A new approach integrating heuristics and nonlinear programming is proposed for topology optimization of discrete Structures under stress and local buckling constraints. In the approach, the optimal ground structures are searched by heuristics, and topology optimization is performed for each ground structure based on nonlinear programming. Two heuristics are applied
namely, tabu search, and a new heuristic method called topology mining, which is based on the apriori algorithm. Three numerical examples are solved to demonstrate the effectiveness of the proposed approach. Moreover, the efficiency in view of computational cost of the two heuristics is discussed by comparing the optimization results.