An Integrated Approach to a Combinatorial Optimisation Problem

Abstract

We take inspiration from a problem from the healthcare domain, where patients with several chronic conditions follow different guidelines designed for the individual conditions, and where the aim is to find the best treatment plan for a patient that avoids adverse drug reactions, respects patient's preferences and prioritises drug efficacy. Each chronic condition guideline can be abstractly described by a directed graph, where each node indicates a treatment step (e.g., a choice in medications or resources) and has a certain duration. The search for the best treatment path is seen as a combinatorial optimisation problem and we show how to select a path across the graphs constrained by a notion of resource compatibility. This notion takes into account interactions between any finite number of resources, and makes it possible to express non-monotonic interactions. Our formalisation also introduces a discrete temporal metric, so as to consider only simultaneous nodes in the optimisation process. We express the formal problem as an SMT problem and provide a correctness proof of the SMT code by exploiting the interplay between SMT solvers and the proof assistant Isabelle/HOL. The problem we consider combines aspects of optimal graph execution and resource allocation, showing how an SMT solver can be an alternative to other approaches which are well-researched in the corresponding domains.

Dialogue Games for Explaining Medication Choices

“…Explanations are an important tool to increase the trust we have on the recommendations of AI systems. Because of their critical importance, numerous approaches have been developed for clinical decision support such as expert systems [21], SMT solvers [5,6], and argumentation [9,15]. Here we use argumentation in an explanatory role to explain the decisions of the SMT solver.…”

“…Satisfiability Modulo Theories (SMT) solvers are popular in analysis and model checking settings because of their expressive power, arithmetic capabilities and scalability [19]. SMT solvers have been used efficiently to identify and minimise ADRs in [5][6][7]. There is, however, still a need to add clarity to the identified optimal path and justify why one combination of paths across different treatment plans may be preferable to another.…”