While researchers have studied generalized network flow problems extensively, the powerful addition of fixed charges on arcs has received scant attention. This work describes network-simplex-based algorithms that efficiently exploit the quasi-tree basis structure of the problem relaxations, proposes heuristics that utilize a candidate list, a tabu search with short and intermediate term memories to do the local search, a diversification approach to solve fixed-charge transportation problems, as well as a dynamic linearization of objective function extension for the transshipment fixed-charge generalized problems. Computational testings for both heuristics demonstrate their effectiveness in terms of speed and quality of solutions to these mixed-integer models. Comparisons with a state-of-the-art solver, CPLEX, show that the extreme-point search algorithm runs, on average, for transportation problems five orders of magnitude faster and produces integer solution values within 2.2% of the optimal solution reported by CPLEX; for transshipment problems, the heuristic solver ran 1,000 faster and the solution values were within 2.5% of the optimal reported by CPLEX.
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Leskovskaya, Angelika, "Extreme-point Tabu Search Heuristics for Fixed-charge Generalized Network Problems" (2019). Engineering Management, Information, and Systems Research Theses and Dissertations. 5.