A key challenge in developing efficient local search solvers is to intelligently balance diversification and intensification. This study proposes a heuristic that integrates a new dynamic scoring function and two different diversification criteria: variable weights and stagnation weights. Our new dynamic scoring function is formulated to enhance the diversification capability in intensification phases using a user-defined diversification parameter. The formulation of the new scoring function is based on a probability distribution to adjust the selecting priorities of the selection between greediness on scores and diversification on variable properties. The probability distribution of variables on greediness is constructed to guarantee the synchronization between the probability distribution functions and score values. Additionally, the new dynamic scoring function is integrated with the two diversification criteria. The experiments show that the new heuristic is efficient on verification benchmark, crafted and random instances.