Multi-objective metaheuristic algorithms for the resource-constrained project scheduling problem with precedence relations

This study addresses the resource-constrained project scheduling problem with precedence relations, and aims at minimizing two criteria: the makespan and the total weighted start time of the activities. To solve the problem, five multi-objective metaheuristic algorithms are analyzed, based on Multi-objective GRASP (MOG), Multi-objective Variable Neighborhood Search (MOVNS) and Pareto Iterated Local Search (PILS) methods. The proposed algorithms use strategies based on the concept of Pareto Dominance to search for solutions and determine the set of non-dominated solutions. The solutions obtained by the algorithms, from a set of instances adapted from the literature, are compared using four multi-objective performance measures: distance metrics, hypervolume indicator, epsilon metric and error ratio. The computational tests have indicated an algorithm based on MOVNS as the most efficient one, compared to the distance metrics; also, a combined feature of MOG and MOVNS appears to be superior compared to the hypervolume and epsilon metrics and one based on PILS compared to the error ratio. Statistical experiments have shown a significant difference between some proposed algorithms compared to the distance metrics, epsilon metric and error ratio. However, significant difference between the proposed algorithms with respect to hypervolume indicator was not observed.     

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.     

Knowledge integration using problem spaces: A study in resource-constrained project scheduling

The need to develop schedules for projects with resource constraints and cash flows arises in organizational settings ranging from construction planning to research and development. Given the intractable nature of the problem, a variety of knowledge sources relevant to the project scheduling task have been identified in the Operations Management literature. These include a large number of heuristic procedures that can be used to generate feasible project schedules as well as recent neural network-based approaches that can select appropriate heuristic procedures to apply to a specific instance of the project scheduling problem. While integrated application of these knowledge sources is required to effectively support scheduling, previous work has focussed on developing and implementing them in isolation. The problem space computational model presented in this paper addresses this shortcoming by integrating these various knowledge sources, thus enabling the development of decision support systems for resource constrained project scheduling. More generally, the modeling approach used in this paper can be applied to create systems to assist knowledge intensive tasks that arise in many organizational settings.     

Event-based MILP models for resource-constrained project scheduling problems

In this paper we make a comparative study of several mixed integer linear programming (MILP) formulations for resource-constrained project scheduling problems (RCPSPs).     

An efficient hybrid algorithm for resource-constrained project scheduling

We propose an efficient hybrid algorithm, known as ACOSS, for solving resource-constrained project scheduling problems (RCPSP) in real-time. The ACOSS algorithm combines a local search strategy, ant colony optimization (ACO), and a scatter search (SS) in an iterative process. In this process, ACO first searches the solution space and generates activity lists to provide the initial population for the SS algorithm. Then, the SS algorithm builds a reference set from the pheromone trails of the ACO, and improves these to obtain better solutions. Thereafter, the ACO uses the improved solutions to update the pheromone set. Finally in this iteration, the ACO searches the solution set using the new pheromone trails after the SS has terminated. In ACOSS, ACO and the SS share the solution space for efficient exchange of the solution set. The ACOSS algorithm is compared with state-of-the-art algorithms using a set of standard problems available in the literature. The experimental results validate the efficiency of the proposed algorithm.     

A new lower bound for the resource-constrained project scheduling problem with generalized precedence relations

In this paper we propose a new lower bound for the resource-constrained project scheduling problem with generalized precedence relationships. The lower bound is based on a relaxation of the resource constraints among independent activities and on a solution of the relaxed problem suitably represented by means of an AON acyclic network. Computational results are presented and confirmed a better practical performance of the proposed method with respect to those present in the literature.     

人工蜂群算法求解资源受限项目调度问题

针对资源受限项目调度问题,提出了一种基于人工蜂群算法的优化方法。人工蜂群算法中每个食物源的位置代表一种项目任务的优先权序列,每个食物源的位置通过扩展串行调度机制转换成可行的调度方案,迭代中由三种人工蜂执行不同的操作来实现全局最优解的更新。实验结果表明,人工蜂群算法是求解资源受限项目调度问题的有效方法,同时扩展调度机制的引入可以加速迭代收敛的进程。     

Theoretical and practical fundamentals for multi-objective optimisation in resource-constrained project scheduling problems

Project scheduling is an inherently multi-objective problem, since managers want to finish projects as soon as possible with the minimum cost and the maximum quality. However, there are only a few papers dealing with multiobjective resource-constrained project scheduling problems (MORCPSPs). Moreover, there is no theoretical study in the literature that establishes the fundamentals for correct algorithmic developments. In this paper we try to close the gap by proving several results for MORCPSPs. With these results as a basis, both exact and heuristic procedures capable of obtaining a set of efficient solutions for several important MORCPSPs can be created.     

A heuristic approach for resource constrained project scheduling with uncertain activity durations

In this paper, we address the resource constrained project scheduling problem with uncertain activity durations. Project activities are assumed to have known deterministic renewable resource requirements and uncertain durations, described by independent random variables with a known probability distribution function. To tackle the problem solution we propose a heuristic method which relies on a stage wise decomposition of the problem and on the use of joint probabilistic constraints.     

A random key based genetic algorithm for the resource constrained project scheduling problem

This paper presents a genetic algorithm for the Resource Constrained Project Scheduling Problem (RCPSP). The chromosome representation of the problem is based on random keys. The schedule is constructed using a heuristic priority rule in which the priorities of the activities are defined by the genetic algorithm. The heuristic generates parameterized active schedules. The approach was tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.     

Enhanced energetic reasoning-based lower bounds for the resource constrained project scheduling problem

We present new and effective lower bounds for the resource constrained project scheduling problem. This problem is widely known to be notoriously difficult to solve due to the lack of lower bounds that are both tight and fast. In this paper, we propose several new lower bounds that are based on the concept of energetic reasoning. A major contribution of this work is to investigate several enhanced new feasibility tests that prove useful for deriving new lower bounds that consistently outperform the classical energetic reasoning-based lower bound. In particular, we present the results of a comprehensive computational study, carried out on 1560 benchmark instances, that provides strong evidence that a deceptively simple dual feasible function-based lower bound is highly competitive with a state-of-the-art lower bound while being extremely fast. Furthermore, we found that an effective shaving procedure enables to derive an excellent lower bound that often outperforms the best bound from the literature while being significantly simpler.     

A mathematical model for the multi-mode resource-constrained project scheduling problem with mode dependent time lags

This paper presents an exact model for the multi-mode resource-constrained project scheduling problem with generalized precedence relations in which the minimal or maximal time lags between a pair of activities may vary depending on the chosen modes. All resources considered are renewable. The objective is to determine a mode and a start time for each activity so that all constraints are obeyed and the project duration is minimized. Project scheduling of this type occurs in many fields, for instance, construction industries. The proposed model has been inspired by the rectangle packing problems. In spite of the fact that it needs a feasible solution to start for conventional models, the new model has no need for a feasible solution to start. Computational results with a set of 60 test problems have been reported and the efficiency of the proposed model has been analyzed.     

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.     

Setup times and fast tracking in resource-constrained project scheduling

Resource-constrained project scheduling with activity pre-emption assumes that activities are allowed to be interrupted and restarted later in the schedule at no extra cost. In the current paper, we extend this pre-emptive scheduling problem with setup times between activity interruptions and the possibility to schedule pre-emptive sub-parts of activities in parallel.

The contribution of the paper is twofold. First, we briefly show that an efficient exact branch-and-bound procedure from the literature to solve the resource-constrained project scheduling problem can be easily adapted to cope with our problem extensions. Second, we extensively test the impact of these pre-emptive extensions to the quality of the schedule from a makespan point-of-view.     

A hybrid estimation of distribution algorithm for solving the resource-constrained project scheduling problem

In this paper, a hybrid estimation of distribution algorithm (HEDA) is proposed to solve the resource-constrained project scheduling problem (RCPSP). In the HEDA, the individuals are encoded based on the extended active list (EAL) and decoded by serial schedule generation scheme (SGS), and a novel probability model updating mechanism is proposed for well sampling the promising searching region. To further improve the searching quality, a Forward-Backward iteration (FBI) and a permutation based local search method (PBLS) are incorporated into the EDA based search to enhance the exploitation ability. Simulation results based on benchmarks and comparisons with some existing algorithms demonstrate the effectiveness of the proposed HEDA.     

An effective shuffled frog-leaping algorithm for resource-constrained project scheduling problem

In this paper, we propose an effective heuristic based on the framework of the shuffled frog-leaping algorithm (SFLA) for solving the resource-constrained project scheduling problem (RCPSP). We encode the virtual frog as the extended activity list (EAL) and decode it by the SFLA-specific serial schedule generation scheme (SSSGS). The initial population is generated by the regret-based sampling method and the priority rule. Then, virtual frogs are partitioned into several memeplexes, and each memeplex evolves by adopting the effective resource-based crossover (RBCO). To enhance the exploitation ability, a combined local search including permutation-based local search (PBLS) and forward-backward improvement (FBI) is performed in each memeplex. To maintain the diversity of each memeplex, virtual frogs are periodically shuffled and reorganized into new memeplexes. Basing on some theoretical analysis, speed-up evaluation methods are proposed to improve the efficiency of the SFLA, which are also suitable for other heuristics designed for RCPSP. In addition, we make use of a design-of-experiment method to determine the set of suitable parameters for the SFLA. Computational results and comparisons with some typical existing algorithms demonstrate the effectiveness of the proposed SFLA.     

New concepts for activity float in resource-constrained project management

The concepts of float and critical path are central to analyzing activity networks in project management. In resource-constrained projects, schedule multiplicity makes it difficult to calculate float and identify critical activities accurately. In this work, new concepts of float and critical activity are developed to ascertain critical activities more precisely without reference to activity start and end times in specific schedules. The notions of float, group float, float set, negative float and zero critical activity are introduced, which the project manager can use to deal more effectively with critical activities, duration uncertainty, activity buffering, and resource allocation than the currently available tools in literature. For practical implementation, algorithms are provided and tested to calculate the new measures on the PSPLIB benchmark instances, specifically the J30, J60 and J120 test sets, for the resource constrained project management, illustrating the effectiveness of the proposed concepts in helping to identify flexibility in scheduling activities.     

An effective estimation of distribution algorithm for the multi-mode resource-constrained project scheduling problem

In this paper, an estimation of distribution algorithm (EDA) is proposed to solve the multi-mode resource-constrained project scheduling problem (MRCPSP). In the EDA, the individuals are encoded based on the activity-mode list (AML) and decoded by the multi-mode serial schedule generation scheme (MSSGS), and a novel probability model and an updating mechanism are proposed for well sampling the promising searching region. To further improve the searching quality, a multi-mode forward backward iteration (MFBI) and a multi-mode permutation based local search method (MPBLS) are proposed and incorporated into the EDA based search framework to enhance the exploitation ability. Based on the design-of-experiment (DOE) test, suitable parameter combinations are determined and some guidelines are provided to set the parameters. Simulation results based on a set of benchmarks and comparisons with some existing algorithms demonstrate the effectiveness of the proposed EDA.     

An optimal procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem

We present an optimal solution procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem. In this problem, we assume the constrained renewable resources are limited to very expensive equipments and machines that are used in other projects and are not available in all periods of time of a project. In other words, for each resource, there is a dictated ready date as well as a due date such that no resource can be available before its ready date but the resources are permitted to be used after their due dates by paying penalty cost depending on the resource type. We also assume that only one unit of each resource type is available and no activity needs more than it for execution. The objective is to determine a schedule with minimal total weighted resource tardiness penalty costs. For this purpose, we present a branch-and-bound algorithm in which the branching scheme starts from a graph representing a set of conjunctions (the classical finish-start precedence constraints) and disjunctions (introduced by the resource constraints). In the search tree, each node is branched to two child nodes based on the two opposite directions of each undirected arc of disjunctions. Selection sequence of undirected arcs in the search tree affects the performance of the algorithm. Hence, we developed different rules for this issue and compare the performance of the algorithm under these rules using a randomly generated benchmark problem set.     

An effective shuffled frog-leaping algorithm for multi-mode resource-constrained project scheduling problem

In this paper, an effective shuffled frog-leaping algorithm (SFLA) is proposed for solving the multi-mode resource-constrained project scheduling problem (MRCPSP). In the SFLA, the virtual frogs are encoded as the extended multi-mode activity list (EMAL) and decoded by the multi-mode serial schedule generation scheme (MSSGS). Initially, the mode assignment lists of the population are generated randomly, and the activity lists of the population are generated by the regret-based sampling method and the latest finish time (LFT) priority rule. Then, virtual frogs are partitioned into several memeplexes that evolve simultaneously by performing the simplified two-point crossover (STPC). To enhance the exploitation ability, the combined local search including the multi-mode permutation based local search (MPBLS) and the multi-mode forward-backward improvement (MFBI) is further performed in each memeplex. To maintain the diversity of each memeplex, virtual frogs are periodically shuffled and reorganized into new memeplexes. Computational results based on the well-known benchmarks and comparisons with some existing algorithms demonstrate the effectiveness of the proposed SFLA.