GENETIC PROGRAMMING WITH LINEAR REPRESENTATION -- A SURVEY <s> Algorithm <s> Abstract Two techniques of population control are currently used in the field of serial genetic algorithms: generational and steady state. Although they have been used somewhat interchangeably in the past, it has become apparent that the two techniques are actually quite different. In this paper, I study the behavior of each with regard to reproduction, and show that while each can be made similar with respect to the schema theorem, in practice their behavior is quite different. <s> BIB001 </s> GENETIC PROGRAMMING WITH LINEAR REPRESENTATION -- A SURVEY <s> Algorithm <s> We describe a Genetic Algorithm that can evolve complete programs. Using a variable length linear genome to govern the mapping of a Backus Naur Form grammar definition to a program, expressions and programs of arbitrary complexity may be evolved. Our system, Grammatical Evolution, has been applied to problems such as a Symbolic Regression problem, and finding Trigonometric Identities. In this paper we describe how we applied GE to a Symbolic Integration problem, that being finding a function which is an integral of . We also show how a Steady State selection mechanism was found to improve the performance of Grammatical Evolution. <s> BIB002
LGP uses a modified steady-state algorithm. GEP uses a generational algorithm.  The standard MEP algorithm uses steady-state evolutionary model BIB001 as its underlying mechanism.  Standard GE algorithm uses steady-state evolutionary model 28 as its underlying mechanism. A generational algorithm was initially used 7 , but due to its poor performance it was later replaced by a steady-state approach BIB002 . Algorithm 4 GE Algorithm @ Randomly create the initial population (P (0) The use of BNF grammars provides a general and a very natural way of evolving computer programs written in programming languages whose instructions may be expressed as BNF rules. In the case of mathematical expressions, their representation is not limited to a single form (such as infix, prefix, postfix etc) as in the case of some other GP techniques. The representation can be simply changed by changing the grammar. The wrapping operator provides a very original way of translating short chromosomes into very long expressions. Wrapping also provides an efficient way of avoiding invalid expressions. The CGP algorithm suggested in 8 is a simple (1+λ)-Evolution Strategy 41 where λ is usually 4. The algorithm may be described as follows: Algorithm 5 CGP Algorithm @ Generate a random solution S. while not stop condition do @ Generate λ solutions by mutating S @ Replace S by the best individual out of the currently existing (1+λ) individuals end while @ Output S as the best solution (individual) found