RELAX-IV: A Faster Version of the RELAX Code for Solving Minimum Cost Flow Problems

The structure of dual ascent methods is particularly well-suited for taking advantage of good initial dual solutions of minimum cost flow problems. For this reason, these methods are extremely efficient for reoptimization and sensitivity analysis. In the absence of prior knowledge of a good initial dual solution, one may attempt to find such a solution by means of a heuristic initialization. RELAX-IV is a minimum cost flow code that combines the RELAX code of [BeT88a], [BeT88b] with an initialization based on a recently proposed auction/sequential shortest path algorithm. This initialization is shown to be extremely helpful in speeding up the solution of difficult problems, involving for example long augmenting paths, for which the relaxation method has been known to be slow. On the other hand, this initialization procedure does not significantly deteriorate the performance of the relaxation method for the types of problems where it has been known to be very fast. T eban puA-eyrn.x osFP .to. Mer D w s m :WED A_-~S-~ =0:. .. ;.(.4·-i -_ _ 1 Research supported by NSF under Grant CCR-9103804 and Grant CCR-9311621. Research supported by NSF under Grant CCR-9103804 and Grant CCR-9311621. 2 Dept. of Electrical Engineering and Computer Science, M.I.T., Cambridge, Mass., 02139. 3 Dept. of Mathematics, Univ. of Washington, Seattle, Wash., 98195.