CS 838 Pervasive Parallelism Fall 2005 Section 3 Instructor Mark D. Hill URL: http://www.cs.wisc.edu/~markhill/cs838/Fall2005/

Crossover Function for Genetic TSP

Please direct questions to Dan Gibson (gibson[at]cs.wisc.edu) who helped create this assignment.

The crossover functions suggested in Shahookar/Mazumder are well-suited to the VLSI problems they intend to solve. They are presented in this assignment as examples of crossover functions--they are not particularly well-suited to solving the traveling salesperson problem genetically. Specifically, they do not easily converge to local minima in the solution space.

We are placing very few requirements on your crossover function. It need only take two (or more) parents as argument, and produce one child. The focus of the assignment is to encourage you to think about how one might parallelize the genetic process, not a particular crossover implementation.

However, if you wish, you may want to explore crossover functions that are well-suited to genetic TSP. A potential example crossover function is described below. You are not required to implement this crossover function.

Suppose Parents A and B are considered for crossover. Identify the "region" within A or B that is most efficient, using some heuristic (possibly distance/nCities, for instance). Copy that efficient region directly into the child. From the other parent, add other cities before or after the region in the position that minimizes distance, operating left-to-right out of the donating parent. Consider this: Five stops, with the following distances between them:

In parent A, the Madison/Madison/Middleton string is very good (only 6 miles for 3 stops). So lets include that in child C.

Note that we may at this point insert the contributions from B either before or after the initial string. I denote this with question marks.

C still doesn't include Milwaukee or La Crosse. These contributions will come from B. Insert LaCrosse (first in left-to-right order in B not already in C):

We insert LaCrosse where the minumum total distance is achieved. Adding it before the initial string would have added 101, not 95. Note that we now have three possible insertion locations--only the Madison/Madison/Middleton group will remain atomic.

Finally, we insert Milwaukee:

Again, Milwaukee was added at the position such that distance was minimized.

Intuitively, the algorithm above may have desireable local minima convergence. It may be difficult to implement in practice, though hopefully it outlines what a good TSP crossover function might look like. Remember, these algorithms are heuristic-based, so there is no right crossover function.

Variants on the ideas above are also possible.