A method for finding a maximum value region with a minimum width in raster space

Abstract

Given a grid of cells, each of which is assigned a numerical value quantifying its suitability for a certain use, one problem in geographic information science concerns the selection of a region, i.e. a connected set of cells, with a specified size that maximizes the sum of all their values. This task can be cast as a combinatorial optimization problem called the maximum value region problem, and exact and heuristic methods exist for its solution. While those solutions are guaranteed to be feasible (if not optimal), they may not be desirable for practical use if they contain too narrow segments (down to the width of a single cell). In this paper, we present a new variation of the maximum value region problem—the maximum value wide region problem—that requires a region to be at least as wide as a specified width. We offer a heuristic method for its solution which models a region as a set of neighborhoods and test its performance through computational experiments. Results demonstrate that the method generates good feasible solutions in terms of connectedness, size, width, and value, but requires more computing time than methods for maximum value regions without minimum width requirements.