VKAS - Linear Regression using Genetic Programming

VKAS is a Java based solver that can be used to find out the relationship between a set of independent and dependent variables. I developed it way back in 2005 based on the paper Gene Expression Programming in Problem Solving. VKAS source code was earlier published on SourceForge. It has been recently moved from SourceForge to GitHub.

What method does VKAS use

VKAS uses GEP (Gene Expression Programming) to discover the relationship between a set of variables. For example, see the following table -

a	b	y
1	2	5
3	1	5
7	5	17

If a and b are independent variables and y is a dependent variable then what is the relationship between a, b and y?

Here it is “y = a+2*b”.

This, off course, was a very simple example. There are many regression methods to discover such relationships. GEP is one of them.

VKAS support four operators - Addition (+), Subtraction (-), Multiplication (*) and Division (/).

Gene Expression Programming

Gene Expression Programming (GEP) is part of the Genetic Algorithm family. It can be used to solve optimization problems, however, it can not be guaranteed that the algorithm will coverge within some predetermined time. The performance of the algorithm can be improved by adjusting the hyper-parameters.

How to use VKAS

In ‘vkas’ the data and config params are passed through two xml files at command-line.

When vkas is run, it creates a population of chromosomes at random. This population is then genetically modified and next population is generated. Each population is subjected to fitness calculation and if a suitable answer chromosome is found then vkas stops and the answer is printed. If a suitable answer is not found then the program stops after specified max generations are over.

a sample run is shown at the end of this file.

Summary of a test run:

***************************************************************************
                          vkas (a genetic function finder)
                          --------------------------------
    version              : 1.0
    webpage              : https://sourceforge.net/projects/vikasg/
    copyright            : (C) 2005 by Shailendra Jain
    email                : SLKJain at Yahoo.Com
***************************************************************************
***************************************************************************
*                                                                         *
*   This program is free software; you can redistribute it and/or modify  *
*   it under the terms of the GNU Lesser General Public License as        *
*   published by the Free Software Foundation; either version 2.1 of the  *
*   License, or (at your option) any later version.                       *
*                                                                         *
***************************************************************************

Final Population 0
Fitness = 100.0
+b-+a++aabbbababa--+ababbaaaaaabaa-aaaab--bbaababaa
Checking Population 1
GeneTransposition is not performed.
Checking Population 2
One mutation declined, codeIdx=0; newCode=a
One mutation declined, codeIdx=0; newCode=a
One mutation declined, codeIdx=0; newCode=a
RIS transposition declined in this chromosome (Len==0).
Checking Population 3
GeneTransposition is not performed.
Checking Population 4
One mutation declined, codeIdx=0; newCode=a
RIS transposition declined in this chromosome (Len==0).
GeneTransposition is not performed.
Checking Population 5
RIS transposition declined in this chromosome (Len==0).
GeneTransposition is not performed.
Checking Population 6
RIS transposition declined in this chromosome (Len==0).
GeneTransposition is not performed.
Checking Population 7
GeneTransposition is not performed.
Checking Population 8
One mutation declined, codeIdx=0; newCode=a
One mutation declined, codeIdx=0; newCode=a
RIS transposition declined in this chromosome (Len==0).
GeneTransposition is not performed.
Checking Population 9
One mutation declined, codeIdx=0; newCode=a
RIS transposition declined in this chromosome (Len==0).
Checking Population 10
One mutation declined, codeIdx=0; newCode=a
One mutation declined, codeIdx=0; newCode=a
Checking Population 11
One mutation declined, codeIdx=0; newCode=a
RIS transposition declined in this chromosome (Len==0).
Checking Population 12
One mutation declined, codeIdx=0; newCode=a
Checking Population 13
RIS transposition declined in this chromosome.
GeneTransposition is not performed.
Checking Population 14
One mutation declined, codeIdx=0; newCode=a
One mutation declined, codeIdx=0; newCode=a
GeneTransposition is not performed.
Checking Population 15
One mutation declined, codeIdx=0; newCode=a
One mutation declined, codeIdx=0; newCode=a
RIS transposition declined in this chromosome (Len==0).
GeneTransposition is not performed.
Checking Population 16
One mutation declined, codeIdx=0; newCode=a
RIS transposition declined in this chromosome (Len==0).
Checking Population 17
One mutation declined, codeIdx=0; newCode=a
Checking Population 18
One mutation declined, codeIdx=0; newCode=a
Checking Population 19
RIS transposition declined in this chromosome.
Checking Population 20
GeneTransposition is not performed.
Checking Population 21
One mutation declined, codeIdx=0; newCode=a
One mutation declined, codeIdx=0; newCode=a
Checking Population 22
One mutation declined, codeIdx=0; newCode=a
Checking Population 23
One mutation declined, codeIdx=0; newCode=a
One mutation declined, codeIdx=0; newCode=a
RIS transposition declined in this chromosome.
Checking Population 24
Checking Population 25
GeneTransposition is not performed.
Checking Population 26
One mutation declined, codeIdx=0; newCode=a
RIS transposition declined in this chromosome (Len==0).
Checking Population 27
One mutation declined, codeIdx=0; newCode=a
GeneTransposition is not performed.
Checking Population 28
RIS transposition declined in this chromosome (Len==0).
GeneTransposition is not performed.
Checking Population 29
Checking chromosome against the data table...
a = 1.0; b = 1.0; Expected = 2.0; Computed = 2.0
a = 1.0; b = 2.0; Expected = 3.0; Computed = 3.0
a = 3.0; b = 1.0; Expected = 4.0; Computed = 4.0
a = 44.0; b = 4.0; Expected = 48.0; Computed = 48.0
a = 3.0; b = 33.0; Expected = 36.0; Computed = 36.0
a = 23.0; b = 11.0; Expected = 34.0; Computed = 34.0
a = 0.0; b = 12.0; Expected = 12.0; Computed = 12.0
a = 13.0; b = 8.0; Expected = 21.0; Computed = 21.0
a = 111.0; b = 2.0; Expected = 113.0; Computed = 113.0
a = 4.0; b = 101.0; Expected = 105.0; Computed = 105.0
Final Population 29
Fitness = 100.0
aa+-+-aababbbabbb-++a-a++bbbbbbaba+bb--bb+abaabbaba
Resultant expression = {a}+{((a+((b+b)-b))-(a+(b+b)))}+{(b+b)}