Global Optimization Toolbox

Product Description

Introduction and Key Features
Defining, Solving, and Assessing Optimization Problems
Global Search and Multistart Solvers
Genetic Algorithm Solver
Multiobjective Genetic Algorithm Solver
Pattern Search Solver
Simulated Annealing Solver
Solving Optimization Problems Using Parallel Computing

Multiobjective Genetic Algorithm Solver

Multiobjective optimization is concerned with the minimization of multiple objective functions that are subject to a set of constraints. The multiobjective genetic algorithm solver is used to solve multiobjective optimization problems by identifying the Pareto front—the set of evenly distributed nondominated optimal solutions. You can use this solver to solve smooth or nonsmooth optimization problems with or without bound and linear constraints. The multiobjective genetic algorithm does not require the functions to be differentiable or continuous.

The following table shows the standard multiobjective genetic algorithm options provided by Global Optimization Toolbox.

Step	Multiobjective Genetic Algorithm Option
Creation	Uniform, feasible
Fitness scaling	Rank-based, proportional, top (truncation), linear scaling, shift
Selection	Tournament
Crossover	Arithmetic, heuristic, intermediate, scattered, single-point, two-point
Mutation	Adaptive feasible, Gaussian, uniform
Plotting	Average Pareto distance, average Pareto spread, distance among individuals, diversity of population, expectation of individuals, Pareto front, rank histogram, selection index, stopping conditions

Global Optimization Toolbox also lets you specify:

Population size
Crossover fraction
Pareto fraction
Distance measure across individuals
Migration among subpopulations (using ring topology)
Linear and bound constraints for an optimization problem

You can customize these algorithm options by providing user-defined functions and represent the problem in a variety of data formats, for example by defining variables that are integers, mixed integers, categorical, or complex.

You can base the stopping criteria for the algorithm on time, fitness limit, or number of generations. And you can vectorize your fitness function to improve execution speed or execute the objective functions in parallel (using Parallel Computing Toolbox).

Multiobjective genetic algorithm defined in the Optimization Tool (top), used to identify the Pareto front containing disconnected regions (middle) for the Kursawe function (bottom).