Abstract
The edge assembly crossover (EAX) is considered the best available
crossover for traveling salesman problems (TSPs).
In this paper, a modified EAX algorithm is proposed. The key idea is
to maintain population diversity by eliminating any exchanges of
edges by the crossover that does not contribute to an improved
evaluation value. For this, a new evaluation function is designed
considering local diversity loss of the population.
The proposed method is applied to several benchmark instances with
up to 4461 cities. Experimental results show that
the proposed method works better than other genetic algorithms
using other improvements of the EAX.
The proposed method can reach optimal solutions for
most benchmark instances with up to 2392 cities with probabilities
higher than 90%. For an instance called fnl4461, this method can reach
an optimal solution with probability 60% when the population size is
set to 300 -- an extremely small population compared to that needed in
previous studies.
