  We propose a new self-organizing algorithm for fixed-charge network flow
problems based on ghost image (GI) processes as proposed in Glover (1994) and
adapted to fixed-charge transportation problems in Glover, Amini and
Kochenberger (2005). Our self-organizing GI algorithm iteratively modifies an
idealized representation of the problem embodied in a parametric ghost image,
enabling all steps to be performed with a primal network flow algorithm
operating on the parametric GI. Computational tests are carried out on an
extensive set of benchmark problems which includes the previous largest set in
the literature, comparing our algorithm to the best methods previously proposed
for fixed-charge transportation problems, though our algorithm is not
specialized to this class. We also provide comparisons for additional more
general fixed-charge network flow problems against Cplex 12.8 to demonstrate
that the new self-organizing GI algorithm is effective on large problem
instances, finding solutions with statistically equivalent objective values at
least 700 times faster. The attractive outcomes produced by the current GI/TS
implementation provide a significant advance in our ability to solve fixed-cost
network problems efficiently and invites its use for larger instances from a
variety of application domains.
