Explicitly Controlling Geometric Characteristics of Corridors in Spatial Optimization

Abstract

Spatially-explicit mixed-integer programming models (MIPs) allow decision makers to explore a variety of complex scenarios and determine optimal sets of actions across a landscape. In reserve selection problems, the landscape is partitioned into units, and the decision maker must select which units to include in a wildlife reserve. As areas of habitat on the landscape are often scarce, connectivity of these regions through wildlife corridors is critical for species protection. Mixed integer programming models have been used in the past to create wildlife corridors, but they lack the capacity to control corridor geometry. In this dissertation, I propose an approach, called the Optimal Corridor Construction Approach (OCCA), that employs path planning techniques from artificial intelligence to account for and control corridor geometry, such as width and length. By combining path planning with network optimization, the OCCA allows the user to control and optimize the geometric characteristics of corridors. The OCCA may be used in other applications involving route construction (e.g., vehicle routing) or barrier construction (e.g., fire break design). I illustrate the use of the OCCA on the 1,363 unit El Dorado forest in California. I find that the OCCA is extremely effective in selecting maximal width corridors, both with and without corridor length restrictions. In many spatial optimization approaches, computational performance issues lead to intractable problems. I explore the computational performance of the OCCA by considering a variety of landscape factors to determine which may affect formulation and solution times, as well as problem size. I determine that the number of units, degree of unit adjacency and variation in unit size all affect problem size and performance. I also find that problem size, specifically the number of gate pairs, is linearly correlated with computational performance, specifically run time. Lastly, I demonstrate how the OCCA can be used in a complex, real world scenario through a case study in Northern Sweden, where I include reindeer corridors in a forest harvest scheduling model. Current commercial forest practices reduce the amount of reindeer habitat and have made it difficult for reindeer to move through the forests. I combine the OCCA with a harvest scheduling model to explore the relationship between timber revenues and the selection and maintenance of reindeer corridors. Since harvest scheduling occurs over a planning horizon, the spatial configuration of corridors can change from one time period to the next in order to accommodate harvesting activities. If no corridors are included in the harvest scheduling model, the optimal harvest schedule results in a forest that is impassable for reindeer. When corridors are included, the combined model produces a harvest schedule that supports reindeer passage on the landscape throughout the planning horizon. Results from this case study indicate that collaborative management is highly beneficial to reindeer herders, with a minimal cost to foresters.