Scalable Relaxations of Sparse Packing Constraints: Optimal Biocontrol in Predator-Prey Network

TL;DR

This paper introduces a scalable randomized algorithm for optimal biocontrol in predator-prey networks with sparse constraints, effectively managing invasive species like the Hemlock Woolly Adelgid.

Contribution

A novel width relaxation-based randomized algorithm that scales better than existing methods for sparse, nonlinear biocontrol optimization problems.

Findings

Outperforms existing methods in scalability and solution quality.

Finds near-optimal biocontrol strategies for complex predator-prey networks.

Effective in real-world ecological management scenarios.

Abstract

Cascades represent rapid changes in networks. A cascading phenomenon of ecological and economic impact is the spread of invasive species in geographic landscapes. The most promising management strategy is often biocontrol, which entails introducing a natural predator able to control the invading population, a setting that can be treated as two interacting cascades of predator and prey populations. We formulate and study a nonlinear problem of optimal biocontrol: optimally seeding the predator cascade over time to minimize the harmful prey population. Recurring budgets, which typically face conservation organizations, naturally leads to sparse constraints which make the problem amenable to approximation algorithms. Available methods based on continuous relaxations scale poorly, to remedy this we develop a novel and scalable randomized algorithm based on a width relaxation, applicable to a broad class of combinatorial optimization problems. We evaluate our contributions in the context of biocontrol for the insect pest Hemlock Wolly Adelgid (HWA) in eastern North America. Our algorithm outperforms competing methods in terms of scalability and solution quality, and finds near optimal strategies for the control of the HWA for fine-grained networks -- an important problem in computational sustainability.