Dual-ascent methods for large-scale multicommodity flow problems

The capacitated multicommodity network flow problem presents itself in a number of problem contexts including transportation, communication, and production. To solve the large-scale multicommodity flow problems encountered in these fields, the paper develops dual-ascent heuristics and a primal solution generator. The dual-ascent solutions, in addition to determining lower bounds on the optimal objective function value, provide advanced starting solutions for use with primal-based solution techniques. The primal solution generator uses the dual-ascent solution to obtain heuristically primal solutions to the multicommodity flow problems. Computational experiments performed on three test problem sets show that the dual-ascent and primal heuristic procedures typically determine near-optimal solutions quickly. In addition, by using the dual-ascent procedure to obtain advanced starting solutions, run times for optimal multicommodity flow procedures are reduced significantly and greatly improved solutions are obtained by the new primal solution generator.