Ways your organization uses technology to gather patient and health care information
Traveling Salesman Problem – Genetic Algorithm
The Traveling Salesman Problem is a famous NP-complete problem involving the generation of the shortest route connecting nodes within a graph, with the condition of starting and stopping at the same node. Given the problem’s classification as NP-complete, there is no polynomial algorithm which can perfectly solve this problem. However, randomized optimization can be utilized to calculate approximate solutions. We will apply our collection of optimization algorithms – Randomized Hill Climbing, Simulated Annealing, Genetic Algorithms, and a newcomer, MIMIC – in order to determine the best-performing optimization algorithm for this specific problem.
In order to determine the optimal algorithm, we designed two experiments; one to see how each algorithm’s accuracy scales to increased problem complexity, and another to observe each algorithm’s optimization efficiency (by determining how accuracy converges over a fixed amount of iterations). We used the default testing hyperparameters provided by our ABAGAIL implementation, which are listed in Table 4.
SA Starting Temp Cooling Factor
1E12 0.95
GA Pop. Size # to Mate # to Mutate
200 150 20
MIMIC Sample Count # to Keep
200 100
Table 4. Optimization algorithm hyperparameters, pulled from ABAGAIL’s Traveling Salesman testing implementation. Randomized Hill Climbing not listed, as no hyperparameters are applicable.
We ran our complexity experiment over Traveling Salesman problems with size from 50 to 250 (with steps of 50), where the size N represents the number of nodes in the graph (Figure 5). It’s evident that for all algorithms, increased graph nodes result in poorer fitness. This isn’t indicative of the algorithm failing to scale, however; the fitness function evaluates the inverse of the calculated path’s distan