Resolución de un problema de selección de áreas óptimas para forestación, representado como un "Knapsack Problem", mediante la aplicación de un algoritmo genético y técnicas de topología

Abstract

Policy initiatives and decision makers dealing with environmental conservation are interested in forestation projects in order to minimize runoff sediment reaching riverbeds. Selecting the optimal areas in which to plant trees to minimize soil erosion, while remaining within budgetary constraints, is a difficult optimization challenge. Potential reforestation terrain can be digitized in raster maps where erosion and cost of planting can be represented for each cell. Due to the resolution used in such raster maps, the number of resultant cells can be unworkable for common global optimization algorithms. This manuscript, uses a CAMF (Cellular Automata Based Heuristic Solu- tion Method for Minimizing Flow) algorithm to construct a ranking of candidate cells based on their associated forestation profit (sediment reduction) and cost of forestation (distance to roads). The two conflicting and concurrent objectives (maximize profit and minimize expense) allows us to model the situation as a Knapsack Problem. Variants of a Genetic Algorithm approach are proposed, using topology techniques as a heuristic, and the values obtained are compared with the value of the global optimum calculated with a Branch and Bound strategy. While Branch and Bound is shown to be superior to strategies such as Shani’s PTAS algorithm integrated to CAMF-B. Branch and Bound is applicable to forestation problems with several thousands of cells. In situations with an excessive number of cells where it is not possible to apply Branch and Bound strategies due to computational costs, Genetic Algorithms always find a feasible solution with cost-benefit values close to the global optimums.