Hybrid genetic algorithms in view of the evolution theories with application for the electrical sounding method

Abstract

ABSTRACTThe classical genetic algorithm is a stochastic process which operates by natural selection. Although the algorithm may localize a point around the global minimum of the misfit function, it is not efficient at finding the precise solution. This paper suggests some hybrid genetic algorithms, derived from evolution theories, to overcome this problem. Firstly, sexual selection has been incorporated in the classical genetic algorithm to obtain a full representation of the Darwinist evolution concept. The simulation of sexual selection is performed by assigning a higher probability of surviving to some parameters that satisfy some algebraic relationships. This method is called the ‘marked constraints’ algorithm since it permits us to insert geological and geophysical constraints into the problem. The algorithm implementation is realized by progressively shrinking the parameter search space through successive generations. In this way, the genetic algorithm gains some degree of determinism. Secondly, since the evolution theory of Lamarck postulates that the acquired traits are passed on to the next generation, a hybrid use of the damped least‐squares method and the genetic algorithm is called Lamarckian inversion. Lamarckian inversion involves some improvement procedures that simulate the reduction of the misfit with the help of a derivative‐based method between two generations. Finally, although there is no correspondence in nature, Lamarckian and Darwinist evolution concepts are combined to strengthen the deterministic part of the solution algorithm. This is called the Lamarckian‐marked‐constraint algorithm. The merits and behaviours of the suggested algorithms are discussed using two examples. The first is a hypothetical example affected by a multiminima problem. The second examines the equivalence problem using vertical electrical sounding data.