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Extra resources for A 2E4-time algorithm for MAX-CUT
CHC-2X never performs as well as CHC-HUX in the range 3 < K _< 13, but the performance of CHC-2X does not degrade as rapidly as C H C - H U X when K > 15, and the performance of CHC-2X does not regress to r a n d o m search until K > 70. 2X produces offspring t h a t are much more like their parents than HUX. This results in much less vigorous search t h a n when using HUX. Thus, the performance of CHC-2X is more like t h a t of the hill-climbers. F u r t h e r m o r e , by comparing Figure 1 with Figure 4 it can be seen t h a t CHC-2X performs at least as well as the SGA (using one-point crossover) over all K's and usually much better.
David Schaffer to form the remaining members of the population. This introduces new genetic diversity into the population in order to continue search but without losing the progress that has already been made. CHC uses no other form of mutation. The CHC algorithm is typically implemented using the HUX recombination operator for binary representations, but any recombination operator may be used with the algorithm. HUX recombination produces two offspring which are maximally distant from their two parent strings by exchanging exactly half of the bits that differ in the two parents.
This, as we have seen, is the point where CHC-HUX rapidly deteriorates, although CHC does somewhat better than random search until K > 20. In effect, this is showing that there is very little in the way of schemata for CHC to exploit after K = 12, the point where it is over taken by R B C + . 9The incest threshold is decremented each generation that no offspring are better than the worst member of the parent population. 43 44 Keith E. Mathia, Larry J. Eshelman, and J. David Schaffer T a b l e 2 Average trials to find best local minima discovered (not necessarily the optimum) and the standard error of the mean (SEM).