Non-commutative path planning strategy

Over the years, various path planning problems have been brought up and addressed. For example, shortest path first algorithm is usually adopted to search for the best route between a source and a destination for packet transmission over a network. In that case, we add up the distance of every segment along each of the available routes and choose the one with the least value. Path planning problems of this sort often use evaluation functions that are commutative in nature. However, in case our objective is to plan a biking or driving route that is safe and / or fun, ordinary evaluation functions, especially commutative ones, usually fail to resolve the issue properly. Accordingly, in this paper, we propose an un-conventional noncommutative path planning strategy as well as algorithm to address the problem in a more efficient manner.