A new model for evolving Evolutionary Algorithms (EAs) is proposed in this paper. The model is based on the Multi Expression Programming (MEP) technique. Each MEP chromosome encodes an evolutionary pattern that is repeatedly used for generating the individuals of a new generation. The evolved pattern is embedded into a standard evolutionary scheme that is used for solving a particular problem. Several evolutionary algorithms for function optimization are evolved by using the considered model. The evolved evolutionary algorithms are compared with a human-designed Genetic Algorithm. Numerical experiments show that the evolved evolutionary algorithms can compete with standard approaches for several well-known benchmarking problems.

Automatic Programming is one of the most important areas of computer science research today. Hardware speed and capability have increased exponentially, but the software is years behind. The demand for software has also increased significantly, but it is still written in old fashion: by using humans. There are multiple problems when the work is done by humans: cost, time, quality. It is costly to pay humans, it is hard to keep them satisfied for a long time, it takes a lot of time to teach and train them and the quality of their output is in most cases low (in software, mostly due to bugs). The real advances in human civilization appeared during the industrial revolutions. Before the first revolution, most people worked in agriculture. Today, very few percent of people work in this field. A similar revolution must appear in the computer programming field. Otherwise, we will have so many people working in this field as we had in the past working in agriculture. How do people know how to write computer programs? Very simple: by learning. Can we do the same for software? Can we put the software to learn how to write software? It seems that is possible (to some degree) and the term is called Machine Learning. It was first coined in 1959 by the first person who made a computer perform a serious learning task, namely, Arthur Samuel. However, things are not so easy as in humans (well, truth to be said - for some humans it is impossible to learn how to write software). So far we do not have software that can learn perfectly to write software. We have some particular cases where some programs do better than humans, but the examples are sporadic at best. Learning from experience is difficult for computer programs. Instead of trying to simulate how humans teach humans how to write computer programs, we can simulate nature.

Multi Expression Programming (MEP) is a Genetic Programming variant that uses a linear representation of chromosomes. MEP individuals are strings of genes encoding complex computer programs. When MEP individuals encode expressions, their representation is similar to the way in which compilers translate $C$ or $Pascal$ expressions into machine code. A unique MEP feature is the ability to store multiple solutions of a problem in a single chromosome. Usually, the best solution is chosen for fitness assignment. When solving symbolic regression or classification problems (or any other problems for which the training set is known before the problem is solved) MEP has the same complexity as other techniques storing a single solution in a chromosome (such as GP, CGP, GEP or GE). Evaluation of the expressions encoded into an MEP individual can be performed by a single parsing of the chromosome. Offspring obtained by crossover and mutation is always syntactically correct MEP individuals (computer programs). Thus, no extra processing for repairing newly obtained individuals is needed.

Finding the optimal parameter setting (i.e. the optimal population size, the optimal mutation probability, the optimal evolutionary model etc) for an Evolutionary Algorithm (EA) is a difficult task. Instead of evolving only the parameters of the algorithm we will evolve an entire EA capable of solving a particular problem. For this purpose the Multi Expression Programming (MEP) technique is used. Each MEP chromosome will encode multiple EAs. An nongenerational EA for function optimization is evolved in this paper. Numerical experiments show the effectiveness of this approach.

An evolutionary approach for computing the winning strategy for Nim-like games is proposed in this paper. The winning strategy is computed by using the Multi Expression Programming (MEP) technique - a fast and efficient variant of the Genetic Programming (GP). Each play strategy is represented by a mathematical expression that contains mathematical operators (such as +, -, *, mod, div, and , or, xor, not) and operands (encoding the current game state). Several numerical experiments for computing the winning strategy for the Nim game are performed. The computational effort needed for evolving a winning strategy is reported. The results show that the proposed evolutionary approach is very suitable for computing the winning strategy for Nim-like games.