Optimisation of temporal networks under uncertainty

A wide variety of decision problems in operations research are defined on temporal networks, that is, workflows of time-consuming tasks whose processing order is constrained by precedence relations. For example, temporal networks are used to formalise the management of projects, the execution of computer applications, the design of digital circuits and the scheduling of production processes. Optimisation problems arise in temporal networks when a decision maker wishes to determine a temporal arrangement of the tasks and/or a resource assignment that optimises some network characteristic such as the network’s makespan (i.e., the time required to complete all tasks) or its net present value. Optimisation problems in temporal networks have been investigated intensively for more than fifty years. To date, the majority of contributions focus on deterministic formulations where all problem parameters are known. This is surprising since parameters such as the task durations, the network structure, the availability of resources and the cash flows are typically unknown at the time the decision problem arises. The tacit understanding in the literature is that the decision maker replaces these uncertain parameters with their most likely or expected values to obtain a deterministic optimisation problem. It is well-documented in theory and practise that this approach can lead to severely suboptimal decisions. The objective of this thesis is to investigate solution techniques for optimisation problems in temporal networks that explicitly account for parameter uncertainty. Apart from theoretical and computational challenges, a key difficulty is that the decision maker may not be aware of the precise nature of the uncertainty. We therefore study several formulations, each of which requires different information about the probability distribution of the uncertain problem parameters. We discuss models that maximise the network’s net present value and problems that minimise the network’s makespan. Throughout the thesis, emphasis is placed on tractable techniques that scale to industrial-size problems

Efficient Scheduling Algorithms for Robot Inverse Dynamics Computation on a Multiprocessor System

Robot manipulators are highly nonlinear systems and their motion control requires the computation of generalized forces/torques to drive all the joint motors at an adequate rate. This paper presents efficient scheduling algorithms for computing the robot inverse dynamics on a multiprocessor system. The problem of scheduling the inverse dynamics computation consisting of m computational modules to be executed on a multiprocessor system consisting of p identical homogeneous processors to achieve a minimum-scheduled length is known to be NP-complete. In order to achieve the minimum computation time, the Newton-Euler equations of motion are expressed in the homogeneous linear recurrence form which results in achieving maximum parallelism. To speed up the searching for a solution, a heuristic search algorithm called Dynamical Highest Level First/Most Immediate Successors First (DHLF /MISF) is first proposed to find a fast but suboptimal schedule. For an optimal schedule, the minimum-scheduled-length problem can be solved by a state- space search method — the A* algorithm coupled with an efficient heuristic function derived from the Fernandez and Bussell bound. The state-space search method is a classical minimum cost graph search algorithm, which is guaranteed to find the optimal solution if the evaluation function is properly defined. An objective function is defined in terms of the task execution time and the optimization of the objective function is based on the minimax of the execution time. The proposed optimization algorithm solves the minimum-scheduled-length problem in pseudo-polynominal time and can be used to solve various large-scale problems in a reasonable time. An illustrative example of computing the inverse dynamics of an n-link manipulator based on the Newton-Euler dynamic equations is performed to show the effectiveness of the A algorithm and the heuristic algorithm DHLF /MISF

Working Notes from the 1992 AAAI Spring Symposium on Practical Approaches to Scheduling and Planning

The symposium presented issues involved in the development of scheduling systems that can deal with resource and time limitations. To qualify, a system must be implemented and tested to some degree on non-trivial problems (ideally, on real-world problems). However, a system need not be fully deployed to qualify. Systems that schedule actions in terms of metric time constraints typically represent and reason about an external numeric clock or calendar and can be contrasted with those systems that represent time purely symbolically. The following topics are discussed: integrating planning and scheduling; integrating symbolic goals and numerical utilities; managing uncertainty; incremental rescheduling; managing limited computation time; anytime scheduling and planning algorithms, systems; dependency analysis and schedule reuse; management of schedule and plan execution; and incorporation of discrete event techniques

Design and control of stochastic manufacturing systems

Many manufacturing systems are subject to uncertainty, which can be described using stochastic processes. These processes might be stable or change with the production quantity. This dissertation analyzes the design and control of such stochastic manufacturing systems. The first article investigates the balancing of an assembly line with stochastic task times and a constraint on the line reliability. We provide a sampling-based model formulation for generally distributed task times. We prove that any lower bound on the number of stations for the related deterministic problem can be transformed into a lower bound for this sampling formulation. We apply these bounds in a reliability-based branch-and-bound algorithm and show that they substantially reduce the required computation time. The second article analyzes the impact of the used sampling method and the sample size on the resulting performance measures and optimal decision by considering the performance evaluation of an M/D/1 queueing system and the optimization of an M/M/c staffing level numerically. The article suggests that managers should be aware that the distribution of the resulting performance measures or optimal solution derived from a sampling-based approach may not be symmetrical and that the chosen sampling method may have an impact on this behavior. The third article investigates the ramp-up of a new product or machine with stochastic and non-stationary yield. We formalize the problem as a Newsvendor problem and prove that any positive optimal ramp-up quantity will always be at least the demand. Furthermore, we characterize the optimal ramp-up quantity for the special case of stationary yield by a critical fractile. The optimal ramp-up quantity tends to be decreasing in the expected yield. However, a numerical analysis shows that an increase in the expected yield can lead to a higher optimal production quantity at first, before the production quantity decreases. There is a gap in the literature for each of the considered optimization problems under the considered assumptions. Future research could integrate the design and control decisions considered in this dissertation into a single optimization model

Simulation and close-to-optimal algorithm for the static load balancing of a network of heterogeneous processors

A close-to-optimal linear programming-based algorithm for the static load balancing of a network of heterogeneous processors is described and implemented. Experimental results suggest that the amount of time required by the implementation of the algorithm to balance the loads of the servers as a function of the number of servers has polynomial complexity

On-line planning and scheduling: an application to controlling modular printers

We present a case study of artificial intelligence techniques applied to the control of production printing equipment. Like many other real-world applications, this complex domain requires high-speed autonomous decision-making and robust continual operation. To our knowledge, this work represents the first successful industrial application of embedded domain-independent temporal planning. Our system handles execution failures and multi-objective preferences. At its heart is an on-line algorithm that combines techniques from state-space planning and partial-order scheduling. We suggest that this general architecture may prove useful in other applications as more intelligent systems operate in continual, on-line settings. Our system has been used to drive several commercial prototypes and has enabled a new product architecture for our industrial partner. When compared with state-of-the-art off-line planners, our system is hundreds of times faster and often finds better plans. Our experience demonstrates that domain-independent AI planning based on heuristic search can flexibly handle time, resources, replanning, and multiple objectives in a high-speed practical application without requiring hand-coded control knowledge

Generalizing List Scheduling for Stochastic Soft Real-time Parallel Applications

Advanced architecture processors provide features such as caches and branch prediction that result in improved, but variable, execution time of software. Hard real-time systems require tasks to complete within timing constraints. Consequently, hard real-time systems are typically designed conservatively through the use of tasks? worst-case execution times (WCET) in order to compute deterministic schedules that guarantee task?s execution within giving time constraints. This use of pessimistic execution time assumptions provides real-time guarantees at the cost of decreased performance and resource utilization. In soft real-time systems, however, meeting deadlines is not an absolute requirement (i.e., missing a few deadlines does not severely degrade system performance or cause catastrophic failure). In such systems, a guaranteed minimum probability of completing by the deadline is sufficient. Therefore, there is considerable latitude in such systems for improving resource utilization and performance as compared with hard real-time systems, through the use of more realistic execution time assumptions. Given probability distribution functions (PDFs) representing tasks? execution time requirements, and tasks? communication and precedence requirements, represented as a directed acyclic graph (DAG), this dissertation proposes and investigates algorithms for constructing non-preemptive stochastic schedules. New PDF manipulation operators developed in this dissertation are used to compute tasks? start and completion time PDFs during schedule construction. PDFs of the schedules? completion times are also computed and used to systematically trade the probability of meeting end-to-end deadlines for schedule length and jitter in task completion times. Because of the NP-hard nature of the non-preemptive DAG scheduling problem, the new stochastic scheduling algorithms extend traditional heuristic list scheduling and genetic list scheduling algorithms for DAGs by using PDFs instead of fixed time values for task execution requirements. The stochastic scheduling algorithms also account for delays caused by communication contention, typically ignored in prior DAG scheduling research. Extensive experimental results are used to demonstrate the efficacy of the new algorithms in constructing stochastic schedules. Results also show that through the use of the techniques developed in this dissertation, the probability of meeting deadlines can be usefully traded for performance and jitter in soft real-time systems

A Hypergraph Framework for Optimal Model-Based Decomposition of Design Problems

Decomposition of large engineering system models is desirable sinceincreased model size reduces reliability and speed of numericalsolution algorithms. The article presents a methodology for optimalmodel-based decomposition (OMBD) of design problems, whether or notinitially cast as optimization problems. The overall model isrepresented by a hypergraph and is optimally partitioned into weaklyconnected subgraphs that satisfy decomposition constraints. Spectralgraph-partitioning methods together with iterative improvementtechniques are proposed for hypergraph partitioning. A known spectralK-partitioning formulation, which accounts for partition sizes andedge weights, is extended to graphs with also vertex weights. TheOMBD formulation is robust enough to account for computationaldemands and resources and strength of interdependencies between thecomputational modules contained in the model.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44780/1/10589_2004_Article_136837.pd