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The concept of backbone variables in the satisfiability problem has been recently introduced as a problem structure property and shown to influence its complexity. This suggests that the performance of stochastic local search algorithms for satisfiability problems can be improved by using backbone information. The Partial MAX-SAT Problem (PMSAT) is a variant of MAX-SAT which consists of two CNF formulas defined over the same variable set. Its solution must satisfy all clauses of the first formula and as many clauses in the second formula as possible. This study is concerned with the PMSAT solution in setting a co-evolutionary stochastic local search algorithm guided by an estimated backbone variables of the problem. The effectiveness of our algorithm is examined by computational experiments. Reported results for a number of PMSAT instances suggest that this approach can outperform state-of-the-art PMSAT techniques.