Automatic unit test generation aims to support developers by alleviating the burden of test writing. Different techniques have been proposed over the years, each with distinct limitations. To overcome these limitations, we present an extension to the EVOSUITE unit test generator that combines two of the most popular techniques for test case generation: Search-Based Software Testing (SBST) and Dynamic Symbolic Execution (DSE). A novel integration of DSE as a step of local improvement in a genetic algorithm results in an adaptive approach, such that the best test generation technique for the problem at hand is favoured, resulting in overall higher code coverage.