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In this paper, we present a new cooperative framework based on using successively two local search algorithms to solve constraint satisfaction and optimization problems. Our technique is based on the integration of local search algorithms as a mechanism to diversify the search instead of using a build on diversification mechanisms. Thus we avoid tuning the multiple parameters to escape from a local optimum. This technique improves the existing methods: it is generic especially when the given problem can be expressed as a constraint satisfaction problem. We present the way the local search algorithm can be used to diversify the search in order to solve real examination timetabling problems. We describe how the local search algorithm can be used to assist any other specific local search algorithm to escape from local optimality.