Heterogeneous multiprocessor platforms are becoming widespread in the embedded system domain, mainly for the opportunity to improve timing performance and to minimize energy/power consumption and costs. Therefore, when using such platforms, it is important to adopt a Design Space Exploration (DSE) strategy that considers compromises among different objectives. Existing DSE approaches are generally based on evolutionary algorithms to solve Multi-Objective Optimization Problems (MOOPs) by minimizing a linear combination of weighted cost functions (i.e., Weighted Sum Method, WSM). In this way, the main issues are related to reduce timing execution while trying to improve the evolutionary algorithm performance, introducing strategies that attempt to bring better solutions. Code parallelization is one of the most used approaches in this field, but no standard methods have been released since different aspects could affect the performance. This approach leads to exploit parallel and distributed processing elements in order to implement evolutionary algorithms. In the latter case, if we consider genetic algorithms, it is possible to talk about Parallel Genetic Algorithms (PGA). Considering this context, this paper focuses on DSE for heterogeneous multi-processor embedded systems and introduces an improvement that reduces execution time using parallel programming languages (i.e., OpenMP) inside the main genetic algorithm approach, while trying to lead to better partitioning solutions. The descriptions of the adopted DSE activities and the OpenMP implementation, validated by means of a case study, represent the core of the paper. CCS CONCEPTS • Computer systems organization → Embedded systems; Embedded hardware;