Two paths to a suboptimal solution – once more about optimality in reserve selection

Abstract

Several studies have compared the performances of exact algorithms (integer programming) and heuristic methods in the solution of conservation resource allocation problems, with the conclusion that exact methods are always preferable. Here, I summarize a potentially major deficiency in how the relationship between exact and heuristic methods has been presented: the above comparisons have all been done using relatively simple (linear) maximum coverage or minimum set models that are by definition solvable using integer programming. In contrast, heuristic or meta-heuristic algorithms can be applied to less simplified nonlinear and/or stochastic problems. The focus of this study is two kinds of suboptimality, first-stage suboptimality caused by model simplification and second-stage suboptimality caused by inexact solution. Evidence from comparisons between integer programming and heuristic solution methods suggests a suboptimality level of around 3%–10% for well-chosen heuristics, much depending on the problem and data. There is also largely anecdotal evidence from a few studies that have evaluated results from simplified conservation resource allocation problems using more complicated (nonlinear) models. These studies have found that dropping components such as habitat loss rates or connectivity effects from the model can lead to suboptimality from 5% to 50%. Consequently, I suggest that more attention should be given to two topics, first, how the performance of a conservation plan should be evaluated, and second, what are the consequences of simplifying the ideal conservation resource allocation model? Factors that may lead to relatively complicated problem formulations include connectivity and evaluation of long-term persistence, stochastic habitat loss and availability, species interactions, and distributions that shift due to climate change.