Sample Solution

do not have too steep a downward slope, as these algorithms tend to perform identically across differently-sized search spaces. Despite this, the Genetic Algorithm clearly wins this test, maintaining the highest fitness throughout.

Figure 5. Optimization algorithm fitness compared to Traveling Salesman problem graph nodes (N). Using hyperparameters listed in Table 4 and 2 seconds of iterations.

Next, we ran our efficiency experiment, running each algorithm for 5,000 iterations on the Traveling Salesman problem with a fixed graph node count (N) of 50. The results show an even more decisive victory for Genetic Algorithms than before; it appears that an optima is reached within the first 100 iterations, and the algorithm converges to this point throughout the remainder of execution. Such a quick convergence suggests that the algorithm may have discovered an abnormally fit local optima, or perhaps the global optima, as a Genetic Algorithm’s population early on in execution tends to rapidly fluctuate as random individuals mutate and mate. The population was likely quickly filled up with similarly optimal hypotheses.
The domination of the Genetic Algorithm within the Traveling Salesman problem could perhaps be attributed to the ABAGAIL engineers’ domain knowledge; the algorithm’s crossover function was specifically tailored to efficiently create ‘offspring’ of two paths. With such an efficient crossover function, the most efficient sub-paths of two parent paths could be merged multiple times through each generation, allowing the algorithm to quickly converge to an optimal solution. Ultimately, in problems like the Traveling Salesman problem where the search space is not well defined (for example, a random graph), Genetic Algorithms tend to be most effective.

Figure 6. Traveling Salesman fitness results compared to optimization algorithm iterations.