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SUMMARYThe paper addresses a generic topological network design problem. The target of the optimisation is to determine a network structure and a demand allocation pattern that would minimise the cost of the network, given a list of potential node locations and a list of admissible interconnections between these nodes. Since the problem is known to be NP-hard, use of specialised heuristic algorithms is proposed. Presented approaches encompass original ideas as well as selected methods described in literature and their enhancements. The algorithms are based on the following concepts and methods: individual and bulk flow shifting, methods based on Minoux and Yaged heuristics, Simulated Allocation, cost function modification and Hybrid GRASP. A numerical study enables us to draw conclusions on the efficiency of the methods.