Abstract
This study evaluates a new solution approach for the Resource -Constrained Project Scheduling with Alternative Subgraphs (RCPSP-AS) in case that complex relations (i.e. nested and linked alternatives) are considered. In the RCPSP-AS, the project activity structure is extended with alternative activity sequences. This implies that only a subset of all activities should be scheduled, which corresponds with a set of activities in the project network that model an alternative execution mode for a work package. Since only the selected activities should be scheduled, the RCPSP-AS comes down to a traditional RCPSP problem when the selection subproblem is solved. It is known that the RCPSP and, hence, its extension to the RCPSP-AS is NP -hard. Since similar scheduling and selection subproblems have already been successfully solved by satisfiability (SAT) solvers in the existing literature, we aim to test the performance of a GA -SAT approach that is derived from the literature and adjusted to be able to deal with the problem -specific constraints of the RCPSP-AS. Computational results on smalland large-scale instances (both artificial and empirical) show that the algorithm can compete with existing metaheuristic algorithms from the literature. Also, the performance is compared with an exact mathematical solver and learning behaviour is observed and analysed. This research again validates the broad applicability of SAT solvers as well as the need to search for better and more suited algorithms for the RCPSP-AS and its extensions.

Abstract
This paper presents a matheuristic solution algorithm to solve the well-known resource-constrained project scheduling problem (RCPSP). The problem makes use of a restricted neighbourhood method using an activity selection and a search space restriction module and implements them as two alternative search algorithms. The first algorithm makes use of the best-performing components of the branch-and-bound procedures from the literature, and embeds them into a greedy neighbourhood search. The second matheuristic implements the exact branch-and-bound procedures into a known and well-performing meta-heuristic search algorithm. Computational experiments have been carried out on seven different datasets consisting of 10,000+ project instances. Experiments reveal that the choice of exact algorithm is key in finding high-quality solutions, and illustrate that the trade-off between selecting an activity set size and search space restriction depends on the specific implementation. The computational tests demonstrate that the matheuristic discovered 24 new best known solutions that could not be found by either a meta-heuristic or an exact method individually. Moreover, a new benchmark dataset has been proposed that can be used to develop new matheuristic search procedures to solve the problem consisting of 461 instances from the literature.

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
The branch-and-bound (B&B) procedure is one of the most widely used techniques to get optimal so-lutions for the resource-constrained project scheduling problem (RCPSP). Recently, various components from the literature have been assembled by Coelho and Vanhoucke (2018) into a unified search algo-rithm using the best performing lower bounds, branching schemes, search strategies, and dominance rules. However, due to the high computational time, this procedure is only suitable to solve small to medium-sized problems. Moreover, despite its relatively good performance, not much is known about which components perform best, and how these components should be combined into a procedure to maximize chances to solve the problem. This paper introduces a structured prediction approach to rank various combinations of components (configurations) of the integrated B&B procedure. More specifically, two regression methods are used to map project indicators to a full ranking of configurations. The objec-tive is to provide preference information about the quality of different configurations to obtain the best possible solution. Using such models, the ranking of all configurations can be predicted, and these predic-tions are then used to get the best possible solution for a new project with known network and resource values. A computational experiment is conducted to verify the performance of this novel approach. Fur-thermore, the models are tested for 48 different configurations, and their robustness is investigated on datasets with different numbers of activities. The results show that the two models are very competitive, and both can generate significantly better results than any single-best configuration.

Abstract
In the past few years, the genetic programming approach (GP) has been successfully used by researchers to design priority rules for the resource-constrained project scheduling problem (RCPSP) thanks to its high generalization ability and superior performance. However, one of the main drawbacks of the GP is that the fitness evaluation in the training process often requires a very high computational effort. In order to reduce the runtime of the training process, this research proposed four different surrogate models for the RCPSP. The experiment results have verified the effectiveness and the performance of the proposed surrogate models. It is shown that they achieve similar performance as the original model with the same number of evaluations and better performance with the same runtime. We have also tested the performance of one of our surrogate models with seven different population sizes to show that the selected surrogate model achieves similar performance for each population size as the original model, even when the searching space is sufficiently explored. Furthermore, we have investigated the accuracy of our proposed surrogate models and the size of the rules they designed. The result reveals that all the proposed surrogate models have high accuracy, and sometimes the rules found by them have a smaller size compared with the original model.