All projects require a structure to meet project requirements and achieve established goals. This framework is called project management. Therefore, project management plays an important role in national development and economic growth. Project management includes various knowledge areas such as project integration management, project scope management, project schedule management, etc. The article focuses on the resource-constrained project scheduling known as problem so- called the resource-constrained project scheduling problem (RCPSP). The RCPSP is a part of schedule management. The standard RCPSP has two important constraints, resource constraints and precedence relationships of activities during project scheduling. The objective of the problem is to optimize and minimize the project duration, subject to the above constraints. In this paper, we develop a convolutional neural network approach to solve the standard single mode RCPSP. The advantage of this algorithm over conventional methods such as metaheuristics is that it does not need to generate many solutions or populations. In this paper, the serial schedule generation scheme (SSGS) is used to schedule the project activities using an evolved convolutional neural network (CNN) as a tool to select an appropriate priority rule to filter out a candidate activity. The evolved CNN learns according to the eight project parameters, namely network complexity, resource factor, resource strength, average work per activity, etc. The above parameters are the inputs of the network and are recalculated at each step of the project planning. Moreover, the developed network has priority rules which are the outputs of the developed neural network. Therefore, after the learning process, the network can automatically select an appropriate priority rule to filter an activity from the eligible activities. In this way, the algorithm is able to schedule all project activities according to the given project constraints. Finally, the performance of the Convolutional Neural Network (CNN) approach is investigated using standard benchmark problems from PSPLIB in comparison to the MLFNN approach and standard metaheuristics.

Project management has a fundamental role in national development, industrial development, and economic growth. Schedule management is also one of the knowledge areas of project management, which includes the processes employed to manage the timely completion of the project. This paper deals with the Resource-Constrained Project Scheduling Problem (RCPSP), which is a part of schedule management. The objective of the problem is to optimize and minimize the project duration while constraining the resource quantities during project scheduling. There are two important constraints in this problem, namely resource constraints and precedence relationships of activities during project scheduling. Many methods such as exact, heuristic, and meta-heuristic have been developed by researchers to solve the problem, but there is a lack of investigation of the problem using methods such as neural networks and machine learning. In this article, we develop a multi-layer feed-forward neural network (MLFNN) to solve the standard single- mode RCPSP. The advantage of this method over evolutionary methods or metaheuristics is that it is not necessary to generate numerous solutions or populations. The developed MLFNN learns based on eight project parameters, namely network complexity, resource factor, resource strength, average work per activity, percentage of remaining work, etc., which are calculated at each step of project scheduling, and identified priority rules, which are the outputs of the developed neural network. Therefore, after the learning process, the network can automatically select an appropriate priority rule to filter out an unscheduled activity from the list of eligible activities and schedule all activities of the project according to the given project constraints. Finally, we investigate the performance of the presented approach using the standard benchmark problems from PSPLIB.

The Resource-Constrained Project Scheduling Problem (RCPSP) remains a critical area of study in project management, focusing on optimizing project schedules under constraints such as limited resources and task interdependencies. This review synthesizes advancements from 2016 to 2024, encompassing problem variants, optimization techniques, objectives, and real-world applications. Key developments include the evolution of hybrid metaheuristics, multi-objective optimization approaches, and the integration of stochastic models to enhance robustness against uncertainties. Furthermore, the application of machine learning and sustainability-driven models has expanded the practical scope of RCPSP in dynamic and complex environments. Challenges such as scalability, uncertainty management, and the need for practical implementations are addressed, with future directions emphasizing AI integration, decentralized scheduling, and real-time adaptive solutions. This study provides a comprehensive perspective on RCPSP, bridging theoretical research with practical implications for diverse industries.

This paper is concerned with an overview of the Resource-Constrained Project Scheduling Problem (RCPSP) and the conventional meta-heuristic solution techniques that have attracted the attention of many researchers in the field. Therefore, researchers have developed algorithms and methods to solve the problem. This paper addresses the single-mode RCPSP where the objective is to optimize and minimize the project duration while the quantities of resources are constrained during the project execution. In this problem, resource constraints and precedence relationships between activities are known to be the most important constraints for project scheduling. In this context, the standard RCPSP is presented. Then, the classifications of the collected papers according to the year of publication and the different meta-heuristic approaches applied are presented. Five weighted articles and their meta-heuristic techniques developed for RCPSP are described in detail and their results are summarized in the corresponding tables. In addition, researchers have developed various conventional meta-heuristic algorithms such as genetic algorithms, particle swarm optimization, ant colony optimization, bee colony optimization, simulated annealing, evolutionary algorithms, and so on. It is stated that genetic algorithms are more popular among researchers than other meta-heuristics. For this reason, the various conventional meta-heuristics and their corresponding articles are also presented to give an overview of the conventional meta-heuristic optimizing techniques. Finally, the challenges of the conventional meta-heuristics are explored, which may be helpful for future studies to apply new suitable techniques to solve the Resource-Constrained Project Scheduling Problem (RCPSP).

The project scheduling problem is both practically and theoretically of paramount importance. From the practical perspective, improvement of project scheduling as a critical part of project management process can lead to successful project completion and significantly decrease of the relevant costs. From the theoretical perspective, project scheduling is regarded as one of the in-teresting optimization issues, which has attracted the attention of many researchers in the area of operations research. Therefore, the project scheduling issue has been significantly evaluated over time and has been developed from various aspects. In this research, the topics related to Re-source-Constrained Project Scheduling Problem (RCPSP) are reviewed, recent developments in this field are evaluated, and the results are presented for future studies. In this regard, first, the standard problem of RCPSP is expressed and related developments are presented from four as-pects of resources, characteristics of activities, type of objective functions, and availability level of information. Following that, details about 216 articles conducted on RCPSP during 1980-2017 are expressed. At the end, in line with the statistics obtained from the evaluation of previ-ous articles, suggestions are made for the future studies in order to help the development of new issues in this area.