Abstract: In this paper, the Constrained Optimization Problem (COP) is converted into a bi-objective optimization problem with preference. Then the problem is solved with a Guiding Multi-objective Differential Evolution (GMODE) algorithm. The other methods based on Pareto dominance treat both objectives as equal importance without bias to either objective. In contrast, the proposed GMODE algorithm is guided by α-domination to search with dynamic bias to different objectives, which overcomes the drawback of the methods based on Pareto dominance and improves the convergence speed of the algorithm. Numerical experiments on several well-known benchmark functions and comparison with the other three state-of-the-art methods demonstrate that the GMODE algorithm is competitive with, in some cases superior to the other methods in terms of the quality, efficiency and robustness.