Multi expression programming

Multi Expression Programming (MEP) is an evolutionary algorithm for generating mathematical functions describing a given set of data. MEP is a Genetic Programming variant encoding multiple solutions in the same chromosome. MEP representation is not specific (multiple representations have been tested). In the simplest variant, MEP chromosomes are linear strings of instructions. This representation was inspired by Three-address code. MEP strength consists in the ability to encode multiple solutions, of a problem, in the same chromosome. In this way, one can explore larger zones of the search space. For most of the problems this advantage comes with no running-time penalty compared with genetic programming variants encoding a single solution in a chromosome. MEP chromosomes are arrays of instructions represented in Three-address code format. Each instruction contains a variable, a constant, or a function. If the instruction is a function, then the arguments (given as instruction's addresses) are also present. Here is a simple MEP chromosome (labels on the left side are not a part of the chromosome): 1: a 2: b 3: + 1, 2 4: c 5: d 6: + 4, 5 7: * 3, 5 When the chromosome is evaluated it is unclear which instruction will provide the output of the program. In many cases, a set of programs is obtained, some of them being completely unrelated (they do not have common instructions). For the above chromosome, here is the list of possible programs obtained during decoding: E1 = a, E2 = b, E4 = c, E5 = d, E3 = a + b. E6 = c + d. E7 = (a + b) * d. Each instruction is evaluated as a possible output of the program. The fitness (or error) is computed in a standard manner. For instance, in the case of symbolic regression, the fitness is the sum of differences (in absolute value) between the expected output (called target) and the actual output. Which expression will represent the chromosome? Which one will give the fitness of the chromosome? In MEP, the best of them (which has the lowest error) will represent the chromosome.

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Concepts associés (3)

Gene expression programming

In computer programming, gene expression programming (GEP) is an evolutionary algorithm that creates computer programs or models. These computer programs are complex tree structures that learn and adapt by changing their sizes, shapes, and composition, much like a living organism. And like living organisms, the computer programs of GEP are also encoded in simple linear chromosomes of fixed length. Thus, GEP is a genotype–phenotype system, benefiting from a simple genome to keep and transmit the genetic information and a complex phenotype to explore the environment and adapt to it.

Multi expression programming

Programmation génétique

La programmation génétique est une méthode automatique inspirée par le mécanisme de la sélection naturelle tel qu'il a été établi par Charles Darwin pour expliquer l'adaptation plus ou moins optimale des organismes à leur milieu. Elle a pour but de trouver par approximations successives des programmes répondant au mieux à une tâche donnée. On nomme programmation génétique une technique permettant à un programme informatique d'apprendre, par un algorithme évolutionniste, à optimiser peu à peu une population d'autres programmes pour augmenter leur degré d'adaptation (fitness) à réaliser une tâche demandée par un utilisateur.