Optimal Harvesting for a Predator-Prey Agent-Based Model using Difference Equations

Authored by Matthew Oremland, Reinhard Laubenbacher

Date Published: 2015

DOI: 10.1007/s11538-014-0060-6

Sponsors: US Army Research Office

Platforms: NetLogo

Model Documentation: ODD Pseudocode Mathematical description

Model Code URLs: Model code not found

Abstract

In this paper, a method known as Pareto optimization is applied in the solution of a multi-objective optimization problem. The system in question is an agent-based model (ABM) wherein global dynamics emerge from local interactions. A system of discrete mathematical equations is formulated in order to capture the dynamics of the ABM; while the original model is built up analytically from the rules of the model, the paper shows how minor changes to the ABM rule set can have a substantial effect on model dynamics. To address this issue, we introduce parameters into the equation model that track such changes. The equation model is amenable to mathematical theory-we show how stability analysis can be performed and validated using ABM data. We then reduce the equation model to a simpler version and implement changes to allow controls from the ABM to be tested using the equations. Cohen's weighted is proposed as a measure of similarity between the equation model and the ABM, particularly with respect to the optimization problem. The reduced equation model is used to solve a multi-objective optimization problem via a technique known as Pareto optimization, a heuristic evolutionary algorithm. Results show that the equation model is a good fit for ABM data; Pareto optimization provides a suite of solutions to the multi-objective optimization problem that can be implemented directly in the ABM.

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Genetic Algorithms Simulation Dynamics population Chronic myelogenous leukemia Epidemic Strategies Agreement