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We investigate the challenging problem of joint topology design and load balancing in FSO networks. Important factors such as FSO link characteristics, cost constraints, traffic characteristics, traffic demand, and QoS requirements are considered in the problem formulation, along with objective functions of network-wide average traffic load and delay. We develop a fast heuristic algorithm to provide highly competitive solutions. The heuristic algorithm iteratively perturbs the current topology and computes network flows for the new topology, thus progressively improving the configuration and load balancing of the FSO network. Our simulation results show that the heuristic algorithm can achieve an optimality gap close to that of a branch-and-bound algorithm developed in our prior work, with significantly reduced computation time. The heuristic algorithm is complementary to the branch-and-bound algorithm. Jointly applying the algorithms can make the FSO network dynamically reconfigurable and adaptive to events occurring at both large and small timescales.