基于Lotka-Volterra模型的企业协同发展资源配置算法

Resource Allocation Algorithm for Enterprise Collaborative Development Based on Lotka-Volterra Model

摘要

针对复杂企业主体间协同发展动态优化困难、资源调控缺乏理论指导的问题,提出一种改进的Lotka-Volterra协同工作模型.首先,通过引入资源投入作为控制变量,推导出协同系统实现有限时间稳定的条件及稳定时间函数,并用Pontryagin极大值原理和Hamilton函数方法,得出协同经济效益最大化下的最优资源调控策略.其次,用仿真对比算法的有效性和可行性,推算出两类企业主体达到最大经济效益时的资源投入比例.实验结果表明,该算法不仅为预测不同企业主体间的协同工作路径提供了新思路,并为制定科学的产业调控策略提供了理论依据.

Abstract

Aiming at the problems that there were difficultes in dynamic optimization and lack of theoretical guidance for resource regulation in the collaborative development among comples enterprise entities,we proposed an improved Lotka-Volterra collaborative work model.Firstly,by introducing resource input as a control variable,we derived the conditions for the collaborative system to achieve stability in a finite time and the stability time function,and used the Pontryagin’s maximum principle and the Hamilton function method to obtain the optimal resource regulation strategy for maximizing the collaborative economic benefits.Secondly,by comparing the effectiveness and feasibility of simulation algorithm,we calculated the resource input ratio for two types of enterprise entities to achieve maximum economic benefits.The experimental results show that the proposed algorithm not only provides a new idea for predicting the collaborative work path among different enterprise entities,but also provides theoretical basis for formulating scientific industrial regulation strategies.

关键词

种群动力学 / Lotka-Volterra模型 / 协同发展 / Pontryagin极大值原理 / 最优资源调控策略

Key words

population dynamic / Lotka-Volterra model / collaborative development / Pontryagin’s maximum principle / optimal resource regulation strategy

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基金资助

吉林省自然科学基金(20240304097SF)