How large spatially-explicit optimal reserve design models can we solve now? An exploration of current models’ computational efficiency

Abstract

Citation: Wang Y, Önal H, Fang W (2018) How large spatially-explicit optimal reserve design models can we solve now? An exploration of current models' computational efficiency. AbstractSpatially-explicit optimal reserve design models select best sites from a set of candidate sites to assemble nature reserves to protect species (or habitats) and these reserves display certain spatial attributes which are desirable for species. These models are formulated with linear 0-1 programming and solved using standard optimisation software, but they were run on different platforms, resulting in discrepant or even conflicting messages with regard to their computational efficiency. A fair and accurate comparison of the convenience of these models would be important for conservation planners who use these models. In this article, we considered eight models presented in literature and tested their computational efficiency using randomly generated data sets containing up to 2000 sites. We focused on reserve contiguity and compactness which are considered crucial to species persistence. Our results showed that two of these models, namely Williams (2002) and Önal et al. (2016), stand out as the most efficient models. We also found that the relative efficiency of these models depends on the scope of analysis. Specifically, the Williams (2002) model solves more of the test problems when contiguity is the only spatial attribute and a large subset of the candidate sites needs to be selected. When compactness is considered also, the Önal et al. (2016) model generally performs better. Large scale models are found to be difficult to solve in a reasonable period of time. We discussed factors that may affect those models' computational efficiency, including model size, share of selected sites, model structure and input data. These results provide useful insight and guidance to conservation practitioners and researchers who focus on spatial aspects and work with large-scale data sets. A peer-reviewed open-access journalYicheng Wang et al. / Nature Conservation 27: 17-37 (2018) 18 Keywords nature reserve design, mixed integer programming, computational efficiency, contiguity, compactness, spatial optimisation

Spatial optimization for land acquisition problems: A review of models, solution methods, and GIS support

“…In addition to these studies, researchers have tested computation issues for more spatially constrained models, notably contiguity models. A review of the size of problems for nature reserve design (Wang, Önal, & Fang, ) shows the difficulties in finding optimal solutions for problems with more than hundreds of units. For regionalization problems, most research efforts show that optimal solutions can only be obtained for problems of 100 units (Duque et al., ; Kim & Xiao, ; Shirabe, ).…”

Systematic Conservation Planning for Sustainable Land-use Policies: A Constrained Partitioning Approach to Reserve Selection and Design.

“…The 50 species without SDM were arbitrarily considered as endangered. According to the recent literature, this problem can be considered as a large one [Wang et al, 2018]. Our model was implemented 1 and ran with Choco-solver and its Choco-graph extension (for graph variables) [Prud'homme et al, 2017], on a Linux laptop with (Intel Core i5-5200U CPU 2.20GHz×4, 8GB RAM).…”

“…Many reserve selection and design models have been devised, e.g. [ReVelle et al, 2002;Williams et al, 2005;Sarkar, 2012;Dilkina et al, 2017]. Usually, these meth- Figure 1: Grid partition with a core area (dark gray), a buffer (light gray), and an out-reserve area (white).…”

“…In addition, no more than two regions can be defined, and the buffer zone constraint is lacking. As a matter of fact, this constraint has, to our knowledge, only been modeled by some MILP approaches [Williams et al, 2005;Billionnet, 2013] in a local fashion for three-regions configurations (core area, buffer zone and out-reserve area). This approach has some limitations since it does not account for the reciprocity between the regions (e.g.…”

“…Some heuristics and metaheuristics are able to, e.g. Marxan with zones [Watts et al, 2009], but they don't provide strict and explicit control over spatial attributes. Finally, no existing model implements a complete buffer zone constraint.…”