In this paper we address the problem of program discovery as deened by Genetic Programming 10]. We have two major results: First, by combining a hierarchical crossover operator with two traditional single point search algorithms: Simulated Annealing and Stochastic Iterated Hill Climbing, we have solved some problems with fewer tness evaluations and a greater probability of a success than Geneti...

In IDEAs, the probability distribution of a selection of solutions is estimated each generation. From this probability distribution, new solutions are drawn. Through the probability distribution, various relations between problem variables can be exploited to achieve efficient optimization. For permutation optimization, only real valued probability distributions have been applied to a real valu...

Correlations between alleles after selection are an important source of information. Such correlations should be exploited for further search and thereby constitute the building blocks of evolutionary exploration. With this background we analyze the structure of the offspring probability distribution, or exploration distribution, for a simple GA with mutation only and a crossover GA and compare...

Genetic Programming (GP) is a powerful optimization algorithm, which employs crossover for a main genetic operator. Because a crossover operator in GP selects sub-trees randomly, the building blocks may be destroyed by crossover. Recently, algorithms called PMBGPs (Probabilistic Model Building GP) based on probabilistic techniques have been proposed in order to improve the problem above. We pro...

The Ellsberg Paradox documented the aversion to ambiguity in the probability of winning a prize. Using an original sample of 266 business owners and managers facing risks from climate change, this paper documents the presence of departures from rationality in both directions. Both ambiguity-seeking behavior and ambiguity-averse behavior are evident. People exhibit ‘fear’ effects of ambiguity fo...

In this paper a new general GP schema theory for headless chicken crossover and subtree mutation is presented. The theory gives an exact formulation for the expected number of instances of a schema at the next generation. The theory includes four main results: microscopic schema theorems for both headless chicken crossover and subtree mutation, and two corresponding macroscopic theorems. The mi...

In this paper, firstly we specialise the exact GP schema theorem for one-point crossover to the case of linear structures of variable length, for example binary strings or programs with arity-1 primitives only. Secondly, we extend this to an exact schema theorem for GP with standard crossover applicable to the case of linear structures. Then we study, both mathematically and numerically, the sc...

We investigate the survival probability Phi(n,c) of particles performing a random walk on a two-dimensional lattice that contains static traps, which are randomly distributed with a concentration c, as a function of the number of steps n. Phi(n,c) is analyzed in terms of a scaling ansatz, which allows us to locate quantitatively the crossover between the Rosenstock approximation (valid only at ...

Since genetic algorithms (GAs) are inspired from the idea of evolution, it is natural to expect that besides original problem conversion to suit GA, also adaptation will be used for tuning internal parameters of genetic algorithms to speed up the iterative solution of the given problem. In this paper we present an approach for modifying crossover and mutation probability rates based on generati...