Multiperiod Dynamic Programming Algorithm for Optimizing a Nature Reserve

Abstract

Zoning adjustments are a key method of improving the conservation efficiency of a nature reserve. Existing studies typically consider the one-period programming method and ignore dynamic ecological changes during the programming of a nature reserve. In this study, a scientific method for nature reserve (NR) programming, namely the multiperiod dynamic programming (MDP) algorithm, is proposed. The MDP algorithm designs an NR over three periods and does so by using ecological suitability values for each grid area. Ecological suitability values for each period were determined based on existing data on rare aquatic animals with Maxent software and cellular automata (CA). CA were used to determine the actual protection effect and to adjust each period's ecological suitability values through comparisons with the sites' surroundings. The maximization of ecological suitability values was used as an objective function; these values were assumed to indicate protection benefits. The objective function of the MDP also includes grid perimeters and numerical minimization for spatial compactness. Moreover, we designed three MDP constraints for the dynamic programming, including base constraints, distinguishing constraints, and multiperiod constraints. In the base and distinguishing constraints, we require a grid square to be a core, buffer, or unselected square, and we require the core and buffer grids to be spatially connected. For the multiperiod constraints, we used virtual points to ensure spatial continuity in different periods while attaining high ecological suitability. Our main contributions are as follows: (1) the novel MDP algorithm combining ecological attributes and multiperiod dynamic planning to optimize NR planning; (2) the use of virtual points to avoid selecting invalid grids and to ensure spatial continuity with significant protection benefits; and (3) the definition of ecological suitability values and use of CA to simulate dynamic changes over the three periods. The results reveal that the MDP algorithm results in a reserve with greater protection benefits than current reserves with superior spatial distribution due to multiperiod programming. The proposed MDP algorithm is a novel method for the scientific optimization and adjustment of nature reserves.