Using Deep Neural Networks for Scheduling Resource-Constrained Activity Sequences

Eines der bekanntesten Planungsprobleme stellt die Planung von Aktivitäten unter Berücksichtigung von Reihenfolgenbeziehungen zwischen diesen Aktivitäten sowie Ressourcenbeschränkungen dar. In der Literatur ist dieses Planungsproblem als das ressourcenbeschränkte Projektplanungsproblem bekannt und wird im Englischen als Resource-Constrained Project Scheduling Problem oder kurz RCPSP bezeichnet. Das Ziel dieses Problems besteht darin, die Bearbeitungszeit einer Aktivitätsfolge zu minimieren, indem festgelegt wird, wann jede einzelne Aktivität beginnen soll, ohne dass die Ressourcenbeschränkungen überschritten werden. Wenn die Bearbeitungsdauern der Aktivitäten bekannt und deterministisch sind, können die Startzeiten der Aktivitäten à priori definiert werden, ohne dass die Gefahr besteht, dass der Zeitplan unausführbar wird. Da jedoch die Bearbeitungsdauern der Aktivitäten häufig nicht deterministisch sind, sondern auf Schätzungen von Expertengruppen oder historischen Daten basieren, können die realen Bearbeitungsdauern von den geschätzten abweichen. In diesem Fall ist eine reaktive Planungsstrategie zu bevorzugen. Solch eine reaktive Strategie legt die Startzeiten der einzelnen Aktivitäten nicht zu Beginn des Projektes fest, sondern erst unmittelbar an jedem Entscheidungspunkt im Projekt, also zu Beginn des Projektes und immer dann wenn eine oder mehrere Aktivitäten abgeschlossen und die beanspruchten Ressourcen frei werden. In dieser Arbeit wird eine neue reaktive Planungsstrategie für das ressourcenbeschränkte Projektplanungsproblem vorgestellt. Im Gegensatz zu anderen Literaturbeiträgen, in denen exakte, heuristische und meta-heuristische Methoden zur Anwendung kommen, basiert der in dieser Arbeit aufgestellte Lösungsansatz auf künstlichen neuronalen Netzen und maschinellem Lernen. Die neuronalen Netze verarbeiten die Informationen, die den aktuellen Zustand der Aktivitätsfolge beschreiben, und erzeugen daraus Prioritätswerte für die Aktivitäten, die im aktuellen Entscheidungspunkt gestartet werden können. Das maschinelle Lernen und insbesondere das überwachte Lernen werden für das Trainieren der neuronalen Netze mit beispielhaften Trainingsdaten angewendet, wobei die Trainingsdaten mit Hilfe einer Simulation erzeugt wurden. Sechs verschiedene neuronale Netzwerkstrukturen werden in dieser Arbeit betrachtet. Diese Strukturen unterscheiden sich sowohl in der ihnen zur Verfügung gestellten Eingabeinformation als auch der Art des neuronalen Netzes, das diese Information verarbeitet. Es werden drei Arten von neuronalen Netzen betrachtet. Diese sind neuronale Netze mit vollständig verbundenen Schichten, 1- dimensionale faltende neuronale Netze und 2-dimensionale neuronale faltende Netze. Darüber hinaus werden innerhalb jeder einzelnen Netzwerkstruktur verschiedene Hyperparameter, z.B. die Lernrate, Anzahl der Lernepochen, Anzahl an Schichten und Anzahl an Neuronen per Schicht, mittels einer Bayesischen Optimierung abgestimmt. Während des Abstimmens der Hyperparameter wurden außerdem Bereiche für die Hyperparameter identifiziert, die zur Verbesserung der Leistungen genutzt werden sollten. Das am besten trainierte Netzwerk wird dann für den Vergleich mit anderen vierunddreißig reaktiven heuristischen Methoden herangezogen. Die Ergebnisse dieses Vergleichs zeigen, dass der in dieser Arbeit vorgeschlagene Ansatz in Bezug auf die Minimierung der Gesamtdauer der Aktivitätsfolge die meisten Heuristiken übertrifft. Lediglich 3 Heuristiken erzielen kürzere Gesamtdauern als der Ansatz dieser Arbeit, jedoch sind deren Rechenzeiten um viele Größenordnungen länger. Eine Annahme in dieser Arbeit besteht darin, dass während der Ausführung der Aktivitäten Abweichungen bei den Aktivitätsdauern auftreten können, obwohl die Aktivitätsdauern generell als deterministisch modelliert werden. Folglich wird eine Sensitivitätsanalyse durchgeführt, um zu prüfen, ob die vorgeschlagene reaktive Planungsstrategie auch dann kompetitiv bleibt, wenn die Aktivitätsdauern von den angenommenen Werten abweichen

A compact reformulation of the two-stage robust resource-constrained project scheduling problem

This paper considers the resource-constrained project scheduling problem with uncertain activity durations. We assume that activity durations lie in a budgeted uncertainty set, and follow a robust two-stage approach, where a decision maker must resolve resource conflicts subject to the problem uncertainty, but can determine activity start times after the uncertain activity durations become known. We introduce a new reformulation of the second-stage problem, which enables us to derive a compact robust counterpart to the full two-stage adjustable robust optimisation problem. Computational experiments show that this compact robust counterpart can be solved using standard optimisation software significantly faster than the current state-of-the-art algorithm for solving this problem, reaching optimality for almost 50% more instances on the same benchmark set

Scheduling and Resource Efficiency Balancing. Discrete Species Conserving Cuckoo Search for Scheduling in an Uncertain Execution Environment

The main goal of a scheduling process is to decide when and how to execute each of the project’s activities. Despite large variety of researched scheduling problems, the majority of them can be described as generalisations of the resource-constrained project scheduling problem (RCPSP). Because of wide applicability and challenging difficulty, RCPSP has attracted vast amount of attention in the research community and great variety of heuristics have been adapted for solving it. Even though these heuristics are structurally different and operate according to diverse principles, they are designed to obtain only one solution at a time. In the recent researches on RCPSPs, it was proven that these kind of problems have complex multimodal fitness landscapes, which are characterised by a wide solution search spaces and presence of multiple local and global optima. The main goal of this thesis is twofold. Firstly, it presents a variation of the RCPSP that considers optimisation of projects in an uncertain environment where resources are modelled to adapt to their environment and, as the result of this, improve their efficiency. Secondly, modification of a novel evolutionary computation method Cuckoo Search (CS) is proposed, which has been adapted for solving combinatorial optimisation problems and modified to obtain multiple solutions. To test the proposed methodology, two sets of experiments are carried out. Firstly, the developed algorithm is applied to a real-life software development project. Secondly, the performance of the algorithm is tested on universal benchmark instances for scheduling problems which were modified to take into account specifics of the proposed optimisation model. The results of both experiments demonstrate that the proposed methodology achieves competitive level of performance and is capable of finding multiple global solutions, as well as prove its applicability in real-life projects

Algorithmic Developments in Two-Stage Robust Scheduling

This thesis considers the modelling and solving of a range of scheduling problems, with a particular focus on the use of robust optimisation for scheduling in two-stage decision-making contexts. One key contribution of this thesis is the development of a new compact robust counterpart for the resource-constrained project scheduling problem with uncertain activity durations. Resource conflicts must be resolved under the assumption of budgeted uncertainty, but start times can be determined once the activity durations become known. This formulation is also applied to the multi-mode version of this problem. In both cases, computational results show the clear dominance of the new formulation over the prior decomposition-based state-of-the-art methods. This thesis also demonstrates the first application of the recoverable robust framework to single machine scheduling. Two variants of this problem are considered, in which a first-stage schedule is constructed subject to uncertain job processing times, but can be amended in some limited way following the realisation of these processing times. The first of these problems is considered under general polyhedral uncertainty. Key results concerning the second-stage subproblem are derived, resulting in three formulations to the full problem which are compared computationally. The second of these problems considers interval uncertainty but allows for a more general recovery action. A 2-approximation is derived and the performance of a proposed greedy algorithm is examined in a series of computational experiments. In addition to these results on two-stage robust scheduling problems, a new deterministic resource-constrained project scheduling model is developed which, for the first time, combines both generalised precedence constraints and flexible resource allocation. This model is introduced specifically for the application of scheduling the decommissioning of the Sellafield nuclear site. A genetic algorithm is proposed to solve this model, and its performance is compared against a mixedinteger programming formulation

Search Based Software Project Management

This thesis investigates the application of Search Based Software Engineering (SBSE) approach in the field of Software Project Management (SPM). With SBSE approaches, a pool of candidate solutions to an SPM problem is automatically generated and gradually evolved to be increasingly more desirable. The thesis is motivated by the observation from industrial practice that it is much more helpful to the project manager to provide insightful knowledge than exact solutions. We investigate whether SBSE approaches can aid the project managers in decision making by not only providing them with desirable solutions, but also illustrating insightful “what-if” scenarios during the phases of project initiation, planning and enactment. SBSE techniques can automatically “evolve” solutions to software requirement elicitation, project staffing and scheduling problems. However, the current state-of- the-art computer-aided software project management tools remain limited in several aspects. First, software requirement engineering is plagued by problems associated with unreliable estimates. The estimations made early are assumed to be accurate, but the projects are estimated and executed in an environment filled with uncertainties that may lead to delay or disruptions. Second, software project scheduling and staffing are two closely related problems that have been studied separately by most published research in the field of computer aided software project management, but software project managers are usually confronted with the complex trade-off and correlations of scheduling and staffing. Last, full attendance of required staff is usually assumed after the staff have been assigned to the project, but the execution of a project is subject to staff absences because of sickness and turnover, for example. This thesis makes the following main contributions: (1) Introducing an automated SBSE approach to Sensitivity Analysis for requirement elicitation, which helps to achieve more accurate estimations by directing extra estimation effort towards those error-sensitive requirements and budgets. (2) Demonstrating that Co-evolutionary approaches can simultaneously co-evolve solutions for both work package sequencing and project team sizing. The proposed approach to these two interrelated problems yields better results than random and single-population evolutionary algorithms. (3) Presenting co-evolutionary approaches that can guide the project manager to anticipate and ameliorate the impact of staff absence. (4) The investigations of seven sets of real world data on software requirement and software project plans reveal general insights as well as exceptions of our approach in practise. (5) The establishment of a tool that implements the above concepts. These contributions support the thesis that automated SBSE tools can be beneficial to solution generation, and most importantly, insightful knowledge for decision making in the practise of software project management