Solving Large Travelling Salesman Problems with Small Populations

A new genetic algorithm for the solution of the travelling salesman problem is presented in this paper. The approach is to introduce several knowledge-augmented genetic operators which guide the genetic algorithm more directly towards better quality of the populationbut are not trapped in local optima prematurely. The algorithm applies a greedy crossover and two advanced mutation operations based on the 2-opt and 3-opt heuristics. One of our particular interests is to investigate whether small populations are adequate for solving large problems. We also want to see how the quality of the initial population and the quality of the final solution are related, especially when the population is small. For this purpose, we designed a selective initialization scheme to generate a better initial population. The algorithm has been implemented in C and tested on several sets of data. The largest data instance used is 2392 cities (i.e., pr2392). The actual population size used is only 32. For small sets of data (less than 100 cities), our algorithm can find the optimal solutions. For large data sets, the quality of the best solutions found is about 1.3-2.3% worse than optimal. The empirical results show that combining the knowledge from the heuristic method and the genetic algorithm is a good approach for solving the large travelling salesman problem. By incorporating the heuristic method, we can develop greedy genetic operators to improve the efficiency of genetic algorithms. Moreover, it makes small population sizes sufficient to solve large problems. By incorporating the genetic algorithm technique, we can escape from local optima in many cases so that much better results can be obtained than with heuristic methods alone.