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This paper is the part II of a paper composed of two parts. In the part I, a memetic approach consisting of applying a local search to the scale factor of a differential evolution framework in order to generate an off-spring with a high quality was proposed. The part II proposes the application of the scale factor local search within a differential evolution framework which integrates a self-adaptive update of the control parameters. In other words, unlike for the part I, the scale factor local search is applied to a an algorithmic framework characterized by multiple scale factors over the individuals of the population and scale factor updates during the evolution. Two simple local search logics have been tested, the first one employs the golden section search and the second one a hill-climber. The local search algorithms thus assist the global search and generates offspring with high performance which are subsequently supposed to promote the generation of better solutions within the evolutionary framework. Numerical results show that the hybridization is beneficial and able to outperform in many cases both the classical differential evolution and a self-adaptive differential evolution recently proposed in literature.