Risk-Averse Antibiotics Time Machine Problem

TL;DR

This paper develops a risk-averse optimization approach for the Antibiotics Time Machine Problem, aiming to improve worst-case treatment outcomes by formulating a scenario-based mixed-integer linear program with advanced decomposition algorithms.

Contribution

It introduces a novel risk-averse scenario decomposition algorithm with enhancements, applicable to antibiotic treatment planning and similar risk-sensitive decision problems.

Findings

Risk-averse solutions outperform risk-neutral ones in worst-case scenarios.

The approach achieves better worst-case performance with minimal impact on average results.

Effective for static and dynamic treatment planning on real datasets.

Abstract

Antibiotic resistance, which is a serious healthcare issue, emerges due to uncontrolled and repeated antibiotic use that causes bacteria to mutate and develop resistance to antibiotics. The Antibiotics Time Machine Problem aims to come up with treatment plans that maximize the probability of reversing these mutations. Motivated by the severity of the problem, we develop a risk-averse approach and formulate a scenario-based mixed-integer linear program with a conditional value-at-risk objective function. We propose a risk-averse scenario batch decomposition algorithm that partitions the scenarios into manageable risk-averse subproblems, enabling the construction of lower and upper bounds. We develop several algorithmic enhancements in the form of stronger no-good cuts and symmetry breaking constraints in addition to scenario regrouping and warm starting. We conduct extensive computational experiments for static and dynamic versions of the problem on a real dataset and demonstrate the effectiveness of our approach. Our results suggest that risk-averse solutions can achieve significantly better worst-case performance compared to risk-neutral solutions with a slight decrease in terms of the average performance, especially for the dynamic version. Although our methodology is presented in the context of the Antibiotics Time Machine Problem, it can be adapted to other risk-averse problem settings in which the decision variables come from special ordered sets of type one.