• Core Algorithms
• Fitness Functions
• Math & Boolean Functions

• Data Visualization & Analysis
• Data Loading & Manipulation
• Analyses & Computations
• Panels & Windows

• Regression
• Classification
• Logistic Regression
• Time Series Prediction
• Logic Synthesis

• Model Evolution & Selection
• Model Visualization & Analysis
• Ensemble Methods

• Model Deployment
• Ensemble Deployment
• Predictions & Forecasting
• Programming Languages

• GEP paper (pdf)
• GEP Book (2nd Edition)

Karva Notation: The Native Code of GeneXproTools

can be represented as a diagram or expression tree (ET):

The translation of the gene into the corresponding ET is straightforward: The first element in the gene (position 0) corresponds to the root of the ET; then, below that node, are attached as many nodes as there are arguments to that function (two, in this case); then these nodes are filled consecutively with the elements in the gene (in this case, positions 1 and 2), and so forth. The process is repeated until a line composed of only terminals is formed (in this case, the third line).

More formally, both the gene and ET above can be represented by the mathematical expression:

Usually the genes evolved by GEP are more interesting than the gene presented above, not only with noncoding regions at their ends but also with more diverse branching structures. For example, consider the gene:

where "Q" represents the square root function. This gene has a head (from position 0 through 7 and shown in blue) of length 8 and a tail (from position 8 through 16) of length 9. Note that the head contains both functions (which may take 1, 2,..., n arguments) and terminals (the variables and constants in a problem), whereas the tail contains exclusively terminals (the existence of a tail with a buffer of terminals is the breakthrough of GEP as it ensures that all the programs encoded in the genes are syntactically correct). The translation of such genes is done exactly as in the previous example, giving:

Note that, in this case, not all the elements in the gene were used to construct the ET, as the translation ends whenever a line containing only terminals is formed. In this particular case, the gene ends at position 16 whereas the K-expression ends at position 9.

Furthermore, GEP chromosomes are usually multigenic, and each gene codes for a sub-ET or sub-program. After translation, the sub-ETs are linked by a particular linking function: addition, subtraction, multiplication, division, average, minimum, or maximum for all kinds of mathematical models in GeneXproTools 5.0 and And, Or, Nand, Nor, Xor, Nxor, Less Than, Greater Than, Less Or Equal, and Greater Or Equal for logical expressions.

For example, the following chromosome composed of three genes (position 0 indicates the beginning of each gene):

encodes the following sub-ETs:

Then the sub-ETs are afterwards linked by one of the available linking functions. For instance, if the linking function were addition, then the following program would be obtained (the linking function is shown in gray):

Note that the ET above can be easily linearized into a single K-expression:

But unless you want to use extraneous models, you don't have to be fluent in Karva as all the models evolved by GeneXproTools in its native Karva code are automatically converted not only into a wide range of programming languages (Ada, C, C++, C#, Fortran, Java, Javascript, Matlab, Octave, Pascal, Perl, PHP, Python, R, Visual Basic, VBA, VB.Net, Verilog, and VHDL) but also into diagram representations or expression trees for an immediate visualization of the model structure.

Gene Expression Programming

What is GEP?

What's New in GeneXproTools 5.0?