Finding rectilinear least cost paths in the presence of convex polygonal congested regions

This paper considers the problem of finding the least cost rectilinear distance path in the presence of convex polygonal congested regions. An upper bound for the number of entry/exit points for a congested region is obtained. Based on this key finding, we demonstrate that there are a finite, though exponential number of potential least cost paths between a specified pair of origin-destination points. A “memory-based probing algorithm” is proposed for the problem and computational experience for various problem instances is reported. Two heuristics are also proposed for larger problem instances.