**Abstract**

Several complex engineering design problems have multiple, conflicting objectives and constraints that are nonlinear, along with mixed discrete and continuous design variables; these problems are inherently difficult to solve. This chapter presents a novel hybrid approach to find solutions to a constrained multi-objective mixed-discrete nonlinear programming problem that combines a two-branch genetic algorithm as a global search tool with a gradient-based approach for the local search. Hybridizing two algorithms can provide a search approach that outperforms the individual algorithms; however, hybridizing the two algorithms, in the traditional way, often does not offer advantages other than the computational efficiency of the gradient-based algorithms and global exploring capability of the evolutionary-based algorithms. The approach here presents a hybridization approach combining genetic algorithm and a gradient-based approach with improved information sharing between the two algorithms. The hybrid approach is implemented to solve three engineering design problems of different complexities to demonstrate the effectiveness of the approach in solving constrained multiobjective mixed-discrete nonlinear programming problems.

**Keywords:** multi-objective, mixed-discrete, constrained, nonlinear, genetic algorithm, gradient-based optimization
