Solving the Resource Constrained Project Scheduling Problem with Generalized Precedences by Lazy Clause Generation

The technical report presents a generic exact solution approach for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedences (Rcpsp/max). The approach uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply nogood learning and conflict-driven search on the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solutions and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. The method is highly robust: it matched or bettered the best known results on all of the 2340 instances we examined except 3, according to the currently available data on the PSPLib. Of the 631 open instances in this set it closed 573 and improved the bounds of 51 of the remaining 58 instances.Comment: 37 pages, 3 figures, 16 table

Optimising Flexibility of Temporal Problems with Uncertainty

Temporal networks have been applied in many autonomous systems. In real situations, we cannot ignore the uncertain factors when using those autonomous systems. Achieving robust schedules and temporal plans by optimising flexibility to tackle the uncertainty is the motivation of the thesis. This thesis focuses on the optimisation problems of temporal networks with uncertainty and controllable options in the field of Artificial Intelligence Planning and Scheduling. The goal of this thesis is to construct flexibility and robustness metrics for temporal networks under the constraints of different levels of controllability. Furthermore, optimising flexibility for temporal plans and schedules to achieve robust solutions with flexible executions. When solving temporal problems with uncertainty, postponing decisions according to the observations of uncertain events enables flexible strategies as the solutions instead of fixed schedules or plans. Among the three levels of controllability of the Simple Temporal Problem with Uncertainty (STPU), a problem is dynamically controllable if there is a successful dynamic strategy such that every decision in it is made according to the observations of past events. In the thesis, we make the following contributions. (1) We introduce an optimisation model for STPU based on the existing dynamic controllability checking algorithms. Some flexibility and robustness measures are introduced based on the model. (2) We extend the definition and verification algorithm of dynamic controllability to temporal problems with controllable discrete variables and uncertainty, which is called Controllable Conditional Temporal Problems with Uncertainty (CCTPU). An entirely dynamically controllable strategy of CCTPU consists of both temporal scheduling and variable assignments being dynamically decided, which maximize the flexibility of the execution. (3) We introduce optimisation models of CCTPU under fully dynamic controllability. The optimisation models aim to answer the questions how flexible, robust or controllable a schedule or temporal plan is. The experiments show that making decisions dynamically can achieve better objective values than doing statically. The thesis also contributes to the field of AI planning and scheduling by introducing robustness metrics of temporal networks, proposing an envelope-based algorithm that can check dynamic controllability of temporal networks with uncertainty and controllable discrete decisions, evaluating improvements from making decisions strongly controllable to temporally dynamically controllable and fully dynamically controllable and comparing the runtime of different implementations to present the scalability of dynamically controllable strategies

08071 Abstracts Collection -- Scheduling

From 10.02. to 15.02., the Dagstuhl Seminar 08071 ``Scheduling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Solving the accessibility windows assembly line problem level 1 and variant 1 (AWALBP-L1-1) with precedence constraints

Assembly line balancing problems (ALBPs) are among the most studied combinatorial optimization problems due to their relevance in many production systems. In particular, the accessibility windows ALBP (AWALBP) may arise when the workpieces are larger than the workstations, which implies that at a given instant the workstations have access to only a portion of the workpieces. Thus, the cycle is split into forward steps and stationary stages. The workpieces advance during the forward steps and the tasks are processed during the stationary stages. Several studies have dealt with the AWALBP assuming that there are no precedence relationships between tasks. However, this assumption is not always appropriate. In this work we solve the first level of AWALBP (AWALBP-L1) considering the existence of precedence relationships. Specifically, this work deals with variant 1 (AWALBP-L1-1), in which each task can be performed at only one workstation and, therefore, only the stationary stages and the starting instants in which the tasks are performed have to be decided. We design a solution procedure that includes pre-processing procedures, a matheuristic and a mixed integer linear programming model. An extensive computational experiment is carried out to evaluate its performance.Peer ReviewedPostprint (author's final draft

Constraint analysis for DSP code generation

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A Decomposition Approach for the Multi-Modal, Resource-Constrained, Multi-Project Scheduling Problem with Generalized Precedence and Expediting Resources

The field of project scheduling has received a great deal of study for many years with a steady evolution of problem complexity and solution methodologies. As solution methodologies and technologies improve, increasingly complex, real-world problems are addressed, presenting researchers a continuing challenge to find ever more effective means for approaching project scheduling. This dissertation introduces a project scheduling problem which is applicable across a broad spectrum of real-world situations. The problem is based on the well-known Resource-Constrained Project Scheduling Problem, extended to include multiple modes, generalized precedence, and expediting resources. The problem is further extended to include multiple projects which have generalized precedence, renewable and nonrenewable resources, and expediting resources at the program level. The problem presented is one not previously addressed in the literature nor is it one to which the existing specialized project scheduling methodologies can be directly applied. This dissertation presents a decomposition approach for solving the problem, including algorithms for solving the decomposed subproblems and the master problem. This dissertation also describes a methodology for generating instances of the new problem, extending the way existing problem generators describe and construct network structures and this class of problem. The methodologies presented are demonstrated through extensive empirical testing

On Zone-Based Analysis of Duration Probabilistic Automata

We propose an extension of the zone-based algorithmics for analyzing timed automata to handle systems where timing uncertainty is considered as probabilistic rather than set-theoretic. We study duration probabilistic automata (DPA), expressing multiple parallel processes admitting memoryfull continuously-distributed durations. For this model we develop an extension of the zone-based forward reachability algorithm whose successor operator is a density transformer, thus providing a solution to verification and performance evaluation problems concerning acyclic DPA (or the bounded-horizon behavior of cyclic DPA).Comment: In Proceedings INFINITY 2010, arXiv:1010.611