Viability Theory

Viability theory is an original way of thinking at multi-criteria problems, notably in the field of sustainable development. Instead of focusing on the search of an “optimal” solution for a given problem, it consists in searching the ensemble of solutions that are satisfying a given set of constraints, thereby fostering the possibility of concertation among stakeholders (Martin 2004). Our work consists in mathematically formalizing key sustainable development concepts within the viability framework (Martin 2004, Rougé et al. 2013, Kittel et al. 2017), developing mathematical and algorithmic tools to determine ensemble sets such as viability kernels or attraction basins, and finding strategies to bridge various scales of interest within a viability problem (Martin et al. 2015). Approximated viability kernels can then be compared and manipulated with our ViNO platform.

Key contributed papers:

Kittel, T., Koch, R., Heitzig, J., Deffuant, G., Mathias, J. D., & Kurths, J. (2017). Operationalization of Topology of Sustainable Management to Estimate Qualitatively Different Regions in State Space. arXiv preprint arXiv:1706.04542.

Martin, S. (2004). The cost of restoration as a way of defining resilience: a viability approach applied to a model of lake eutrophication. Ecology and Society, 9(2).

– Martin, S., Alvarez, I., & Kant, J. D. (2015). Micro/macro viability analysis of individual‐based models: Investigation into the viability of a stylized agricultural cooperative. Complexity, 21(2), 276-296.

– Rougé, C., Mathias, J. D., & Deffuant, G. (2013). Extending the viability theory framework of resilience to uncertain dynamics, and application to lake eutrophication. Ecological indicators, 29, 420-433.