Many image processing and pattern recognition problems can be formulated as binary quadratic programming (BQP) problems. However, solving a large BQP problem with a good quality solution and low computational time is still a challenging unsolved problem. In this work, we propose a BQP solver that alternatingly applies a deterministic search and a stochastic neighborhood search. The deterministic search iteratively improves the solution quality until it satisfies the KKT optimality conditions. The stochastic search performs bootstrapping sampling to the objective function constructed from the potential solution to find a stochastic neighborhood vector. These two steps are repeated until the obtained solution is better than many of its stochastic neighborhood vectors. We compare the proposed solver with several state-of-the-art methods for a range of image processing and pattern recognition problems. Experimental results showed that the proposed solver not only outperformed them in solution quality but also with the lowest computational complexity.