R-NSGA-II

R-NSGA-II or Reference Point Based NSGA-II proposed by Kalyanmoy Deb et al.

Status

References

This implemention is based on the following paper:

Deb, Kalyanmoy, and J. Sundar. "Reference point based multi-objective optimization using evolutionary algorithms." In Proceedings of the 8th annual conference on Genetic and evolutionary computation, pp. 635-642. ACM, 2006.

How to install

This project uses GitHub as a Maven Repository. Then you have just add the following section to your repositories tag in pom.xml

<repositories>
    <repository>
        <id>mvn-repo</id>
        <url>https://github.com/gres-ufpr/mvn-repo/raw/master/releases</url>
        <releases>
            <enabled>true</enabled>
        </releases>
        <snapshots>
            <enabled>true</enabled>
        </snapshots>
    </repository>
</repositories>

Then add a dependency into tag of your pom.xml

<dependency>
    <groupId>ufpr.gres</groupId>
    <artifactId>r-nsga-ii</artifactId>
    <version>3.0.0</version>
</dependency>

Simulation Results

The following results were found based on the following parameter settings.

For Binary Problem

populationSize = 100;
maxEvaluations = 10000 * populationSize;
SinglePointCrossover(0.9)
BitFlipMutation(0.001)

For Double Problem
populationSize = 100;
maxEvaluations = 10000 * populationSize;
SBXCrossover(0.9, 10.0)
PolynomialMutation(0.01, 20.0)

Results

Problem	Encoding	ε = 0.01	ε = 0.001	ε =0.0001
Knapsack	Binary Solution
ZDT 1	Double Solution
ZDT 2	Double Solution
ZDT 3	Double Solution
DTLZ 2	Double Solution

R-Metric: R-HV and R-IGD

This project implements and the R-HV and R-IGD quality attributes

R-HV: Hypervolume by using R-Metric
R-IGD: Inverted Generational Distance by using R-Metric

Both of them were implemented based on the paper entitled "R-Metric: Evaluating the Performance of Preference-Based Evolutionary Multi-Objective Optimization Using Reference Points" by Ke Li, Member, IEEE, Kalyanmoy Deb, Fellow, IEEE, and Xin Yao, Fellow, IEEE