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This paper introduces SHOM, a mutation-based test data generation approach that combines Dynamic Symbolic Execution and Search Based Software Testing. SHOM targets strong mutation adequacy and is capable of killing both first and higher order mutants. We report the results of an empirical study using 17 programs, including production industrial code from ABB and Daimler and open source code as well as previously studied subjects. SHOM achieved higher strong mutation adequacy than two recent mutation-based test data generation approaches, killing between 8% and 38% of those mutants left unkilled by the best performing previous approach.