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The dynamic slope scaling procedure is an approximation method successfullywhich solves the fixed charge network flow (FCNF) problem by iterativelylinearizing the fixed cost. The parameterized dynamic slope scaling procedureadds an additional $\psi$ parameter to the procedure which can significantlyimprove the solution quality. Finding the optimal value of $\psi$ for a givenproblem is non-trivial. This paper employs multiple metaheuristic techniques,including simulated annealing, tabu search, and particle swarm optimization, toguide the search for good parameter values. In rigorous testing, we examine thesearch results, compare the improvement efficiencies among the techniques, andevaluate the final solution quality of the FCNF problem. The experiments showthat the solution improvement is robust with respect to these metaheuristicsand the complexity of FCNF problem.

Empirical analysis of metaheuristic search techniques for the parameterized dynamic slope scaling procedure