Tunneling between optima: partition crossover for the traveling salesman problem

A new recombination operator is introduced for the Traveling Salesman Problem called partition crossover. Theoretical and empirical results indicate that when two local optima are recombined using partition crossover, two offspring are produced that are highly likely to also be local optima. Thus, the operator is capable of jumping or tunneling from two local optima to two new and distinct local optima without searching intermediate solutions. The operator is respectful and it transmits alleles which means that 1) all common edges from the two parents are inherited and 2) the offspring are constructed using only edges inherited from the two parents. Partition crossover is not always feasible: sometimes two new Hamiltonian circuits cannot be constructed by the operator using only edges inherited from the two parents. But empirical results indicate that partition crossover is feasible 95 percent of the time when recombining randomly selected local optima. Furthermore, from a sample of local optima that are within a short random walk of the global optimum, partition crossover typically relocates the global optimum in a single move when crossover is feasible.