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This paper investigates the optimal access point (AP) placement (OAPP) in simultaneous broadcast system using orthogonal frequency division multiplexing (OFDM) for high data rate indoor wireless LAN. We aim to determine the best combination of multiple AP placements that minimizes average bit error rate (BER) of terminals when in put information including an indoor configuration, a number APs, and total transmission power is given a priori. Since OAPP is categorized as a hard combinatorial problem with many variables and constraints, we applied a nonlinear optimization scheme called uniform design simulated annealing (UDSA) to search for an approximate optimal solution and analyzed its performance in detail. The simulation results demonstrate that the UDSA algorithm has been successfully applied to OAPP and its effectiveness was also confirmed in comparison with very fast simulated annealing (VFSA) and local search (LS) algorithms.