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In this paper, a new dynamical evolutionary algorithm (DEA) is presented basedon the theory of statistical mechanics. The novelty of this kind of dynamical evolutionary algorithmis that all individuals in a population (called particles in a dynamical system) are running andsearching with their population evolving driven by a nev selecting mechanism. This mechanismsimulates the principle of molecular dynamics, which is easy to design and implement. A basictheoretical analysis for the dynamical evolutionary algorithm is given and as a consequence twostopping criteria of the algorithm are derived from the principle of energy minimization and the lawof entropy increasing. In order to verify the effectiveness of the scheme, DEA is applied to solvingsome typical numerical function minimization problems which are poorly solved by traditionalevolutionary algorithms. The experimental results show that DEA is fast and reliable.