Abstract
The resource-constrained project scheduling problem (RCPSP) is a well-known scheduling problem that has attracted attention since several decades. Despite the rapid progress of exact and (meta-)heuristic procedures, the problem can still not be solved to optimality for many problem instances of relatively small size. Due to the known complexity, many researchers have proposed fast and efficient meta-heuristic solution procedures that can solve the problem to near optimality. Despite the excellent results obtained in the last decades, little is known why some heuristics perform better than others. However, if researchers better understood why some meta-heuristic procedures generate good solutions for some project instances while still falling short for others, this could lead to insights to improve these meta-heuristics, ultimately leading to stronger algorithms and better overall solution quality. In this study, a new hardness indicator is proposed to measure the difficulty of providing near-optimal solutions for meta-heuristic procedures. The new indicator is based on a new concept that uses the o-distance metric to describe the solution space of the problem instance, and relies on current knowledge for lower and upper bound calculations for problem instances from five known datasets in the literature. This new indicator, which will be called the o -D indicator, will be used not only to measure the hardness of existing project datasets, but also to generate a new benchmark dataset that can be used for future research purposes. The new dataset contains project instances with different values for the o -D indicator, and it will be shown that the value of the o-distance metric actually describes the difficulty of the project instances through two fast and efficient meta-heuristic procedures from the literature.

Abstract

Abstract
In recent years, machine learning techniques, especially genetic programming (GP), have been a powerful approach for automated design of the priority rule-heuristics for the resource-constrained project scheduling problem (RCPSP). However, it requires intensive computing effort, carefully selected training data and appropriate assessment criteria. This research proposes a GP hyper-heuristic method with a duplicate removal technique to create new priority rules that outperform the traditional rules. The experiments have verified the efficiency of the proposed algorithm as compared to the standard GP approach. Furthermore, the impact of the training data selection and fitness evaluation have also been investigated. The results show that a compact training set can provide good output and existing evaluation methods are all usable for evolving efficient priority rules. The priority rules designed by the proposed approach are tested on extensive existing datasets and newly generated large projects with more than 1,000 activities. In order to achieve better performance on small-sized projects, we also develop a method to combine rules as efficient ensembles. Computational comparisons between GP-designed rules and traditional priority rules indicate the superiority and generalization capability of the proposed GP algorithm in solving the RCPSP.

Abstract
In this research, we present several extensions for the resource-constrained project scheduling problem with alternative subgraphs (RCPSP-AS). First of all, we investigate more complex variants of the alternative project structure. More precisely, we consider nested alterative subgraphs, linked alternative branches, multiple selection, caused and closed choices, and split choices. Secondly, we introduce non-renewable resources in the RCPSP-AS in order to implicitly avoid certain combinations of alternatives given a limited availability of this resource over the complete project horizon. We formulate both the basic RCPSP-AS and its extensions as an ILP model and solve it using Gurobi. The computational experiments are conducted on a large set of artificial project instances as well as three case studies. The results show the impact of the different extensions on the project makespan and the computational complexity. We observe that combinations of the proposed extensions might imply complex alternative project structures, resulting in an increasing computational complexity or even infeasible solutions. The analysis of the three case studies shows that it is hard to find feasible solutions with a small time limit or optimal solutions with a larger time limit for projects with a realistic size in terms of the number of activities or alternatives.

Abstract
Priority rules are applied in many commercial software tools for scheduling projects under limited resources because of their known advantages such as the ease of implementation, their intuitive working, and their fast speed. Moreover, while numerous research papers present comparison studies between different priority rules, managers often do not know which rules should be used for their specific project, and therefore have no other choice than selecting a priority rule at random and hope for the best. This paper introduces a decision tree approach to classify and detect the best performing priority rule for the resource-constrained project scheduling problem (RCPSP). The research relies on two classification models to map project indicators onto the performance of the priority rule. Using such models, the performance of each priority rule can be predicted, and these predictions are then used to automatically select the best performing priority rule for a specific project with known network and resource indicator values. A set of computational experiment is set up to evaluate the performance of the newly proposed classification models using the most well-known priority rules from the literature. The experiments compare the performance of multi-label classification models with multi-class classification models, and show that these models can outperform the average performance of using any single priority rule. It will be argued that this approach can be easily extended to any extension of the RCPSP without changing the methodology used in this study. © 2020 Elsevier Ltd