A Cellular Automaton Approach to Optimising the Choice of Tree Species

Abstract

This paper presents a cellular automaton approach to optimising the choice of tree species in afforestation. The case study deals with 180 ha of recently afforested land which is located at the northwest coast of Zealand, Denmark. A two-dimensional automaton containing approximately 100,000 active cells is used for optimising the land use setup in this area. Four land use alternatives are considered: pasture, beech (Fagus sylvatica (L.)), Norway spruce (Picea abies (L.) Karst.), and oak (Quercus robur L.). Accordingly, the task of finding the optimal solution constitutes a tremendous combinatorial problem comprising a total number of approximately 4^100,000 combinations. Obviously, no heuristic is able to solve such a problem. However, in this paper it is shown that appropriately formulated cellular automata may converge towards near-optimum solutions within a comparatively low number of iterations. It is concluded that a major advantage of self-organising algorithms is that the overall maximisation problem is solved as a decentralised optimisation problem where the use of the individual forest components is optimised in parallel. In that respect, self-organising algorithms contrast with the centralistic top-down approach known from most traditional optimisation methods. Geographical data on water retention capacity is used to estimate the soil expectation value of the suggested land use alternatives. The objectives are to maximise the total soil expectation value, minimise the deviation from a target diversity index, minimise a scale-dependent fixed cost function, and maximise the aesthetic value.