Edge Generation Scheduling for DAG Tasks using Deep Reinforcement Learning

Directed acyclic graph (DAG) tasks are currently adopted in the real-time domain to model complex applications from the automotive, avionics, and industrial domain that implement their functionalities through chains of intercommunicating tasks. This paper studies the problem of scheduling real-time DAG tasks by presenting a novel schedulability test based on the concept of trivial schedulability. Using this schedulability test, we propose a new DAG scheduling framework (edge generation scheduling -- EGS) that attempts to minimize the DAG width by iteratively generating edges while guaranteeing the deadline constraint. We study how to efficiently solve the problem of generating edges by developing a deep reinforcement learning algorithm combined with a graph representation neural network to learn an efficient edge generation policy for EGS. We evaluate the effectiveness of the proposed algorithm by comparing it with state-of-the-art DAG scheduling heuristics and an optimal mixed-integer linear programming baseline. Experimental results show that the proposed algorithm outperforms the state-of-the-art by requiring fewer processors to schedule the same DAG tasks.Comment: Under revie

Weighted tardiness minimization for unrelated machines with sequence-dependent and resource-constrained setups

Motivated by the need of quick job (re-)scheduling, we examine an elaborate scheduling environment under the objective of total weighted tardiness minimization. The examined problem variant moves well beyond existing literature, as it considers unrelated machines, sequence-dependent and machine-dependent setup times and a renewable resource constraint on the number of simultaneous setups. For this variant, we provide a relaxed MILP to calculate lower bounds, thus estimating a worst-case optimality gap. As a fast exact approach appears not plausible for instances of practical importance, we extend known (meta-)heuristics to deal with the problem at hand, coupling them with a Constraint Programming (CP) component - vital to guarantee the non-violation of the problem's constraints - which optimally allocates resources with respect to tardiness minimization. The validity and versatility of employing different (meta-)heuristics exploiting a relaxed MILP as a quality measure is revealed by our extensive experimental study, which shows that the methods deployed have complementary strengths depending on the instance parameters. Since the problem description has been obtained from a textile manufacturer where jobs of diverse size arrive continuously under tight deadlines, we also discuss the practical impact of our approach in terms of both tardiness decrease and broader managerial insights

Combining Optimisation and Simulation Using Logic-Based Benders Decomposition

Operations research practitioners frequently want to model complicated functions that are are difficult to encode in their underlying optimisation framework. A common approach is to solve an approximate model, and to use a simulation to evaluate the true objective value of one or more solutions. We propose a new approach to integrating simulation into the optimisation model itself. The idea is to run the simulation at each incumbent solution to the master problem. The simulation data is then used to guide the trajectory of the optimisation model itself using logic-based Benders cuts. We test the approach on a class of stochastic resource allocation problems with monotonic performance measures. We derive strong, novel Benders cuts that are provably valid for all problems of the given form. We consider two concrete examples: a nursing home shift scheduling problem, and an airport check in counter allocation problem. While previous papers on these applications could only approximately solve realistic instances, we are able to solve them exactly within a reasonable amount of time. Moreover, while those papers account for the inherent variance of the problem by including estimates of the underlying random variables as model parameters, we are able to compute sample average approximations to optimality with up to 100 scenarios.Comment: 30 page

Stochastic scheduling and workload allocation : QoS support and profitable brokering in computing grids

Abstract: The Grid can be seen as a collection of services each of which performs some functionality. Users of the Grid seek to use combinations of these services to perform the overall task they need to achieve. In general this can be seen as aset of services with a workflow document describing how these services should be combined. The user may also have certain constraints on the workflow operations, such as execution time or cost ----t~ th~ user, specified in the form of a Quality of Service (QoS) document. The users . submit their workflow to a brokering service along with the QoS document. The brokering service's task is to map any given workflow to a subset of the Grid services taking the QoS and state of the Grid into account -- service availability and performance. We propose an approach for generating constraint equations describing the workflow, the QoS requirements and the state of the Grid. This set of equations may be solved using Mixed-Integer Linear Programming (MILP), which is the traditional method. We further develop a novel 2-stage stochastic MILP which is capable of dealing with the volatile nature of the Grid and adapting the selection of the services during the lifetime of the workflow. We present experimental results comparing our approaches, showing that the . 2-stage stochastic programming approach performs consistently better than other traditional approaches. Next we addresses workload allocation techniques for Grid workflows in a multi-cluster Grid We model individual clusters as MIMIk. queues and obtain a numerical solutio~ for missed deadlines (failures) of tasks of Grid workflows. We also present an efficient algorithm for obtaining workload allocations of clusters. Next we model individual cluster resources as G/G/l queues and solve an optimisation problem that minimises QoS requirement violation, provides QoS guarantee and outperforms reservation based scheduling algorithms. Both approaches are evaluated through an experimental simulation and the results confirm that the proposed workload allocation strategies combined with traditional scheduling algorithms performs considerably better in terms of satisfying QoS requirements of Grid workflows than scheduling algorithms that don't employ such workload allocation techniques. Next we develop a novel method for Grid brokers that aims at maximising profit whilst satisfying end-user needs with a sufficient guarantee in a volatile utility Grid. We develop a develop a 2-stage stochastic MILP which is capable of dealing with the volatile nature . of the Grid and obtaining cost bounds that ensure that end-user cost is minimised or satisfied and broker's profit is maximised with sufficient guarantee. These bounds help brokers know beforehand whether the budget limits of end-users can be satisfied and. if not then???????? obtain appropriate future leases from service providers. Experimental results confirm the efficacy of our approach.Imperial Users onl

Optimization Models and Approximate Algorithms for the Aerial Refueling Scheduling and Rescheduling Problems

The Aerial Refueling Scheduling Problem (ARSP) can be defined as determining the refueling completion times for fighter aircrafts (jobs) on multiple tankers (machines) to minimize the total weighted tardiness. ARSP can be modeled as a parallel machine scheduling with release times and due date-to-deadline window. ARSP assumes that the jobs have different release times, due dates, and due date-to-deadline windows between the refueling due date and a deadline to return without refueling. The Aerial Refueling Rescheduling Problem (ARRP), on the other hand, can be defined as updating the existing AR schedule after being disrupted by job related events including the arrival of new aircrafts, departure of an existing aircrafts, and changes in aircraft priorities. ARRP is formulated as a multiobjective optimization problem by minimizing the total weighted tardiness (schedule quality) and schedule instability. Both ARSP and ARRP are formulated as mixed integer programming models. The objective function in ARSP is a piecewise tardiness cost that takes into account due date-to-deadline windows and job priorities. Since ARSP is NP-hard, four approximate algorithms are proposed to obtain solutions in reasonable computational times, namely (1) apparent piecewise tardiness cost with release time rule (APTCR), (2) simulated annealing starting from random solution (SArandom ), (3) SA improving the initial solution constructed by APTCR (SAAPTCR), and (4) Metaheuristic for Randomized Priority Search (MetaRaPS). Additionally, five regeneration and partial repair algorithms (MetaRE, BestINSERT, SEPRE, LSHIFT, and SHUFFLE) were developed for ARRP to update instantly the current schedule at the disruption time. The proposed heuristic algorithms are tested in terms of solution quality and CPU time through computational experiments with randomly generated data to represent AR operations and disruptions. Effectiveness of the scheduling and rescheduling algorithms are compared to optimal solutions for problems with up to 12 jobs and to each other for larger problems with up to 60 jobs. The results show that, APTCR is more likely to outperform SArandom especially when the problem size increases, although it has significantly worse performance than SA in terms of deviation from optimal solution for small size problems. Moreover CPU time performance of APTCR is significantly better than SA in both cases. MetaRaPS is more likely to outperform SAAPTCR in terms of average error from optimal solutions for both small and large size problems. Results for small size problems show that MetaRaPS algorithm is more robust compared to SAAPTCR. However, CPU time performance of SA is significantly better than MetaRaPS in both cases. ARRP experiments were conducted with various values of objective weighting factor for extended analysis. In the job arrival case, MetaRE and BestINSERT have significantly performed better than SEPRE in terms of average relative error for small size problems. In the case of job priority disruption, there is no significant difference between MetaRE, BestINSERT, and SHUFFLE algorithms. MetaRE has significantly performed better than LSHIFT to repair job departure disruptions and significantly superior to the BestINSERT algorithm in terms of both relative error and computational time for large size problems