Most former studies of Distributed Constraint Optimization Problems (DisCOPs) search considered only complete search algorithms, which are practical only for relatively small problems. Distributed local search algorithms can be used for solving DisCOPs. However, because of the differences between the global evaluation of a system's state and the private evaluation of states by agents, agents are unaware of the global best state which is explored by the algorithm. Previous attempts to use local search algorithms for solving DisCOPs reported the state held by the system at the termination of the algorithm, which was not necessarily the best state explored. A general framework for implementing distributed local search algorithms for DisCOPs is proposed. The proposed framework makes use of a BFS-tree in order to accumulate the costs of the system's state in its different steps and to propagate the detection of a new best step when it is found. The resulting framework enhances local search algorithms for DisCOPs with the anytime property. The proposed framework does not require additional network load. Agents are required to hold a small (linear) additional space (beside the requirements of the algorithm in use). The proposed framework preserves privacy at a higher level than complete DisCOP algorithms which make use of a pseudo-tree (ADOPT, DPOP).