The production of a tubular hydroformed part often requires a combination of internal pressure and axial force at the tube ends to fully form the tube to its specified geometry. A successful hydroforming process requires not only achieving a part that conforms to the design specifications, but also ensures that the part has a reasonably uniform thickness distribution and is free of defects, such as wrinkles, severe thinning, or fractures. The load path design (pressure vs. end feed history) largely determines the robustness of the process and the quality of the finished parts. In this paper, a hybrid constrained optimization method was proposed to solve this type of multi-objective problem by coupling a multi-objective genetic algorithm and a local search. The load path design procedure was developed by considering five objectives: four formability objectives (i.e., to minimize the risk of wrinkling, global and local thinning, and fracture) and a geometric objective (to minimize the corner radius). A Kriging predictor was used to accelerate the computation of genetic operations and generate new feasible solutions. Finite element simulations of the hydroforming process were also used after each generation to accurately evaluate the objectives of the offspring, and solutions with rank 1 were retained throughout all generations. Once the Pareto solutions were obtained by multi-objective genetic algorithm, a local search was carried out in the regions of interest with the assistance of visualization. This optimization method was applied to the hydroforming of a straight tube to create a part with an expanded region with a square cross section; the optimum load path produced a very safe part with a corner radius of only 9.115 mm and a maximum thinning of only 23.9%.