Mathematical viability theory offers concepts and methods that are suitable to study the compatibility between a dynamical system described by a set of differential equations and constraints in the state space. The result sets built during the viability analysis can give very useful information regarding management issues in fields where it is easier to discuss constraints than objective functions.
egarding management issues in fields where it is easier to discuss constraints than objective functions.
Viability kernels can rarely be described analytically, so it is necessary to compute approximation. First algorithm to be implemented was Patrick Saint-Pierre’s [1].
Viabilitree is a framework in which the viability sets are represented and approximated with particular kd-trees [2]. The computation of the viability kernel is seen as an active learning problem. We prove the convergence of the algorithm and assess the approximation it produces for known problems with analytical solution. This framework aims at simplifying the declaration of the viability problem and provides useful methods to assist further use of viability sets produced by the computation [3].
More information can be found here : https://gitlab.iscpif.fr/viability/viabilitree
References
[1] Saint-Pierre, P. (1994). Approximation of the viability kernel. Applied Mathematics & Optimisation, 29(2), 187–209.
[2] Rouquier et al, A kd-tree algorithm to discover the boundary of a black box hypervolume, Annals of Mathematics and Artificial Intelligence, vol 75, 3, pp “335–350, 2015.
[3] Alvarez, Reuillon, de Aldama. Viabilitree: A kd-tree Framework for Viability-based Decision. hal-01319738.