This paper presents an optimization tool for jacket structures to support Offshore Wind Turbines (OWTs). The tool incorporates several combinations of optimization algorithms and constraint-handling techniques (CHTs): Genetic Algorithm; Differential Evolution (DE); Tournament Selection Method; Multiple Constraint Ranking (MCR); Adaptive Penalty Method, and Helper-and-Equivalent Optimization. The objective function regards the minimization of the jacket weight; the design variables are the diameter and thickness of the tubular members. The constraints are related to natural frequencies and Ultimate Limit State criteria. The candidate solutions are evaluated by full nonlinear time-domain Finite Element coupled analyses. To assess the optimization algorithms and CHTs, a case study is presented for the standardized OWT/jacket structure from the Offshore Code Comparison Collaboration Continuation project. First, a numerical model is built and validated, in terms of masses, natural frequencies, and vibration modes; then, this model is employed to run the optimization tool for all combinations of optimization algorithms and CHTs. The results indicate that, while all methods lead to feasible optimal solutions that comply with the constraints and present considerable weight reductions, the best performer is the combination of the DE algorithm with the MCR constraint-handling technique.