In this article, we propose new analog neural approaches to combinatorial optimization problems, in particular, quadratic assignment problems (QAPs). Our proposed methods are based on an analog version of the λ-opt heuristics, which simultaneously changes assignments for λ elements in a permutation. Since we can take a relatively large λ value, our new methods can achieve a middle-range search over possible solutions, and this helps the system neglect shallow local minima and escape from local minima. In experiments, we have applied our methods to relatively large-scale (N = 80–150) QAPs. Results have shown that our new methods are comparable to the present champion algorithms; for two benchmark problems, they are obtain better solutions than the previous champion algorithms.