Nature reserve selection and design problems solved using heuristic concentration.

摘要

Several problems of nature reserve selection and design are approached using an exact method and Heuristic Concentration (HC). Some of these problems have been formulated previously, such as the Maximal Multiple-Representation Species Problem (MMRSP), the Maximal Expected Covering Species Problem (MEXCSP) and the Probabilistic Maximal Covering Species Problem (PMCSP).; Other problems are extensions of previous linear programs. The External Border - Species Covering Problem (EBSCP) is a combination of the Maximal Covering Species Problem (MCSP) and the land acquisition problem, which tries to select parcels of land that are contiguous and compact. The Maximal Covering Percent Area Reservation (MCPAR) problem is a maximal covering modification of the Percent Area Reservation problem that is traditionally formulated in a set-covering setting. Finally, the Multi-Objective Buffering-Maximal Covering Species Problem (MOB-MCSP) trades off between protection in core zones that are surrounded by buffer areas and protection in the entire reserve network.; In the MMRSP and the PMCSP, HC solved much more quickly than LP-IP in several cases and was competitive in the rest. Furthermore, the objective function value gap between the heuristic and exact method was very small.; In the MEXCSP, there is no known linear formulation, so a linear approximation was used for comparison. HC found better solutions than the linear approximation in 6 cases and found solutions at least as good in all but one case.; In the EBSCP and the MCPAR problem, there were many instances in which the exact method did not terminate in the allowed 12 hours. HC, however, finished in less than 25 minutes for the EBSCP and approximately an hour and 40 minutes for the MCPAR problem. In both problems, HC often found better solutions than LP-IP in many cases when LP-IP did not terminate in under 12 hours, and near-optimal solutions otherwise.; For the MOB-MCSP, LP-IP required substantial branching and bounding. HC solved much more quickly, but with questionable solution quality. However, it is believed that with further modification HC could prove a useful method for this problem.