2024 [ nach oben ]

Neubert, Stefan; Casel, Katrin Incremental Ordering for Scheduling ProblemsProceedings of the International Conference on Automated Planning and Scheduling 2024: 405–413
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Given an instance of a scheduling problem where we want to start executing jobs as soon as possible, it is advantageous if a scheduling algorithm emits the first parts of its solution early, in particular before the algorithm completes its work. Therefore, in this position paper, we analyze core scheduling problems in regards to their enumeration complexity, i.e. the computation time to the first emitted schedule entry (preprocessing time) and the worst case time between two consecutive parts of the solution (delay). Specifically, we look at scheduling instances that reduce to ordering problems. We apply a known incremental sorting algorithm for scheduling strategies that are at their core comparison-based sorting algorithms and translate corresponding upper and lower complexity bounds to the scheduling setting. For instances with n jobs and a precedence DAG with maximum degree Δ, we incrementally build a topological ordering with O(n) preprocessing and O(Δ) delay. We prove a matching lower bound and show with an adversary argument that the delay lower bound holds even in case the DAG has constant average degree and the ordering is emitted out-of-order in the form of insert operations. We complement our theoretical results with experiments that highlight the improved time-to-first-output and discuss research opportunities for similar incremental approaches for other scheduling problems.
@inproceedings{neubert2024incremental, abstract = {Given an instance of a scheduling problem where we want to start executing jobs as soon as possible, it is advantageous if a scheduling algorithm emits the first parts of its solution early, in particular before the algorithm completes its work. Therefore, in this position paper, we analyze core scheduling problems in regards to their enumeration complexity, i.e. the computation time to the first emitted schedule entry (preprocessing time) and the worst case time between two consecutive parts of the solution (delay). Specifically, we look at scheduling instances that reduce to ordering problems. We apply a known incremental sorting algorithm for scheduling strategies that are at their core comparison-based sorting algorithms and translate corresponding upper and lower complexity bounds to the scheduling setting. For instances with n jobs and a precedence DAG with maximum degree Δ, we incrementally build a topological ordering with O(n) preprocessing and O(Δ) delay. We prove a matching lower bound and show with an adversary argument that the delay lower bound holds even in case the DAG has constant average degree and the ordering is emitted out-of-order in the form of insert operations. We complement our theoretical results with experiments that highlight the improved time-to-first-output and discuss research opportunities for similar incremental approaches for other scheduling problems.}, author = {Neubert, Stefan and Casel, Katrin}, booktitle = {Proceedings of the International Conference on Automated Planning and Scheduling}, keywords = {icaps katrincasel stefanneubert year2024}, month = {may}, number = 1, pages = {405-413}, publisher = {AAAI Press}, title = {Incremental Ordering for Scheduling Problems}, volume = 34, year = 2024 }

2019 [ nach oben ]

Peters, Jannik; Stephan, Daniel; Amon, Isabel; Gawendowicz, Hans; Lischeid, Julius; Salabarria, Julius; Umland, Jonas; Werner, Felix; Krejca, Martin S.; Rothenberger, Ralf; Kötzing, Timo; Friedrich, Tobias Mixed Integer Programming versus Evolutionary Computation for Optimizing a Hard Real-World Staff Assignment ProblemInternational Conference on Automated Planning and Scheduling (ICAPS) 2019: 541–554
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Assigning staff to engagements according to hard constraints while optimizing several objectives is a task encountered by many companies on a regular basis. Simplified versions of such assignment problems are NP-hard. Despite this, a typical approach to solving them consists of formulating them as mixed integer programming (MIP) problems and using a state-of-the-art solver to get solutions that closely approximate the optimum. In this paper, we consider a complex real-world staff assignment problem encountered by the professional service company KPMG, with the goal of finding an algorithm that solves it faster and with a better solution than a commercial MIP solver. We follow the evolutionary algorithm (EA) metaheuristic and design a search heuristic which iteratively improves a solution using domain-specific mutation operators. Furthermore, we use a flow algorithm to optimally solve a subproblem, which tremendously reduces the search space for the EA. For our real-world instance of the assignment problem, given the same total time budget of \(100\) hours, a parallel EA approach finds a solution that is only \(1.7\)% away from an upper bound for the (unknown) optimum within under five hours, while the MIP solver Gurobi still has a gap of \(10.5\) %.
@inproceedings{peters2019mixed, abstract = {Assigning staff to engagements according to hard constraints while optimizing several objectives is a task encountered by many companies on a regular basis. Simplified versions of such assignment problems are NP-hard. Despite this, a typical approach to solving them consists of formulating them as mixed integer programming (MIP) problems and using a state-of-the-art solver to get solutions that closely approximate the optimum. In this paper, we consider a complex real-world staff assignment problem encountered by the professional service company KPMG, with the goal of finding an algorithm that solves it faster and with a better solution than a commercial MIP solver. We follow the evolutionary algorithm (EA) metaheuristic and design a search heuristic which iteratively improves a solution using domain-specific mutation operators. Furthermore, we use a flow algorithm to optimally solve a subproblem, which tremendously reduces the search space for the EA. For our real-world instance of the assignment problem, given the same total time budget of \(100\) hours, a parallel EA approach finds a solution that is only \(1.7\)\% away from an upper bound for the (unknown) optimum within under five hours, while the MIP solver Gurobi still has a gap of \(10.5\) \%.}, author = {Peters, Jannik and Stephan, Daniel and Amon, Isabel and Gawendowicz, Hans and Lischeid, Julius and Salabarria, Julius and Umland, Jonas and Werner, Felix and Krejca, Martin S. and Rothenberger, Ralf and Kötzing, Timo and Friedrich, Tobias}, booktitle = {International Conference on Automated Planning and Scheduling (ICAPS)}, keywords = {danielstephan felixwerner hansgawendowicz icaps isabelamon jannikpeters jonasumland juliuslischeid lennartsalabarria martinskrejca ralfrothenberger timokoetzing tobiasfriedrich year2019}, pages = {541-554}, title = {Mixed Integer Programming versus Evolutionary Computation for Optimizing a Hard Real-World Staff Assignment Problem}, year = 2019 }

2007 [ nach oben ]

Sutton, Andrew M.; Howe, Adele E.; Whitley, L. Darrell Using Adaptive Priority Weighting to Direct Search in Probabilistic SchedulingInternational Conference on Automated Planning and Scheduling (ICAPS) 2007: 320–327
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Many scheduling problems reside in uncertain and dynamic environments - tasks have a nonzero probability of failure and may need to be rescheduled. In these cases, an optimized solution for a short-term time horizon may have a detrimental impact over a broader time scale. We examine a scheduling domain in which time and energy on a phased array radar system is allocated to track objects in orbit around the earth. This domain requires probabilistic modeling to optimize the expected number of successful tasks on a particular day. Failed tasks must be attempted again on subsequent days. Given a set of task requests, we study two long-term objectives: percentage of requests initially successful, and the average time between successful request updates. We investigate adaptive priority weighting strategies that directly influence the short-term objective function and thus indirectly influence the long-term goals. We find that adapting priority weights based on when individual tasks succeed or fail allows a catalog of requests to be filled more quickly. Furthermore, with adaptive priorities, we observe a Pareto-front effect between the two long-term objectives as we modify how priorities are weighted, but an inverse effect of weighting when the priorities are not adapted.
@inproceedings{DBLP:conf/aips/SuttonHW07, abstract = {Many scheduling problems reside in uncertain and dynamic environments - tasks have a nonzero probability of failure and may need to be rescheduled. In these cases, an optimized solution for a short-term time horizon may have a detrimental impact over a broader time scale. We examine a scheduling domain in which time and energy on a phased array radar system is allocated to track objects in orbit around the earth. This domain requires probabilistic modeling to optimize the expected number of successful tasks on a particular day. Failed tasks must be attempted again on subsequent days. Given a set of task requests, we study two long-term objectives: percentage of requests initially successful, and the average time between successful request updates. We investigate adaptive priority weighting strategies that directly influence the short-term objective function and thus indirectly influence the long-term goals. We find that adapting priority weights based on when individual tasks succeed or fail allows a catalog of requests to be filled more quickly. Furthermore, with adaptive priorities, we observe a Pareto-front effect between the two long-term objectives as we modify how priorities are weighted, but an inverse effect of weighting when the priorities are not adapted.}, author = {Sutton, Andrew M. and Howe, Adele E. and Whitley, L. Darrell}, booktitle = {International Conference on Automated Planning and Scheduling (ICAPS)}, keywords = {andrewmsutton icaps imported year2007}, pages = {320-327}, publisher = {{AAAI}}, title = {Using Adaptive Priority Weighting to Direct Search in Probabilistic Scheduling}, year = 2007 }

2006 [ nach oben ]

Sutton, Andrew M.; Howe, Adele E.; Whitley, L. Darrell Spacetrack: Trading off Quality and Utilization in Oversubscribed SchedulesInternational Conference on Automated Planning and Scheduling (ICAPS) 2006: 430–433
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Many scheduling problems are posed as optimization problems where the goal is to find a feasible schedule that maximizes the utilization of some resource. In some domains it is also necessary to consider the quality of the resulting schedule. In most research these two quantities are independent. This paper introduces a real world problem in which radar tasks must be allocated to track objects in space. We explore the trade-off between off-line task resource utilization and a measure of task quality that correlates to whether tasks are actually successfully executed. We develop two general types of algorithms that differ in the way they reason about quality and explore the trade-off between high quality solutions and solutions with high resource utilization.
@inproceedings{DBLP:conf/aips/SuttonHW06, abstract = {Many scheduling problems are posed as optimization problems where the goal is to find a feasible schedule that maximizes the utilization of some resource. In some domains it is also necessary to consider the quality of the resulting schedule. In most research these two quantities are independent. This paper introduces a real world problem in which radar tasks must be allocated to track objects in space. We explore the trade-off between off-line task resource utilization and a measure of task quality that correlates to whether tasks are actually successfully executed. We develop two general types of algorithms that differ in the way they reason about quality and explore the trade-off between high quality solutions and solutions with high resource utilization.}, author = {Sutton, Andrew M. and Howe, Adele E. and Whitley, L. Darrell}, booktitle = {International Conference on Automated Planning and Scheduling (ICAPS)}, keywords = {andrewmsutton icaps imported year2006}, pages = {430-433}, publisher = {{AAAI}}, title = {Spacetrack: Trading off Quality and Utilization in Oversubscribed Schedules}, year = 2006 }