The Hierarchical-if-and-only-if (H-IFF) GA test function.

The HIFF C code

H-IFF is a hierarchical Building-Block (BB) test function for GAs. It has a hierarchical BB structure somewhat like the Royal Roads (R2) (Forrest, Mitchell, Holland 1993), but unlike the Royal Roads the BBs are not separable. The strong interdependencies between building-blocks means that they cannot be solved independently, and this in turn means that H-IFF cannot be solved by any kind of hill-climber (unlike the Royal Roads). This makes H-IFF an appropriate test algorithm for recombinative GAs. Our work demonstrates that your GA will only work on H-IFF if your GA combines BBs effectively, and has good diversity maintenance. If you want to know whether recombination in your GA is working like the Building-Block Hypothesis (Holland 1975) says it should - then H-IFF is the test problem for you.

Here's the abstract from "Hierarchically-Consistent GA Test Problems: Summary and Additional Results"

"The Building-Block Hypothesis suggests that the genetic algorithm (GA) will perform well when it is able to identify above-average-fitness low-order schemata and recombine them to produce higher-order schemata of higher fitness. We suppose that the recombinative process continues recursively, combining schemata of successively higher orders as search progresses. Historically, attempts to illustrate this intuitively straight-forward process on abstract test problems, most notably the Royal Road problems, have been somewhat perplexing. More recent building-block test problems have abandoned the multi-level hierarchical structure of the Royal Roads, and thus departed from the original recursive aspects of the hypothesis. This paper defines the concept of hierarchical consistency, which captures the recursive nature of problems implied by the Building-Block Hypothesis. We introduce several variants of problems that are hierarchically consistent and begin to explore aspects of problem difficulty with respect to these models. "

For explanation please see related papers:

Watson RA, Hornby GS, & Pollack JB, 1998, "Modelling Building-Block
Interdependency", PPSN-V, 1998.

Watson RA & Pollack JB, 1999, "Hierarchically-Consistent GA Test
Problems", CEC, 1999.

Watson RA & Pollack JB, 1999, "Incremental Commitment in Genetic
Algorithms", GECCO, 1999.

"Hierarchically-Consistent GA Test Problems: Summary and Additional Results", GECCO-99 Late
Breaking Papers, 1999, pp 292-297. (pdf version)

these and others can be found here:

HIFF and other GA test functions can also be found here:

If HIFF is useful to you please let me know and I can forward anything
else you need/ answer any questions you might have.

Have fun.