Experimental evaluation of state-of-the-art heuristics for the resource-constrained project scheduling problem
Introduction
The resource-constrained project scheduling problem (RCPSP) can be stated as follows. A single project consists of n+1 activities where each activity has to be processed in order to complete the project. The fictitious activities 0 and n+1 correspond to the `project start' and to the `project end', respectively. The activities are interrelated by two kinds of constraints. First, precedence constraints force activity j not to be started before all its immediate predecessor activities have been finished. Second, performing the activities requires resources with limited capacities. Altogether we have a set of resource types, the number of resource types is K. While being processed, activity j requires rj,k units of resource type during every time instant of its non-preemptable duration pj. Resource type k has a limited capacity of Rk at any point in time. The parameters pj, rj,k, and Rk are assumed to be non-negative and deterministic; for the project start and end activities we have pj=0 and rj,k=0 for all . The objective of the RCPSP is to find precedence and resource feasible completion times for all activities such that the makespan of the project is minimized.
Since its advent the RCPSP has been of interest for practitioners and researchers. Recent years have witnessed a tremendous increase in research for the RCPSP, both in terms of heuristic and optimal procedures. We refer to the surveys provided by Icmeli et al. [13], Özdamar and Ulusoy [29], Herroelen et al. [12], Kolisch and Padman [20] and Brucker et al. [6]. Recently, Kolisch and Hartmann [19] have given a specific overview of heuristics for the RCPSP. The paper focuses on the building blocks (schedule generation schemes, priority rules, schedule representations, operators, and search strategies) and the way these building blocks are combined to methods such as X-pass methods (single pass methods, multi-pass methods, sampling procedures) and different types of metaheuristics (simulated annealing, genetic algorithms, and tabu search). This paper is a follow-up study which provides an in-depth investigation of the performance of recent RCPSP heuristics as well as explanations for the observed results. Based on these observations, we subsequently give recommendations about prosperous directions for further research efforts.
Section snippets
Proposed heuristics
This section gives a short survey of the tested heuristics. We start with the description of schedule generation schemes which are (with the exception of the method of Baar et al. [3]) a core building block of all procedures.
Test design
As test instances we have employed the standard sets j30, j60, and j120 for the RCPSP presented in [21]. The sets j30 and j60 consist of 480 projects with four resource types as well as n=30 and n=60 activities, respectively. The levels of the three independent problem parameters network complexity, resource factor, and resource strength are systematically altered to define a full factorial experimental design.
The network complexity (NC) defines the average number of non-redundant precedence
Summary and guidance for future research
Based on our findings we can give the following recommendations towards the development of further improvements for project scheduling heuristics.
The most successful approaches in our numerical evaluation are metaheuristics, namely the simulated annealing procedure of Bouleimen and Lecocq [5] and the genetic algorithm of Hartmann [11]. Nevertheless, priority rule based sampling methods are indispensable to construct initial solutions for metaheuristics. Hence, research in both directions –
Acknowledgements
We are indebted to Tonius Baar, Peter Brucker, and Sigrid Knust (University of Osnabrück), Kamel Bouleimen and Henri Lecocq (University of Liège), Jorge Leon and Balakrishnan Ramamoorthy (Texas A&M University) as well as Andreas Schirmer (University of Kiel) for their help in this research. Furthermore, we would like to thank Andreas Drexl (University of Kiel) for his support.
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