Akaike information criterion).

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1 An Excel Tool The application has three main tabs visible to the User and 8 hidden tabs. The first tab, User Notes, is a guide for the User to help in using the application. Here the User will find all the information needed in order to run the program, along with an outline of what is being calculated and the process by which it is done so. The second tab, Main, is where the User will import their data set as well as input information specific to their data and the function they wish to generate. In addition, after a run is complete, the final regression model will output to the Main tab. The third tab, Generations, provides an additional summary to the User which outlays what occurs during the run. Because this process is random, it is not always true that the final model generated is the BEST model. Furthermore, it is possible for User specific needs that a different model, with similar fitness, would be more appropriate in this case, the generations tab provides all the best fit models generated. How the Program Works When the User enters the appropriate information on the Main tab and hits OK, the program automatically generates the number of Initial Models indicated by the User. A model is a binary string chromosome that lets the program know whether or not to include a variable or leave it out. For example let s assume the Include Intercept option is chosen and the follow model is created: The initial 1, implies that an intercept term is being included, and the following implies that the first variable should be included and the second variable should be left out and so on The program uses matrix algebra to determine the Sum of Squares Error (SSE) and then determines the AIC (Akaike information criterion). AIC is used to determine the fitness of the model. The lower the AIC a model has, the better fit it is. Once fitness has been calculated for all models, the models are ranked according to their fitness. The top 50% best fit models are automatically used to generate offspring for the next generation (Parent 1). Each Parent 1 then goes through a mating process (depending on which option the User specifies). A random Parent 2 will be assigned to them from the Total Population (randomization is according to fitness level; the more fit a model is, the more likely it is to be chosen). Two offspring are generated from each mating and moved forward to the next generation, where the process repeats itself for as many generations as the User has indicated. After each generation, the Best Fit model is output to the Generations tab, and other informative statistics accompany it.

2 In addition, the Main tab will output the best model from all the generations: How To Use the Program The User should start by reading the User Notes tab to familiarize themselves with the program. Next, the User should go to the Main tab. Here is where the User imports their data set and sets all the user specific inputs. The following print screen is an image of what the User will see:

3 The Main tab: Generations: Here the User inputs the number of generations they wish to run the program. Each generation will derive a best fit model Initial Models: Here the User inputs the number of models they would like to run the program with. The program requires that the User input an even number of models for calculations purposes. If the User enters an odd number, the following error message box will appear:

4 In addition, we have recommended that the number of initial models used not exceed, where K is the number of explanatory variables. An error message box will also appear here, should the User input a value that exceeds this amount: Mating Type: Here there are three options for the User - If the Uniform option is chosen then randomization occurs at every gene (number 0 or 1) of the chromosomes (binary codes) of Parent 1 and Parent 2. Offspring 1 is a random mix of Parent 1 and Parent 2, while Offspring 2 is the compliment of its sibling. If the Single-Point Crossover option is chosen, then randomization occurs at a single point along the binary string. A random point is calculated so that Offspring 1 will obtain all genes prior to this point from Parent 1 and all genes after this point from Parent 2. Offspring 2 is again the compliment of its sibling. If the Double-Point Crossover option is chosen, then randomization occurs at two points along the binary string. In this case, two random points are chosen along the string. Offspring 1 is created by assigning all genes prior to the first point from Parent 1, all genes between the two points from Parent 2 and genes after the 2 nd point, from Parent 1. Migration: There are three options for the User: 5%, 10%, 15%. Halfway through the run, the program will automatically insert new members to the population. This occurs only once during the run and the number of new members inserted will be the number of Initial Models multiplied by the Migration percentage chosen (Rounded Up). Once the new members are inserted into the population, the program will calculate fitness for all existing members as well as new members. In order to keep the Population size consistent, an equal number of members will be removed at this point. Half will be randomly removed from among the 50% best fit members, and the other half removed will be those members with the least fitness. Include Intercept: This option specifies whether or not the User would like to include an intercept term in their model. For most cases this would be a recommended option, however, for specific data, the option without intercept may be preferable to the User. Elitism: This option lets the program know whether or not to allow the best fit models to move to the next generation (the alternate option only moves forward the offspring of the best fit models). If Elitism is chosen then the top 10% best fit models will move forward with the two offspring they create. The method described under Migration will be applied to remove excess members keeping the Total Population consistent.

5 Bibliography Buckles, B. P., & Petry, F. (1992). Genetic Algorithms. (Ieee Computer Society Press Technology Series. Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison- Wesley Professional. Haupt, R. L., & Haupt, S. E. (2004). Practical Genetic Algorithms. Wiley-Interscience; 2 edition. Howe, A., & Bozdogan, H. (2010). MATLAB Routine for GA Regression Variable Selection. Technical Report. Leardi, R., & Gonzales, A. L. (1998). Genetic algorithms applied to feature selection in PLS regression: how and when to use them. Chemometrics and Intelligent Laboratory Systems, Wasserman, G. S., & Sudjianto, A. (1994). All Subsets Regression Using a Genetic Search Algorithm. Computers and Inductrial Engineering,