Documentation/Modules/ContinuousMOTestProblems

Summary

The module ContinuousMOTestProblems contains a set of multi-objective optimization problems, which can be used to test optimization algorithms.

Properties

General

Algorithm	deterministic test function
Design Variables	continuous design variables only
Objectives	multi-objective for minimization
Constraints	none
Boundaries	problem dependent
Initial Search Region	problem dependent
Typical X	not set

Connections

Starting at his module	none
Ending at this module	Connections of type optimization

Actions

Name	Description
-	-

Options

The options are the number of discrete and continuous variables and an optional time delay for per evaluation.

Module Description

Multi-Objective Sphere

The multi-objective sphere function f is a set of quadratic functions. More precisely, each f_i is computed as the square of all continuous variables.

f_i(x) = (x_i - 1)² + sum_{j, j~=i} (x_j²)

For example

f₁(x) = (x₁ - 1)² + x₂² + x₃^{2 + ...}

f₂(x) = x₁² + (x₂ - 1)² + x₃^{2 + ...}

...

The Pareto front for the two-objective case is given in the following picture:

Pareto front of the multi-objective sphere function

Usage

-

Source Code

https://sourceforge.net/p/opendino/code/HEAD/tree/trunk/src/org/opendino/modules/problems/ContinuousMOTestProblems.java

References

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