Multiobjective Optimization

Minimize multiple objective functions subject to constraints

Multiobjective optimization involves minimizing or maximining multiple objective functions subject to a set of constraints. Example problems include analyzing design tradeoffs, selecting optimal product or process designs, or any other application where you need an optimal solution with tradeoffs between two or more conflicting objectives.

You can solve multiobjective optimization problems with MATLAB and Optimization Toolbox. The toolbox transforms multiobjective problems into standard constrained optimization problems and then solves them using an active-set approach.

• Goal attainment: reduces the values of a linear or nonlinear vector function to attain the goal values given in a goal vector. The relative importance of the goals is indicated using a weight vector. Goal attainment problems may also be subject to linear and nonlinear constraints.
• Minimax: minimizes the worst-case values of a set of multivariate functions, possibly subject to linear and nonlinear constraints.

Global Optimization Toolbox, also for use with MATLAB, provides an additional multiobjective solver for nonsmooth problems.

• Multiobjective genetic algorithm: solves multiobjective optimization problems by finding an evenly distributed set of points on the Pareto front. You can use this solver to optimize smooth or nonsmooth problems with or without bound and linear constraints.

Examples and How To

• Goal Attainment Multiobjective Optimization (Example)
• Performing a Multiobjective Optimization Using the Genetic Algorithm (Example)
• Multiobjective Genetic Algorithm Options (Example)
• Signal Processing Using fgoalattain (Example)
• Using fminimax with a Simulink Model (Example)
• Introduction to Optimization Graphical User Interface 6:08 (Video)

Software Reference

• Minimax Optimization Function in Optimization Toolbox (Function)
• Multiobjective Goal Attainment Function in Optimization Toolbox (Function)
• Multiobjective Genetic Algorithm Function in Global Optimization Toolbox (Function)
• What Is Multiobjective Optimization? (Documentation)

See also: Optimization Toolbox, Global Optimization Toolbox, linear programming, quadratic programming, nonlinear programming, genetic algorithm, simulated annealing