Abstract
This paper considers the problem of finding the least cost rectilinear distance path in the presence of convex polygonal congested regions. We demonstrate that there are a finite, though exponential number of potential staircase least cost paths between a specified pair of origin–destination points. An upper bound for the number of entry/exit points of a rectilinear path between two points specified
a priori in the presence of a congested region is obtained. Based on this key finding, a “memory-based probing algorithm” is proposed for the problem and computational experience for various problem instances is reported. A special case where polynomial time solutions can be obtained has also been outlined.