Optimal Harvesting for a Predator-Prey Agent-Based Model using Difference Equations
Optimal Harvesting for a Predator-Prey Agent-Based Model using Difference Equations
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DOI：
10.1007/s11538-014-0060-6
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发表时间：
2015-03-01
影响因子：
3.5
通讯作者：
Laubenbacher, Reinhard
中科院分区：
文献类型：
--
作者：
Oremland, Matthew;Laubenbacher, Reinhard
在本文中，被称为帕累托优化的方法被应用于解决多目标优化问题。所讨论的系统是一个基于代理的模型（ABM），其中的全球动态出现从本地的相互作用。一个系统的离散数学方程，以捕捉动态的反弹道导弹，而原来的模型是建立在分析的规则模型，本文显示了如何微小的变化，反弹道导弹规则集可以有一个实质性的影响模型动态。为了解决这个问题，我们引入参数的方程模型，跟踪这种变化。方程模型是服从数学理论，我们展示了如何稳定性分析，可以使用ABM数据进行验证。然后，我们减少了方程模型到一个更简单的版本，并实施更改，以允许控制从ABM进行测试使用的方程。科恩的加权被提出作为一种措施之间的相似性方程模型和ABM，特别是相对于优化问题。简化的方程模型是用来解决多目标优化问题，通过一种技术称为帕累托优化，启发式进化算法。结果表明，该方程模型能较好地拟合反弹道导弹数据，帕累托优化方法为反弹道导弹多目标优化问题提供了一套可直接实现的解决方案。
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.