How does the CHC Algorithm deal with child populations with lower fitness? I am basing my question on the pseudocode for the CHC Adaptive Search Algorithm by Eshelman given in this answer by deong:

delta = k/4               # k = chromosome length
while not done
    create new child population
    for i = 1 to n/2     # n = population size
        select p1, p2 from population without replacement
        if hamming_distance(p1, p2) &gt; delta
            c1, c2 = HUX crossover(p1, p2)
            insert c1, c2 into child pop
        end if
    end for
    if child pop is empty
        delta = delta - 1
    else
        take best n individuals from union of parent and child populations as next population
    end if
    if delta &lt; 0
        keep one copy of best individual in population
        generate n-1 new population members by flipping 35% of the bits of the best individual
        delta = k/4
    end if


How does this algorithm deal with situations where the child population has lower fitness than the parent population?

Consider a population of two parent with a large enough hamming distance to produce children. Now if both children have a lower fitness than their parents, doesn't the survivor selection ("take best n") select the same parents again, resulting in an infinite loop?
CHC never has a next generation's population with lower fitness than the current one due to the use of a truncation selection step. It combines the parents and offspring, sorts by fitness, and takes the best $n$ individuals. So if including any child would lower the fitness of the population, it would just select the parents as the next generation and the average fitness would stay the same.

In principle, you could indefinitely select the same two parents over and over, continually producing inferior offspring. But generally you're running CHC with a population size of 50 or more, so you don't expect to continually pair the same two parents. Also, it's technically an infinite loop anyway, as most GAs are. In practice you define some stopping condition based on evaluation count or wall clock time or whatever.