Using the two-branch tournament genetic algorithm for multiobjective design

The two-branch tournament genetic algorithm is presented as an approach to determine a set of Pareto-optimal solutions to multiobjective design problems. Because the genetic algorithm searches using a population of points rather than using a point-to-point search, it is possible to generate a large number of solutions to multiobjective problems in a single run of the algorithm. The two-branch tournament and its implementation in a genetic algorithm (GA) to provide these solutions are discussed. This approach differs from most traditional methods for GA-based multiobjective design; it does not require the nondominated ranking approach nor does it require additional fitness manipulations. A multiobjective mathematical benchmark problem and a 10-bar truss problem were solved to illustrate how this approach works for typical multiobjective problems. These problems also allowed comparison to published solutions. The two-branch GA was also applied to a problem combining discrete and continuous variables to illustrate an additional advantage of this approach for multiobjective design problems. Results of all three problems were compared to those of single-objective approaches providing a measure of how closely the Pareto-optimal set is estimated by the two-branch GA. Finally, conclusions were made about the benefits and potential for improvement of this approach.