Experimental evaluation of algorithmic solutions for the maximum generalised network flow problem

Abstract

The maximum generalised network flow problem is to maximise the net flow into a specified node in a network with capacities and gain-loss factors associated with edges. In practice, input instances of this problem are usually solved using general-purpose linear programming codes, but this may change because a number of specialised combinatoria generalised-flow algorithms have been recently proposed. To complement the knwon theoretical analyses of these algorithms, we develop their implementations and investigate their actual performance. We focus in this study on Goldfarb, Jin and Orlin's excess-scaling algorithm and Tardos and Wayne's push-relabel algorithm. We develop variants of these algorithms to implementations of simple, but non-polynomial, combinatorial algorithms proposed by Onaga and Truemper, and with performance of CPLEX, a commercial general-purpose linear progamming package.