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T. Shirabe:
"Minimum Work Paths in Elevated Networks";
Networks, 52 (2008), 2; 88 - 97.

A new variant of the shortest path problem involves a
bicycle traveling from an origin to a destination through a
network situated on a hilly geography. Determining a path
that takes the least amount of pedaling work involves a
conservative force, gravity, and a nonconservative force,
friction, acting on the bicycle. The cyclist´s pedaling work
to overcome the friction of each arc varies with the bicycle´s
kinetic and gravitational potential energies, which
transform to one another. Although geometric characteristics
of the network are invariable, arc weights representing
required pedaling work are variable. This problem is
formulated as a quadratic integer program and an approximation
procedure is presented.

shortest paths; physical constraints; state-dependent

http://dx.doi.org/10.1002/net.20225