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Parallel Stretched Simulated Annealing (PSSA) solves unconstrained multilocal programming optimization problems in distributed memory clusters, by applying the Stretched Simulated Annealing optimization method, in parallel, to multiple sub-domains of the original feasible region. This work presents coPSSA (constrained Parallel Stretched Simulated Annealing), an hybrid application that combines shared memory based parallelism with PSSA, in order to efficiently solve constrained multilocal programming problems. We devise and evaluate two different parallel strategies for the search of solutions to these problems. Evaluation results from a small set of test problems often reach superlinear speedup in the solution search time, thus proving the merit of the coPSSA parallelization approach.