R. Heckendorn, S. Rana, and D. Whitley. Polynomial time summary statistics for a generalization of MAXSAT. In GECCO-99, pages 281--288. Morgan Kaufmann, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....ESA research is the recognition of the need to assess ESAs within the context of general theories of computation. There has been a growing body of work that looks at the relationship between ESAs and the theory of NP completeness (Duvivier, Preux, Talbi, 1996; Rana, Heckendorn, Whitley, 1998; Heckendorn, Rana, Whitley, 1999) a theory that puts serious boundaries on the performance of any algorithm let al..one an evolutionary algorithm (Garey Johnson, 1979) Chapter 1. Introduction 6 Furthermore, if ESAs are to be taken seriously as an engineering tool then they must compete with other potential candidates for ....

....is possible to design then the problem becomes trivially easy to solve. However, most of the time our domain knowledge is only sufficient to ensure that these characteristics will hold in general rather than all the time and hence the resulting search space is more difficult to search. Indeed (Heckendorn et al. 1999) have shown how it cannot be possible to design in polynomial time a Mt.Fuji representation of NP complete problems, as otherwise we could solve all NPcomplete problems in polynomial time, proving that P = NP. Assuming, as most people do, that P 6= NP then we can be fairly confident that the ....

Heckendorn, R., Rana, S., & Whitley, D. (1999). Polynomial time summary statistics for a generalization of MAXSAT. In GECCO-99: Proceedings of the Genetic and Evolutionary Computation Conference.

....is the following: 10 If P 6= NP then, in the general case, exactly knowing the static schema fitness averages up to some fixed order cannot provide information that can be used to infer the location of a global optimum, or even an above average solution, in polynomial time. For proofs see: [22, 21]) This seems like a very negative result. But it is dangerous to over interpret either positive or negative results. In practice, random MAXSAT problems are characterized by highly inconsistent schema information so that there is really little or no information that can be exploited to guide ....

R. Heckendorn, S. Rana, and D. Whitley. Polynomial time summary statistics for a generalization of MAXSAT. In GECCO-99, pages 281--288. Morgan Kaufmann, 1999.

....to a problem. So, for a problem defined over 2 possible inputs, the distribution would be comprised of all 2 evaluations of the inputs. Goldberg and Rudnick [5] have used Walsh coefficients to calculate fitness variance for fitness distributions and schemata. Heckendorn, Rana and Whitley [6] show how higher order statistics such as skew and kurtosis can be also be computed from the Walsh coefficients using a general formula for computing the r moment for any fitness distribution; they also show that for certain special types of functions, the Walsh coefficients and summary ....

....skew and kurtosis for any fitness distribution provided we are given the Walsh coefficients. variance = 2 = oe skew = 3 kurtosis = 4 For example, since a 1 Phi a 2 = 0 if and only if a 1 = a 2 the variance for any function is given by w i w i Heckendorn, Rana and Whitley [6] show that in the special case of Embedded Landscapes [7] there are only a polynomial number of nonzero Walsh coefficients and we can identify and compute them in polynomial time. MAX3SAT and NKLandscapes are instances of an Embedded Landscape. Thus, an exact Walsh analysis can be done in ....

[Article contains additional citation context not shown here]

R. Heckendorn, S. Rana, and D. Whitley. Polynomial time summary statistics for a generalization of MAXSAT. GECCO-99, Morgan Kaufmann, 1999.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC