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In this paper, we present a new approach for solving a large class of bound-constrained global optimization problems for objective functions which are only continuous. This method is based on the reducing transformation technique by running in the feasible domain a single parametrized Lissajous curve, which becomes increasingly denser and progressively fills the feasible domain. By means of the one-dimensional Evtushenko algorithm, we realize a mixed method that explores the feasible domain. To speed up the mixed exploration algorithm, we have incorporated a DIRECT local search type algorithm to explore promising regions. This method converges in a finite number of iterations to the global minimum within a prescribed accuracy. Numerical experiments are achieved on some typical test problems and comparison with well-known methods is carried out to show the performance of our algorithm.
