The paper includes studying the method of calculating joint design and then building a multi-objective optimization problem model using the weighted sum and Taguchi methods. The research object is the joint between the gantry crane leg and the beam. Due to the characteristics of the connection bearing large and changing loads, research is necessary to improve safety, longevity, and reliability. The experimental problem model has four design variables and four value levels. The study uses the orthogonal matrix L16 to calculate the response values for each objective function at each stage. To apply the weighted sum method, the study selects the objective function weights for equivalent stress, contact stress, and fatigue strength, transforming the multi-objective problem into a single-objective problem. The test results identified a new set of parameters meeting the goals. The fatigue criterion was reduced by 8.9%, and the fatigue safety factor increased from 1.36 to 1.39. The equivalent stress was decreased by 9%, and the safety factor increased from 2.58 to 2.84. Contact stress was reduced by 37%, and the safety factor increased from 1.29 to 2. Combining these two methods not only solves problems in engineering but can also solve many problems in different fields.