Industrial Applications of Genetic Algorithms:Data Mining Using Genetic Algorithms

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F3 Fitness Function Simulation Conclusions

The first two F3 fitness function simulations (simulations 7 and 8) converged on the correct solution while the third (simulation 9) did not completely converge but did perform well. Overall, fitness function F3 performed better than both fitness functions F1 and F2.

Fitness Function Simulation Summary

Of the three fitness functions that were investigated (F1, F2, and F3), fitness function F3 outperformed both F1 and F2. Thus, F3 appeared to be the best alternative and was therefore used in the remaining simulations.

Crossover Operator Simulation Results

As discussed in the prior section on crossover, two unique crossover operators, aligned single-point crossover (ASPX) and unmatched crossover with single child offspring (UXSCO), were developed and investigated. The results of each crossover operator simulation are discussed below.

UXSCO Simulations

Each of the preceding fitness function simulations (simulations 1 through 9) were performed with the UXSCO crossover operator. Thus, those simulation results will be used for comparison with the ASPX simulations and will not be duplicated here.

ASPX Simulations

Each ASPX crossover simulation was run with the fitness function, mutation, and genetic algorithm parameters as noted in the simulation test matrix.

Simulation 10 was run with database configuration 1. As can be seen from Figure 9.11, the item combination of interest entered the population around generation 5 and the simulation converged on the solution around generation 15. Comparing this to the corresponding UXSCO simulation (simulation 7), it can be seen that each simulation converged at essentially the same generation. In the ASPX simulation, however, it can be seen that the average fitness curve is much smoother than that of the UXSCO simulation. This is most likely due to the fact that the UXSCO operator is more random in nature than the ASPX operator.

Figure 9.11 Simulation 10 results

Simulation 11 consisted of two runs, 11A and 11B, each with database configuration 2. The only difference between runs 11A and 11B is that a different random number generator seed was used for each. As can be seen from Figure 9.12, the simulation converged on a false solution rather early on and never recovered (Note: This simulation was run for 400 generations, yet no improvement took place. Thus, only the first 75 generations are shown.).

Figure 9.12 Simulation 11A results

Simulation 11B, on the other hand, converged on the solution around generation 12 (See Figure 9.13). Thus, it may have been the case that the initial population for run 11A was not diverse enough, and the mutation operator never introduced the lost allele into the population. This possibility is addressed in simulations 17 and 18 in the section, “Genetic Algorithm Parameter Simulation Results.”

Figure 9.13 Simulation 11B results

Comparing Simulation 11B to the corresponding UXSCO simulation (simulation 8), we can see that the ASPX simulation converged a bit sooner (generation 12 vs. generation 20).

Simulation 12 was run with database configuration 3. As can be seen from Figure 9.14, the item combination of interest entered the population around generation 8 and the simulation converged on the solution around generation 20. Comparing this to the corresponding UXSCO simulation (simulation 9), we can see that the ASPX simulation completely converged on the solution while in the UXSCO simulation, the population, even though it contained a majority of solution members, did not completely converge.

Figure 9.14 Simulation 12 results

Crossover Operator Simulation Summary

Of the three simulation environments in which the ASPX and UXSCO crossover operators were tested, those implementing the ASPX operator performed as well or better than the corresponding UXSCO simulations. The first two simulations (using database configurations 1 and 2) converged on the solution around the same generation. In the simulations involving database configuration 3, however, the ASPX simulation clearly outperformed the UXSCO simulation in that the population totally converged on the solution. Therefore, due to the overall better performance of the ASPX crossover operator, it was used in the remaining simulations.

Mutation Operator Simulation Results

As discussed in the prior section on mutation, two unique mutation operators, random mutation and window mutation, were developed and investigated. The results of each mutation operator simulation are discussed below.

Random Mutation Simulations

Each of the previous simulations were run with the random mutation operator. Thus, those simulation results, namely the results from simulation 11A, will be used for comparison with the window mutation operator simulations and will not be duplicated here.

Window Mutation Simulations

The window mutation simulation was run with the fitness function, crossover operator, and genetic algorithm parameters as noted in the simulation test matrix.

Using the same test environment as that in simulation 11A, simulation 13 implemented the window mutation operator instead of the random mutation operator in an attempt to recover the allele that was assumed to be lost. Running with the window mutation operator, however, yielded essentially the same results as simulation 11A. In addition, the window mutation operator was run in several other simulation environments and in each case, the simulation results were essentially identical to those obtained in the corresponding random mutation operator simulations. Since the results were the same in each case, no graphs are shown.

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