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

Content Provider	Springer Nature Link
Author	Oremland, Matthew Laubenbacher, Reinhard
Copyright Year	2015
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 $$\kappa $$ 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.
Starting Page	434
Ending Page	459
Page Count	26
File Format	PDF
ISSN	00928240
Journal	Bulletin of Mathematical Biology
Volume Number	77
Issue Number	3
e-ISSN	15229602
Language	English
Publisher	Springer US
Publisher Date	2015-01-06
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Agent-based modeling Optimization Heuristic algorithm Statistics Dynamical systems Mathematical and Computational Biology Life Sciences Cell Biology
Content Type	Text
Resource Type	Article
Subject	Neuroscience Biochemistry, Genetics and Molecular Biology Mathematics Pharmacology Immunology Computational Theory and Mathematics Environmental Science Agricultural and Biological Sciences

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