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The paper presents two formalizations, called binary (BACO) and continuous (CACO) ant colony optimization, for the design of ant colony algorithm (ACOA) to solve continuous global optimization problem. With different coding methods and ACOA decision policies, BACO and CACO have distinct characters. In this paper, BACO adopts disturbance factor and CACO uses adaptive search steps to avoid premature convergence, and both of them combine with dynamic evaporation factor to find the best solution, then a convergence proof is presented. The differences of performance between them are compared in the optimization problem of multi-dimension and multi-minima continuous function, especially with the adaptive genetic algorithm (AGA), and experimental result shows that CACO is effective as it outperforms BACO and AGA.