LagrangianHeuristics for Strictly Convex Quadratic Minimum Cost Network Flow Problems

This thesis presents a study of five different Lagrangian heuristics applied to the strictly convex quadratic minimum cost network flow problem. Tests are conducted on randomly generated transportation networks with different degrees of sparsity and nonlinearity according to a system devised by Ohuchi and Kaji [18]. The different heuristics performance in time and quality are compared. The unconstrained dual version of the problem is first solved to near-optimality using the conjugate gradient method with an exact line search. Then a Lagrangian heuristic is applied to obtain (near-optimal) primal solutions to the original problem. In the computational study, we show results for two modifications of the Lagrangian heuristic Flowroute, FlowrouteBS and FlowrouteD, and one modification of the Lagrangian heuristic Shortest Path, Shortest PathL. FlowrouteBS, FlowrouteD and Shortest PathL are novel Lagrangian heuristics, but Flowroute and Shortest Path are constructed according to Marklund [15]. The results demonstrate that although FlowrouteBS has the drawback of being significantly slower than Flowroute and FlowrouteD, it produces results of almost as good quality as Shortest Path and Shortest PathL, and is therefore the most promising Lagrangian heuristic.