D.C. OPTIMIZATION METHODS FOR SOLVING MINIMUM MAXIMAL NETWORK FLOW PROBLEM
We consider the minimum maximal ﬂow problem, i.e., minimizing the ﬂow value among maximal ﬂow, which is an NP-hard problem. This problem is formulated as an optimization problem over the Pareto set of a linear vector program. We use a d.c. optimization formulation of the problem to obtain solution methods for the problem. Two solution approaches are described. The ﬁrst one is a global optimization method based upon a branch-and-bound strategy. The second is a local search technique based upon a d.c. optimization algorithm.