Schemata as Building Blocks: Does Size Matter?

We analyze the schema theorem and the building block hypothesis using a recently derived, exact schemata evolution equation. We derive a new schema theorem based on the concept of effective fitness showing that schemata of higher than average effective fitness receive an exponentially increasing number of trials over time. The building block hypothesis is a natural consequence in that the equation shows how fit schemata are constructed from fit sub-schemata. However, we show that generically there is no preference for short, low-order schemata. In the case where schema reconstruction is favoured over schema destruction large schemata tend to be favoured. As a corollary of the evolution equation we prove Geiringer's theorem. We give supporting numerical evidence for our claims in both non-epsitatic and epistatic landscapes.Comment: 17 pages, 10 postscript figure

Exact computation of the expectation curves of the bit-flip mutation using landscapes theory

Chicano, F., & Alba E. (2011). Exact computation of the expectation curves of the bit-flip mutation using landscapes theory. Proceedings of 13th Annual Genetic and Evolutionary Computation Conference, Dublin, Ireland, July 12-16, 2011. pp. 2027–2034.Bit-flip mutation is a common operation when a genetic algorithm is applied to solve a problem with binary representation. We use in this paper some results of landscapes theory and Krawtchouk polynomials to exactly compute the expected value of the fitness of a mutated solution. We prove that this expectation is a polynomial in p, the probability of flipping a single bit. We analyze these polynomials and propose some applications of the obtained theoretical results.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. This research has been partially funded by the Spanish Ministry of Science and Innovation and FEDER under contract TIN2008-06491-C04-01 (the M∗ project) and the Andalusian Government under contract P07-TIC-03044 (DIRICOM project)

Bridging Contested Terrain: Linking Incentive-Based and Learning Perspectives on Organizational Evolution

In this paper we present a general model of organizational problem-solving in which we explore the relationship between problem complexity, decentralization of tasks and reward schemes. When facing complex problems which require the coordination of large numbers of interdependent elements, organization face a decomposition problem which has both a cognitive dimension and a reward and incentive dimension. The former relates to the decomposition and allocation of the process of generation of new solutions: since the search space is too vast to be searched extensively, organizations employ heuristics for reducing it. The decomposition heuristic takes the form of division of cognitive labor and determines which solutions are generated and become candidates for selection. The reward and incentive dimension defines the selection environment which chooses over alternative solutions. The model we present studies the interrelationships between these two dimensions, in particular we compare the problem solving performance of organizations characterized by various decompositions (of coarser of finer grain) and various reward schemes (at the level of the entire organization, team and individual). Moreover we extend our model in a still tentative fashion - in order to account for such power and authority relationships (giving some parts of the organization the power to stop changes in other parts), and to discuss the co-evolution of problem representations and incentive mechanisms.-

Problem Understanding through Landscape Theory

In order to understand the structure of a problem we need to measure some features of the problem. Some examples of measures suggested in the past are autocorrelation and fitness-distance correlation. Landscape theory, developed in the last years in the field of combinatorial optimization, provides mathematical expressions to efficiently compute statistics on optimization problems. In this paper we discuss how can we use optimización combinatoria in the context of problem understanding and present two software tools that can be used to efficiently compute the mentioned measures.Ministerio de Economía y Competitividad (TIN2011-28194

Where are Bottlenecks in NK Fitness Landscapes?

Usually the offspring-parent fitness correlation is used to visualize and analyze some caracteristics of fitness landscapes such as evolvability. In this paper, we introduce a more general representation of this correlation, the Fitness Cloud (FC). We use the bottleneck metaphor to emphasise fitness levels in landscape that cause local search process to slow down. For a local search heuristic such as hill-climbing or simulated annealing, FC allows to visualize bottleneck and neutrality of landscapes. To confirm the relevance of the FC representation we show where the bottlenecks are in the well-know NK fitness landscape and also how to use neutrality information from the FC to combine some neutral operator with local search heuristic

2-bit Flip Mutation Elementary Fitness Landscapes

Genetic Programming parity is not elementary. GP parity cannot be represented as the sum of a small number of elementary landscapes. Statistics, including fitness distance correlation, of Parity\u27s fitness landscape are calculated. Using Walsh analysis the eigen values and eigenvectors of the Laplacian of the two bit flip fitness landscape are given and a ruggedness measure for elementary landscapes is proposed. An elementary needle in a haystack (NIH) landscape is given