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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.
- 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.
- 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.
- The multi-mode resource-constrained project scheduling problemPublication . Coelho, José; Vanhoucke, MarioThis chapter reports on a new solution approach for the multi-mode resource-constrained project scheduling problem (MRCPSP, MPS | prec | C max ). This problem type aims at the selection of a single activity mode from a set of available modes in order to construct a precedence and a (renewable and nonrenewable) resource-feasible project schedule with a minimal makespan. The problem type is known to be NP -hard and has been solved using various exact as well as (meta-)heuristic procedures. The new algorithm splits the problem type into a mode assignment and a single mode project scheduling step. The mode assignment step is solved by a satisfiability (SAT) problem solver and returns a feasible mode selection to the project scheduling step. The project scheduling step is solved using an efficient meta-heuristic procedure from literature to solve the resource-constrained project scheduling problem (RCPSP). However, unlike many traditional meta-heuristic methods in literature to solve the MRCPSP, the new approach executes these two steps in one run, relying on a single priority list. Straightforward adaptations to the pure SAT solver by using pseudo boolean nonrenewable resource constraints has led to a high quality solution approach in a reasonable computational time. Computational results show that the procedure can report similar or sometimes even better solutions than found by other procedures in literature, although it often requires a higher CPU time.
- Various extensions in resource-constrained project scheduling with alternative subgraphsPublication . Servranckx, Tom; Coelho, José; Vanhoucke, MarioIn 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.
- 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.