Explaining Propagators for String Edit Distance Constraints

Abstract

The computation of string similarity measures has been thoroughly studied in the scientific literature and has applications in a wide variety of different areas. One of the most widely used measures is the so called string edit distance which captures the number of required edit operations to transform a string into another given string. Although polynomial time algorithms are known for calculating the edit distance between two strings, there also exist NP-hard problems from practical applications like scheduling or computational biology that constrain the minimum edit distance between arrays of decision variables. In this work, we propose a novel global constraint to formulate restrictions on the minimum edit distance for such problems. Furthermore, we describe a propagation algorithm and investigate an explanation strategy for an edit distance constraint propagator that can be incorporated into state of the art lazy clause generation solvers. Experimental results show that the proposed propagator is able to significantly improve the performance of existing exact methods regarding solution quality and computation speed for benchmark problems from the literature.

A large neighborhood search approach for the paint shop scheduling problem

“…Using state-of-the-art CP solvers, the exact approach could be successfully used to find optimal solutions for 7 of the smaller-sized benchmark instances of the PSSP. The CP approach was later improved in Winter et al (2020) with the introduction of a string edit distance global constraint, which could be used to efficiently model parts of the objective function of the PSSP leading to much faster optimality proofs for the smaller instances. However, experiments further showed that the exact approach is not able to produce solutions for instances 11-24, and therefore, the simulated annealing-based approach currently represents the state-of-the-art solution method for larger instances.…”

“…Note that instances 1-12 are considered to be small instances, as the round capacity as well as the number of colors, carrier types, and demands are much smaller than for instances 13-24. Many of these small instances could be previously solved to optimality using exact methods in Winter and Musliu (2021); Winter et al (2020). Instances 13-24 on the other hand represent real-life scheduling scenarios from a large-scale industrial paint shop; therefore, they all use the same round capacity, colors, and carrier types.…”

“…Recently, we have introduced a paint shop scheduling problem (PSSP) from the automotive supply industry together with a set of 24 real-life problem instances in Winter et al (2019). Furthermore, we have investigated exact approaches based on constraint programming for the PSSP and provided a NP-hardness proof Winter and Musliu (2021); Winter et al (2020). Experimental results with the practical benchmark instances revealed that exact approaches could prove several optimal results for small-to medium-sized instances; however, optimal solutions for many large real-life instances are still unknown.…”

Machine Reasoning Explainability

“…[83] • What are the next propagation steps? [65,208] • Which choices should I relax in order to recover consistency? [7,82] • Which choices should I relax in order to render such a value available for such a variable?…”

“…Similar ideas using a lazy clause generation solver for explaining propagation via constraints from which nogoods can be computed can be applied to string edit distance constraints, e.g. in [208] Winter et al use explanations that consist of literals which logically entail the truth of a Boolean variable that encodes propagation of some variable's value.…”