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Parallel (or loop) flows consist in the undesired circulation of power flows through certain interconnection corridors. Remedial actions available to transmission system operators or system planners include installation and operation of phase-shifting transformers and of dc transmission systems. Moreover, the invaluable experience of transmission system operators has shown that the network can be operated so as to reduce parallel flows also by properly selecting the topology of the system. In the present paper, a genetic algorithm-based procedure is designed for the topological optimization of the network against parallel flows. The control variables considered are the status of substation breakers and the location (and angle) of phase-shifting transformers. The problem is formulated as a multiobjective optimization. The main objective is that of reducing the power transfer distribution factor of an assigned transaction with reference to a set of lines; N and N-1 security levels are accounted for by means of subsidiary objective functions. The procedure is tested on a small CIGRE sample system and on a 4500-bus network representative of the European electric system (UCTE).