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- New resource-constrained project scheduling instances for testing (meta-)heuristic scheduling algorithmsPublication . Coelho, José; Vanhoucke, MarioThe 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 𝜎 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 𝜎𝐷 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 𝜎𝐷 indicator, and it will be shown that the value of the 𝜎 distance metric actually describes the difficulty of the project instances through two fast and efficient meta-heuristic procedures from the literature.
- A tool to test and validate algorithms for the resource-constrained project scheduling problemPublication . Vanhoucke, Mario; Coelho, JoséIn a paper written by by Vanhoucke et al. (2016), an overview of artificial and empirical project databases has been given for integrated project management and control. These databases are collections of the most well-known and widespread data instances available in literature for the construction of a baseline schedule, the analysis of schedule risk or the use for project control. The current paper serves as a follow-up study to further elaborate on the use of these data instances, and to give researchers an incentive to use these datasets for their research on the development and validation of new algorithms for project scheduling. Therefore, unlike the general focus of the previous paper on baseline scheduling, schedule risk analysis and project control, the focus on the current paper is restricted to resource-constrained project scheduling. The intention of this follow-up overview is fourfold. First and foremost, a procedure is proposed to facilitate the reporting of best known solutions for the well-known single- and multi-mode resource-constrained project scheduling problem to minimize the project makespan. Secondly, the paper reports our best known solutions we obtained so far, and reflects on the network and resource parameters that increase the project complexity. In doing so, areas to focus on for future research are detected, and an attempt to define hard problem instances is given. Thirdly, a new dataset is presented for the resource-constrained project scheduling problem that is much more diverse in both the network topology and resource scarceness and will enable the future researcher to develop algorithms to solve a wider range of project problems. Finally, the paper also adds some links to tutorials and other relevant information to stimulate researchers to download the data and update best known solutions once available.
- Going to the core of hard resource-constrained project scheduling instancesPublication . Coelho, José; Vanhoucke, MarioThe resource-constrained project scheduling problem (RCPSP) is one of the most studied problems in the project scheduling literature, and aims at constructing a project schedule with a minimum makespan that satisfies both the precedence relations of the network and the limited availability of the renewable resources. The problem has attracted attention due to its NP hardness status, and different algorithms have been proposed that solve a wide variety of RCPSP instances to optimality or near-optimality. In this paper, we analyse the hardness of this problem from an experimental point-of-view by testing different algorithms on a huge set of existing instances and detect which ones are difficult to solve. To that purpose, we propose a three-phased approach that makes use of five elementary blocks, well-performing algorithms and a huge amount of computational power to transform easy RCPSP instances into very hard ones. The purpose of this study is to create insight and understanding into what makes an RCPSP instance hard, and propose a new dataset that consists of a small set of instances that are impossible to solve with the algorithms currently existing in the literature. These instances should be as small as possible in terms of number of activities and resources, and should be as diverse as possible in terms of network structure and resource strictness. Such a dataset should enable researchers to focus their attention on the development of radically new algorithms to solve the RCPSP rather than gradually improving current algorithms that can solve the existing RCPSP instances only slightly better.
- Automated design of priority rules for resource-constrained project scheduling problem using surrogate-assisted genetic programmingPublication . Luo, Jingyu; Vanhoucke, Mario; Coelho, JoséIn 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.
- Reducing the feasible solution space of resource-constrained project instancesPublication . Vanhoucke, Mario; Coelho, JoséThis paper present an instance transformation procedure to modify known instances of the resource-constrained project scheduling problem to make them easier to solve by heuristic and/or exact solution algorithms.The procedure makes use of a set of transformation rules that aim at reducing the feasible search space without excluding at least one possible optimal solution. The procedure will be applied to a set of 11,183 instances and it will be shown by a set of experiments that these transformations lead to 110 improved lower bounds,16 new and better schedules (found by three meta-heuristic procedures and a set of branch-and-bound procedures) and even 64 new optimal solutions which were never not found before.
- An efficient genetic programming approach to design priority rules for resource-constrained project scheduling problemPublication . Luo, Jingyu; Vanhoucke, Mario; Coelho, José; Guo, WeikangIn 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.
- An analysis of network and resource indicators for resource-constrained project scheduling problem instancesPublication . Vanhoucke, Mario; Coelho, JoséIn the past decades, the resource on the resource-constrained project scheduling problem (RCPSP) has grown rapidly, resulting in an overwhelming amount of solution procedures that provide (near)-optimal solutions in a reasonable time. Despite the rapid progress, little is still known what makes a project instance hard to solve. Inspired by a previous research study that has shown that even small instances with only up to 30 activities is sometimes hard to solve, the current study provides an analysis of the project data used in the academic literature. More precisely, it investigates the ability of four well-known resource indicators to predict the hardness of an RCPSP instance. The study introduces a new instance equivalence concept to show that instances might have very different values for their resource indicators without changing any possible solution for this instance. The concept is based on four theorems and a search algorithm that transforms existing instances into new equivalent instances with more compact resources. This algorithm illustrates that the use of resource indicators to predict the hardness of an instance is sometimes misleading. In a set of computational experiment on more than 10,000 instances, it is shown that the newly constructed equivalent instances have values for the resource indicators that are not only different than the values of the original instances, but also often are better in predicting the hardness the project instances. It is suggested that the new equivalent instances are used for further research to compare results on the new instances with results obtained from the original dataset.
- An exact composite lower bound strategy for the resource-constrained project scheduling problemPublication . Coelho, José; Vanhoucke, MarioThis paper reports on results for the well-known resource-constrained project scheduling problem. A branch-and-bound procedure is developed that takes into account all best performing components from literature, varying branching schemes and search strategies, using the best performing dominance rules and assembling these components into a unified search algorithm. A composite lower bound strategy that statically and dynamically selects the best performing bounds from literature is used to find optimal solutions within reasonable times. An extensive computational experiment is set up to determine the best combination of the various components used in the procedure, in order to benchmark the current existing knowledge on four different datasets from the literature. By varying the network topology, resource scarceness and the size of the projects, the computational experiments are carried out on a diverse set of projects. The procedure was able to find some new lower bounds and optimal solutions for the PSPLIB instances. Moreover, new best known results are reported for other, more diverse datasets that can be used in future research studies. The experiments revealed that even project instances with 30 activities cannot be solved to optimality when the topological structure is varied.