This thesis addresses the design of self-healing Asynchronous Transfer Mode (ATM) networks which is a special aspect of a more general problem, referred to as capacity and flow assignment (CFA) problem in self-healing ATM networks. We have proposed two nonlinear mathematical models for global reconfiguration strategy and failure-oriented reconfiguration strategy in our thesis. Our restoration strategies aim to minimize the capacity installation cost and the routing cost when a single link failure occurs in the network. A special case of the augmented Lagrangian method so-called Separable Augmented Lagrangian Algorithm (SALA) is proposed for solving the proposed nonlinear mathematical models. Numerical results are presented comparing the two restoration strategies in terms of five performance metrics which are capacity installation cost, total required capacity, routing cost, total network cost and required CPU time for convergence of the algorithms. Our results show that the global reconfiguration strategy has always performed better than the failure-oriented reconfiguration strategy for all the network scenarios, topologies and bandwidth requirements.