Pareto Sets for Multiobjective Optimization

Find points on the Pareto front for multiobjective optimization problems with Global Optimization Toolbox™. The Pareto front is the set of points where one objective cannot be improved without hurting others. The objective functions need not be smooth, as the solvers use derivative-free algorithms. 

Apply multiobjective optimization to design optimization problems where there are competing objectives and optional bound, linear and nonlinear constraints. The structural design problem addressed in this video is to determine beam and weld dimensions with objectives of minimizing cost and maximizing strength. 

The example shows the characteristics of both Global Optimization Toolbox multiobjective solvers. The paretosearch function generates points on the front with many fewer function evaluations than the gamultiobj function. However, gamultiobj finds some Pareto front points more accurately. The example shows using the Optimization Toolbox fgoalattain solver on both paretosearch and gamultiobj solutions to further improve their accuracy.