A robust optimization approach for solving problems in conservation planning

Abstract

In conservation planning, the data related to size, growth and diffusion of populations is sparse, hard to collect and unreliable at best. If and when the data is readily available, it is not of sufficient quantity to construct a probability distribution. In such a scenario, applying deterministic or stochastic approaches to the problems in conservation planning either ignores the uncertainty completely or assumes a distribution that does not accurately describe the nature of uncertainty. To overcome these drawbacks, we propose a robust optimization approach to problems in conservation planning that considers the uncertainty in data without making any assumption about its probability distribution. We explore two of the basic formulations in conservation planning related to reserve selection and invasive species control to show the value of the proposed robust optimization. Several novel techniques are developed to compare the results produced by the proposed robust optimization approach and the existing deterministic approach. For the case when the robust optimization approach fails to find a feasible solution, a novel bi-objective optimization technique is developed to handle infeasibility by modifying the level of uncertainty. Some numerical experiments are conducted to demonstrate the efficacy of our proposed approach in finding more applicable conservation planning strategies.