A general MINLP algorithmic approach to the optimal synthesis of heat exchanger networks reaching specified topology targets is presented. The approach regards the network structure as composed of two types of primary components : individual units and parallel arrangements of heat matches, all connected in series over each process stream. Proper sets of decision variables are introduced to stand for the existence and relative location of (a) the primary components in the network and (b) the individual units within each parallel arrangement. In this manner, the designer can gain control on the network structure synthesis task by specifying some desired topological features. Nonlinearities are just confined to parallels sub-structures involving non-isothermal mixers and/or multiple units in series over a split stream. Topology targets normally lowering the problem size are taken into account from the beginning to compute both the least utility usage and-the minimum number of units. Application of the new synthesis method to the widely known 4SP2 example problem provides an optimal network configuration not reported before.