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Risk-Averse Antibiotics Time Machine Problem

Deniz Tuncer, Burak Kocuk

TL;DR

This paper tackles the risk-averse Antibiotics Time Machine Problem, aiming to maximize the probability of reversing bacterial mutations under uncertainty. It introduces a scenario-based MILP framework with a CVaR objective and develops a risk-averse scenario batch decomposition algorithm, augmented by Cartesian cuts, symmetry breaking, scenario regrouping, and warm-start techniques. The authors provide static and dynamic formulations, prove bounds via batch subproblems, and demonstrate that risk-averse solutions significantly improve worst-case performance, particularly in the dynamic setting, with only moderate losses in average performance. The work offers a scalable methodology that extends beyond antibiotics to other risk-averse problems where decisions come from special ordered sets of type one, with practical implications for treatment planning under uncertainty.

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.

Risk-Averse Antibiotics Time Machine Problem

TL;DR

This paper tackles the risk-averse Antibiotics Time Machine Problem, aiming to maximize the probability of reversing bacterial mutations under uncertainty. It introduces a scenario-based MILP framework with a CVaR objective and develops a risk-averse scenario batch decomposition algorithm, augmented by Cartesian cuts, symmetry breaking, scenario regrouping, and warm-start techniques. The authors provide static and dynamic formulations, prove bounds via batch subproblems, and demonstrate that risk-averse solutions significantly improve worst-case performance, particularly in the dynamic setting, with only moderate losses in average performance. The work offers a scalable methodology that extends beyond antibiotics to other risk-averse problems where decisions come from special ordered sets of type one, with practical implications for treatment planning under uncertainty.

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.
Paper Structure (25 sections, 4 theorems, 17 equations, 4 figures, 4 tables, 2 algorithms)

This paper contains 25 sections, 4 theorems, 17 equations, 4 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction and Literature Review
  2. Deterministic Problem
  3. Static Stochastic Problem
  4. Risk-Neutral Version
  5. Risk-Averse Version
  6. Scenario Decomposition Algorithm
  7. Enhancements
  8. Cartesian Cuts
  9. Symmetry Breaking Inequalities and Symmetry-Enhanced Cartesian Cuts
  10. Scenario Regrouping
  11. Warm Start
  12. Dynamic Stochastic Problem
  13. Risk-Averse Version
  14. Scenario Decomposition Algorithm
  15. Enhancements
  16. ...and 10 more sections

Key Result

Proposition 1

nemirovskiLO Consider the function $s_\alpha (\bm{\upsilon})$ defined above. Then,

Figures (4)

  • Figure 1: Illustration of an Antibiotics Time Machine Problem instance with $a=3$ alleles and $K=2$ antibiotics.
  • Figure 2: Comparison of risk-neutral and risk-averse solutions for the initial genotype 0001 and $N=5$.
  • Figure 3: Comparison of risk-averse and risk-neutral solutions for the static version.
  • Figure 4: Comparison of risk-averse and risk-neutral solutions for the dynamic version.

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4