scheduling problem or SRCPSP, where project activities have stochastic durations. A solution is a scheduling policy, and we propose a new class of policies that is a generalization of most of the classes described in the literature. A policy in this new class makes a number of a priori decisions in a preprocessing phase, while the remaining scheduling decisions are made online. A two-phase local search algorithm is proposed to optimize within the class. Our computational results show that the algorithm has been efficiently tuned toward finding high-quality solutions and that it outperforms all existing algorithms for large instances. The results also indicate that the optimality gap even within the larger class of elementary policies is very small.     

Total flow time minimization in no-wait job shop using a hybrid discrete group search optimizer

The no-wait job shop scheduling problem is a well-known NP-hard problem and it is typically decomposed into timetabling subproblem and sequencing subproblem. By adopting favorable features of the group search technique, a hybrid discrete group search optimizer is proposed for finding high quality schedules in the no-wait job shops with the total flow time criterion. In order to find more promising sequences, the producer operator is designed as a destruction and construction (DC) procedure and an insertion-based local search, the scrounger operator is implemented by differential evolution scheme, and the ranger operator is designed by hybridizing best insert moves. An efficient initialization scheme based on Nawaz–Enscore–Ham (NEH) heuristic is designed to construct the initial population with both quality and diversity. A speed-up method is developed to accelerate the evaluation of the insertion neighborhood. Computational results based on well-known benchmark instances show that the proposed algorithm clearly outperforms a hybrid differential evolution algorithm and an iterated greedy algorithm. In addition, the proposed algorithm is comparable to a local search method based on optimal job insertion, especially for large-size instances.     

Three self-adaptive multi-objective evolutionary algorithms for a triple-objective project scheduling problem

Finding a Pareto-optimal frontier is widely favorable among researchers to model existing conflict objectives in an optimization problem. Project scheduling is a well-known problem in which investigating a combination of goals eventuate in a more real situation. Although there are many different types of objectives based on the situation on hand, three basic objectives are the most common in the literature of the project scheduling problem. These objectives are: (i) the minimization of the makespan, (ii) the minimization of the total cost associated with the resources, and (iii) the minimization of the variability in resources usage. In this paper, three genetic-based algorithms are proposed for approximating the Pareto-optimal frontier in project scheduling problem where the above three objectives are simultaneously considered. For the above problem, three self-adaptive genetic algorithms, namely (i) A two-stage multi-population genetic algorithm (MPGA), (ii) a two-phase subpopulation genetic algorithm (TPSPGA), and (iii) a non-dominated ranked genetic algorithm (NRGA) are developed. The algorithms are tested using a set of instances built from benchmark instances existing in the literature. The performances of the algorithms are evaluated using five performance metrics proposed in the literature. Finally according to the technique for order preference by similarity to ideal solution (TOPSIS) the self-adaptive NRGA gained the highest preference rank, followed by the self-adaptive TPSPGA and MPGA, respectively.     

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.     

A novel global optimization technique for high dimensional functions

Several types of line search methods are documented in the literature and are well known for unconstraint optimization problems. This paper proposes a modified line search method, which makes use of partial derivatives and restarts the search process after a given number of iterations by modifying the boundaries based on the best solution obtained at the previous iteration (or set of iterations). Using several high‐dimensional benchmark functions, we illustrate that the proposed line search restart (LSRS) approach is very suitable for high‐dimensional global optimization problems. Performance of the proposed algorithm is compared with two popular global optimization approaches, namely, genetic algorithm and particle swarm optimization method. Empirical results for up to 2000 dimensions clearly illustrate that the proposed approach performs very well for the tested high‐dimensional functions. © 2009 Wiley Periodicals, Inc.     

求解Job-Shop调度问题的禁忌搜索算法的研究

本文针对最小完工时间的Job-Shop调度问题提出了一种禁忌搜索算法，该算法使用插入算法构造尽可能好的初始解，然后用禁忌搜索算法改进当前解，在算法中对未被选中的候选解信息进行记忆，合理平衡了集中搜索与分散搜索。最后用基准实例进行仿真，实验结果表明该算法是可行的和有效的。     

Using meta-heuristics for project scheduling under mode identity constraints

Mode identity and resource constrained project scheduling problem (MIRCPSP) is a substantial generalization of the well-known multi-mode problem. It arises when certain activities in the project are interdependent. That is, the set of all activities in the project are partitioned into disjoint subsets where all activities forming one subset have to be processed in the same mode. This paper addresses project scheduling problem with resource and mode identity constraints to minimize the project makespan. This problem is strongly NP-hard and three meta-heuristic algorithms namely imperialist competitive algorithm, simulated annealing and differential evolution are proposed to solve it. In order to improve the quality of the employed algorithms a local search and learning module is combined with the meta-heuristic algorithms. The performance of the algorithms is evaluated on 180 test problems by statistically comparing their solution in term of the objective function and computational times. The obtained computational results indicate that the integration of the learning module and the proposed algorithm is efficient and effective.     

Multiple Phase Neighborhood Search-GRASP for the Capacitated Vehicle Routing Problem

Greedy Randomized Adaptive Search Procedure (GRASP) has been proved to be a very efficient algorithm for the solution of the Traveling Salesman Problem. Also, it has been proved that expanding the local search with the use of two or more different local search strategies helps the algorithm to avoid trapping in a local optimum. In this paper, a new modified version of GRASP, called Multiple Phase Neighborhood Search-GRASP (MPNS-GRASP), for the solution of the Vehicle Routing Problem is proposed. In this method, a stopping criterion based on Lagrangean Relaxation and Subgradient Optimization is utilized. In addition, a different way for expanding the neighborhood search is used based on a new strategy, the Circle Restricted Local Search Moves strategy. The algorithm was tested on two sets of benchmark instances and gave very satisfactory results. In both sets of instances the results have solution qualities with average values near to the optimum values and in a number of them the algorithm finds the optimum. The computational time of the algorithm is decreased significantly compared to other heuristic and metaheuristic algorithms due to the fact that the new strategy, the Expanding Neighborhood Search Strategy, is used.     

An evolutionary search procedure for optimizing time–cost performance of projects under multiple renewable resource constraints

This paper presents an effective procedure for optimizing time–cost performance of multi-mode resource constrained project scheduling problems in which activities are subject to finish-start precedence constraints under renewable limited resources. Associated with each execution mode of activities, there exists a direct cost, a processing time, and a set of required renewable resources. In optimizing time–cost performance, the procedure treats the cost as a non-renewable resource whose limit can affect the duration of the project and balances cost versus time through the notion of priority-rank. This is performed by the use of a module which handles multimode projects, and since the procedure has to call this module with different limits on the cost, the effectiveness of this module plays a key role in the overall efficiency. For this reason, an effective evolutionary search technique has been developed to create the basis of this module. For testing its effectiveness, this module has been tested on 552 largest multimode benchmark instances of the PSPLIB and the results are promising: For over 98% of instances, the module finds the best available solutions in the literature. The module also produces a solution for one of these benchmark instances that is better than all of the current solutions in the literature.     

A new ant colony algorithm for makespan minimization in permutation flow shops

The problem of scheduling in permutation flow shop with the objective of minimizing the maximum completion time, or makespan, is considered. A new ant colony optimization algorithm is developed for solving the problem. A novel mechanism is employed in initializing the pheromone trails based on an initial sequence. Moreover, the pheromone trail intensities are limited between lower and upper bounds which change dynamically. When a complete sequence of jobs is constructed by an artificial ant, a local search is performed to improve the performance quality of the solution. The proposed ant colony algorithm is applied to Taillard’s benchmark problems. Computational experiments suggest that the algorithm yields better results than well-known ant colony optimization algorithms available in the literature.     

An effective hybrid tabu search algorithm for multi-objective flexible job-shop scheduling problems

This paper proposes an effective hybrid tabu search algorithm (HTSA) to solve the flexible job-shop scheduling problem. Three minimization objectives – the maximum completion time (makespan), the total workload of machines and the workload of the critical machine are considered simultaneously. In this study, a tabu search (TS) algorithm with an effective neighborhood structure combining two adaptive rules is developed, which constructs improved local search in the machine assignment module. Then, a well-designed left-shift decoding function is defined to transform a solution to an active schedule. In addition, a variable neighborhood search (VNS) algorithm integrating three insert and swap neighborhood structures based on public critical block theory is presented to perform local search in the operation scheduling component. The proposed HTSA is tested on sets of the well-known benchmark instances. The statistical analysis of performance comparisons shows that the proposed HTSA is superior to four existing algorithms including the AL + CGA algorithm by Kacem, Hammadi, and Borne (2002b), the PSO + SA algorithm by Xia and Wu (2005), the PSO + TS algorithm by Zhang, Shao, Li, and Gao (2009), and the Xing’s algorithm by Xing, Chen, and Yang (2009a) in terms of both solution quality and efficiency.     

A discrete differential evolution algorithm for the single machine total weighted tardiness problem with sequence dependent setup times

This paper is concerned with solving the single machine total weighted tardiness problem with sequence dependent setup times by a discrete differential evolution algorithm developed by the authors recently. Its performance is enhanced by employing different population initialization schemes based on some constructive heuristics such as the well-known NEH and the greedy randomized adaptive search procedure (GRASP) as well as some priority rules such as the earliest weighted due date (EWDD) and the apparent tardiness cost with setups (ATCS). Additional performance enhancement is further achieved by the inclusion of a referenced local search (RLS) in the algorithm together with the use of destruction and construction (DC) procedure when obtaining the mutant population. Furthermore, to facilitate the greedy job insertion into a partial solution which will be employed in the NEH, GRASP, DC heuristics as well as in the RLS local search, some newly designed speed-up methods are presented for the insertion move for the first time in the literature. They are novel contributions of this paper to the single machine tardiness related scheduling problems with sequence dependent setup times. To evaluate its performance, the discrete differential evolution algorithm is tested on a set of benchmark instances from the literature. Through the analyses of experimental results, its highly effective performance with substantial margins both in solution quality and CPU time is shown against the best performing algorithms from the literature, in particular, against the very recent newly designed particle swarm and ant colony optimization algorithms of Anghinolfi and Paolucci [A new discrete particle swarm optimization approach for the single machine total weighted tardiness scheduling problem with sequence dependent setup times. European Journal of Operational Research 2007; doi:10.1016/j.ejor.2007.10.044] and Anghinolfi and Paolucci [A new ant colony optimization approach for the single machine total weighted tardiness scheduling problem. http://www.discovery.dist.unige.it/papers/Anghinolfi_Paolucci_ACO.pdf, respectively. Ultimately, 51 out of 120 overall aggregated best known solutions so far in the literature are further improved while other 50 instances are solved equally.     

MaxSAT-based large neighborhood search for high school timetabling

High School Timetabling (HSTT) is a well known and wide spread problem. The problem consists of coordinating resources (e.g. teachers, rooms), times, and events (e.g. lectures) with respect to various constraints. Unfortunately, HSTT is hard to solve and just finding a feasible solution for simple variants of HSTT have been proven to be NP-complete. We propose a new algorithm for HSTT which combines local search with a novel maxSAT-based large neighborhood search. A local search algorithm is used to drive an initial solution into a local optimum and then more powerful large neighborhood search (LNS) techniques based on maxSAT are used to further improve the solution. We prove the effectiveness of our approach with experimental results on instances taken from the Third International Timetabling Competition 2011 and the XHSTT-2014 benchmark archive. We were able to model 27 out of 39 instances. The remaining 12 instances were not modeled because the currently used maxSAT formulation for XHSTT does not support resource assignments in general. For the instances which could be modeled, our algorithm shows good performance when compared to other XHSTT state-of-the-art solvers and for several instances new best known upper bounds have been computed.