Philipp Wanko

A warehouse delivery problem consists of a set of robots that undertake delivery jobs within a warehouse. Items are moved around the warehouse in response to events. A solution to a warehouse delivery problem is a collision-free schedule of robot movements and actions that ensures that all delivery jobs are completed and each robot is returned to its docking station. While the warehouse delivery problem is related to existing research, such as the study of multi-agent path finding (MAPF), the specific industrial requirements necessitated a novel approach that diverges from these other approaches. For example, our problem description was more suited to formalizing the warehouse in terms of a weighted directed graph rather than the more common grid-based formalization. We formalize and encode the warehouse delivery problem in Answer Set Programming (ASP) extended with difference constraints. We systematically develop and study different encoding variants, with a view to computing good quality solutions in near real-time. In particular, application specific criteria are contrasted against the traditional notion of makespan minimization as a measure of solution quality. The encoding is tested against both crafted and industry data and experiments run using the Hybrid ASP solver clingo[dl].

Over the last decades, the development of Answer Set Programming (ASP) has brought about an expressive modeling language powered by highly performant systems. At the same time, it gets more and more difficult to provide semantic underpinnings capturing the resulting constructs and inferences. This is even more severe when it comes to hybrid ASP languages and systems that are often needed to handle real-world applications. We address this challenge and introduce the concept of abstract and structured theories that allow us to formally elaborate upon their integration with ASP. We then use this concept to make the semantic characterization of clingo’s theory-reasoning framework precise. This provides us with a formal framework in which we can elaborate upon the formal properties of existing hybridizations of clingo, such as clingcon, clingo[dl], and clingo[lp].