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In this study, a new approach using a multi-objective genetic algorithm (MOGA) is proposed to determine the optimal state assignment with less area and power dissipations for completely and incompletely specified sequential circuits. The goal is to find the best assignments which reduce the component count and switching activity. The MOGA employs a Pareto ranking scheme and produces a set of state assignments, which are optimal in both objectives. The ESPRESSO tool is used to optimise the combinational parts of the sequential circuits. Experimental results are given using a personal computer with an Intel CPU of 2.4 GHz and 2 GB RAM. The algorithm is implemented using C and fully tested with benchmark examples. The experimental results show that saving in components and switching activity are achieved in most of the benchmarks tested compared with recent published research.