Isomorphisms Of Genetic Algorithms

Determining concepts by group membership

“…If f is a deceptive function, and M is the matrix of an invertible linear transformation of G (we regard G as a k dimensional vector space over the finite field ~2), then the function g(x) =fo M(x) might be nondeceptive for suitable M. In this case, Battle and Vose [1 ] have shown that if M-schemata were to direct the genetic search of f, then f would be nondeceptive. We will define M-schemata below, but first note that according to [7], since these M-schemata are subsets of G, they satisfy the schema theorem.…”

“…If these M-schemata could somehow be made invariant under crossover, then they (instead of Holland schemata) might gain the upper hand and begin to direct the optimization off. This is in fact the case; genetic optimization ofg is isomorphic to optimizing f with a modified crossover operator which leaves the M-schemata invariant [1].…”

“…Finally, Battle and Vose [1 ] showed how transforming a deceptive problem with a matrix is equivalent to leaving the problem unchanged, but arranging for the subsets of G which direct genetic search to be different from Holland schemata.…”

Group Properties of Crossover and Mutation

“…Binary Strings An early example of N -schemata are the M -schemata introduced by Battle and Vose (1993) for the case of length binary strings under componentwise addition modulo 2. He took N to be the set of subgroups generated by rows of an invertible × matrix M .…”

Evolutionary Algorithms as fitness function debuggers

“…The design of an efficient representation is also recognized as a crucial step, as witnessed by the never-ending debate binary vs real for real-parameter search spaces [6,1,9], or more recent attempts to actually separate representation from operators [22]. The choice of operators, somehow dual of the choice of representation [2], also raised a lot of discussions [5,11]. And, to a less extend, some works addressed the initialization issue [23,12].…”