Modelling and Solving Online Optimisation Problems

Abstract

Many optimisation problems are of an online—also called dynamic—nature, where new information is expected to arrive and the problem must be resolved in an ongoing fashion to (a) improve or revise previous decisions and (b) take new ones. Typically, building an online decision-making system requires substantial ad-hoc coding to ensure the offline version of the optimisation problem is continually adjusted and resolved. This paper defines a general framework for automatically solving online optimisation problems. This is achieved by extending a model of the offline optimisation problem, from which an online version is automatically constructed, thus requiring no further modelling effort. In doing so, it formalises many of the aspects that arise in online optimisation problems. The same framework can be applied for automatically creating sliding-window solving approaches for problems that have a large time horizon. Experiments show we can automatically create efficient online and sliding-window solutions to optimisation problems.

Aggregation and Garbage Collection for Online Optimization

“…And third, once all constraints have been analyzed and aggregated, the garbage from all constraints is collected and removed to ensure it does not form part of the update instance. We note that this paper significantly extends our previous problem-independent online modeling approach [7], with a much more sophisticated and effective method for garbage collection. We also note that our online approach can also be used for solving large-scale offline optimization problem, when applying an iterative solving approach over a rolling horizon [19].…”

“…The parameterization also applies to its components (X[Data], D[Data], C[Data]). This allows us to extend the online approach of [7] by representing a DCSP as the list DP = (P [δ 1 ], P [δ 2 ], • • • ), where data can change over time, while the underlying model remains unchanged.…”

“…The overlap constraints add information about how earlier information affects the current session. In the approach of [7], which we extend, these are constructed automatically from annotations of the original model. The overlap constraints focus on old decisions that must be committed, that is, decisions taken by the previous session (or modified by external sources) that cannot change in the current one.…”

“…We consider a rolling horizon version where jobs are spaced out by earliest start time. To highlight the advantages of automated garbage collection over the simple approach of [7], some of the jobs are given very long running times compared to other jobs. In the simple approach a job is garbage only if all tasks that arrived earlier are also garbage.…”

“…These long running jobs prevent effective garbage collection under this policy, representing its worst case. We run a similar experiment to that of [7], with the same model and data file ft20 from the MiniZinc benchmarks, 2 and the same method to obtain an endless queue of jobs by repeatedly adding copies of the jobs in sequence. In each session we increase the current time τ by 408 scheduling time units, add the next 4 jobs in the queue, and set a time limit of 1 second.…”