Automatic Streamlining for Constrained Optimisation

Abstract

Augmenting a base constraint model with additional constraints can strengthen the inferences made by a solver and therefore reduce search effort. We focus on the automatic addition of streamliner constraints, which trade completeness for potentially very significant reduction in search. Recently an automated approach has been proposed, which produces streamliners via a set of streamliner generation rules. This existing automated approach to streamliner generation has two key limitations. First, it outputs a single streamlined model. Second, the approach is limited to satisfaction problems. We remove both limitations by providing a method to produce automatically a portfolio of streamliners, each representing a different balance between three criteria: how aggressively the search space is reduced, the proportion of training instances for which the streamliner admitted at least one solution, and the average reduction in quality of the objective value versus the unstreamlined model. In support of our new method, we present an automated approach to training and test instance generation, and provide several approaches to the selection and application of the streamliners from the portfolio. Empirical results demonstrate drastic improvements both to the time required to find good solutions early and to prove optimality on three problem classes.

Half-checking propagators

“…We think that scheduling problems may be an interesting future area of research for this. Also, studying automatically generated streamliner constraints [42,39] could be an interesting source of ideas for new half-checking propagators.…”

Towards Portfolios of Streamlined Constraint Models: A Case Study with the Balanced Academic Curriculum Problem

“…We employ the same set of streamliner generation rules as [40,41]. These rules are generic, developed around the structured abstract types provided by Essence.…”

“…Moreover, different models are also likely to benefit from the addition of streamliner constraints differently. In existing work [40,41] this choice is handled by utilising the default heuristic of Conjure. This is a heuristic employed during refinement to commit greedily to promising modelling choices at each point where an abstract type or a constraint expression may be refined in multiple ways [3].…”

“…More recently, it has been shown how this process can be automated to derive candidate streamliners directly from the Essence specification of a problem class of interest [40,41]. Essence [15][16][17] is an abstract constraint specification language that allows a problem to be described directly in terms of the combinatorial structure to be found, through support for abstract type constructors like set, relation, function and partition, as well as arbitrary nesting of these, such as set of multisets.…”

“…The existing work [40,41] uses the Conjure automated modelling system [3,5] to refine a streamlined Essence specification into a constraint model for evaluation. This work is limited to accepting Conjure's default choice for each of the modelling decisions that need to be made, such as how to represent abstract variables as constrained collections of more primitive variables, resulting in a single streamlined model.…”