Multicore has emerged as a typical architecture model since its advent and stands now as a standard. The trend is to increase the number of cores and improve the performance of the memory system. Providing an efficient multicore implementation for a important algorithmic kernel is a genuine contribution. From a methodology standpoint, this should be done at the level of the underlying paradigm if any. In this paper, we study the cases of {\em dynamic programming} and {\em greedy algorithms}, which are two major algorithmic paradigms. We exclusively consider directives-based loop parallelization through OpenMP and investigate necessary pre-transformations to reach a regular parallel form. We evaluate our methodology with a selection of well-known combinatorial optimization problems on an INTEL Broadwell processor. Key points for scalability are discussed before and after experimental results. Our immediate perspective is to extend our study to the manycore case, with a special focus on NUMA configurations.