This study is concerned with developing a heuristic algorithm for solving a class of ninlinear integer programs(NLIP). Exact algrithm for solving a NLIP either may not exist, or may take an unrealistically large amount of computing time. This study develops a new heuristic, the Excursion Algorithm(EA), for solving a class of NLIP's. It turns out that excursions over a bounded feasible and/or infeasible region is effective in alleviation the risks of being trapped at a lical optimum. The developed EA is applied to the redundancy optimization problems for improving the system safety, and is compared with other existing heuristic methods. We also include simulated annealing(SA) method in the comparision experiment due to ist populatrity for solving complex combinatorial problems. Computational results indicate that the proposed EA performs consistently better than the other in terms of solution quality, with moderate increase in computing time. Therefore, the proposed EA is believed to be an attractive alternative to other heuristic methods.