CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Cedex 05, Paris, France.
Capital Fund Management, 21 rue de l'université, 75007 Paris, France.
Phys Rev Lett. 2014 Feb 7;112(5):050602. doi: 10.1103/PhysRevLett.112.050602. Epub 2014 Feb 5.
Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or economic growth, portfolio optimization, evolutionary dynamics, or the problem of optimal pinning of vortices or dislocations in disordered materials. We find the exact growth rate of this model for treelike geometries and prove the existence of an optimal migration rate in this case. Numerical simulations in the one-dimensional case confirm the generic existence of an optimum.
在开发已知资源和探索未知但潜在更有利可图的选择之间找到一个良好的平衡是一个普遍存在的问题，它出现在许多不同的科学学科中。我们提出了一个用于这些探索-开发情况的简化模型，包括人口或经济增长、投资组合优化、进化动力学或在无序材料中最优固定涡旋或位错的问题。我们找到了这种树状几何形状的模型的精确增长率，并证明了在这种情况下存在最优迁移率。一维情况下的数值模拟证实了一般存在最优解。
