Multiobjective Optimization

Solve multiobjective optimization problems in serial or parallel

Solve problems that have multiple objectives by the goal attainment method. For this method, you choose a goal for each objective, and the solver attempts to find a point that satisfies all goals simultaneously, or has relatively equal dissatisfaction. One important special case of this problem is to minimize the maximum objective, and this problem has a special solver, fminimax.

Functions

`fgoalattain`	Solve multiobjective goal attainment problems
`fminimax`	Solve minimax constraint problem

Live Editor Tasks

Optimize

Optimize or solve equations in the Live Editor (Since R2020b)

Topics

Multiobjective Solutions

Generate and Plot Pareto Front
Example showing how to plot a Pareto front in a two-objective problem.
Compare fminimax and fminunc
Shows how minimax problems are solved better by the dedicated fminimax function than by solvers for smooth problems.
Multi-Objective Goal Attainment Optimization
This example shows how to solve a pole-placement problem using multiobjective goal attainment.
Using fminimax with a Simulink Model
Example showing how to minimize the maximum discrepancy in a simulation.
Signal Processing Using fgoalattain
Example showing filter design using multiobjective goal attainment.
Minimax Optimization
This example shows how to solve a nonlinear filter design problem.

Parallel Computing

What Is Parallel Computing in Optimization Toolbox?
Use multiple processors for optimization.
Using Parallel Computing in Optimization Toolbox
Perform gradient estimation in parallel.
Improving Performance with Parallel Computing
Investigate factors for speeding optimizations.

Algorithms and Other Theory

Multiobjective Optimization Algorithms
Minimizing multiple objective functions in n dimensions.
Smooth Formulations of Nonsmooth Functions
Reformulate some nonsmooth functions as smooth functions by using auxiliary variables.
Optimization Options Reference
Explore optimization options.