Algebraic Objective Functions

Here are the formulas to calculate the error between multiple data sets and simulations files.

Mean Square Error (MSE): \(\left( \frac{1}{m} \sum_{i=1}^{m} \mathrm{exp}_i - \frac{1}{n} \sum_{j=1}^{n} \mathrm{sim}_j \right) ^{2}\) Mean Absolute Error (MAE): \(\mathrm{abs} \left( \frac{1}{m} \sum_{i=1}^{m} \mathrm{exp}_i - \frac{1}{n} \sum_{j=1}^{n} \mathrm{sim}_j \right)\) Pair-Wise Square Deviation (PWSD): \(\frac{1}{mn} \sum_{i=1}^{m} \sum_{j=1}^{n} \left({\mathrm{exp}_i - \mathrm{sim}_j } \right)^{2}\) Absolute Pair-Wise Deviation (APWSD): \(\frac{1}{mn} \sum_{i=1}^{m} \sum_{j=1}^{n} \mathrm{abs} \left( \mathrm{exp}_i - \mathrm{sim}_j \right)\) Normalized Pair-Wise Square Deviation (NPWSD): \(\frac{1}{mn} \sum_{i=1}^{m} \sum_{j=1}^{n} \left( \frac{ \mathrm{exp}_i - \mathrm{sim}_j }{ \mathrm{exp}_i } \right)^{2}\)

Absolute Normalized Pair-Wise Deviation (ANPWSD): \(\frac{1}{mn} \sum_{i=1}^{m} \sum_{j=1}^{n} \mathrm{abs} \left( \frac{ \mathrm{exp}_i - \mathrm{sim}_j }{ \mathrm{exp}_i } \right)\) Sum of SQuares (SSQ): \(\sum_{i=1}^{m} \sum_{j=1}^{n} \left({\mathrm{exp}_i - \mathrm{sim}_j } \right)^{2}\) Chi-Square (CHISQ): \(\sum_{i=1}^{m} \sum_{j=1}^{n} \left( \frac{ \mathrm{exp}_i - \mathrm{sim}_j }{ \sigma_{\mathrm{exp}} } \right)^{2}\) Mean Normalized Square Error (MNSE): \(\sum_{i=1}^{m} \sum_{j=1}^{n} \left( \frac{ \mathrm{exp}_i - \mathrm{sim}_j }{ \overline{\mathrm{exp}} } \right)^{2}\)

Note

Need a different Objective Function? The code that calculates the error is separated from the main Genetic Algorithm. This make useful to encode other Objective Functions if the already implemented does not apply to your necessities. You could contact us to add your function to the pleione package.