Ozlem O. Garibay

The Modular Genetic Algorithm: Exploiting Regularities in the Problem Space

We introduce the modular genetic algorithm (MGA). The modular genetic algorithm is a search algorithm designed for a class of problems pervasive throughout nature and engineering: problems with modularity and regularity in their solutions. We hypothesize that genetic search algorithms with explicit mechanisms to exploit regularity and modularity on the problem space would not only outperform conventional genetic search, but also scale better for this problem class. In this paper we present experimental evidence in support of our hypothesis. In our experiments, we compare a limited version of the modular genetic algorithm with a canonical genetic algorithm (GA) applied to the checkerboard-pattern discovery problem for search spaces of sizes 232, 2128, and 2512. We observe that the MGA significantly outperforms the GA for high complexities. More importantly, while the performance of the GA drops 22.50% when the complexity of the problem increases, the MGA performance drops only 11.38%. These results indicate that the MGA has a strong scalability property for problems with regularity and modularity in their solutions.

Effects of Module Encapsulation in Repetitively Modular Genotypes on the Search Space

We introduce the concept of modularity-preserving representations. If a representation is modularity-preserving, the existence of modularity in the problem space is translated into a corresponding modularity in the search space. This kind of representation allows us to analyze the impact of modularity at the genomic level. We investigate the question of what constitutes a module at the genomic level of evolutionary search and provide a static analysis of how to identify good and bad modules based on their ability to reduce the search space, thus, biasing the search space towards a solution. We also prove, under a set of assumptions, that the systematic encapsulation of lower order modules into higher order modules does not change the size or bias of a search space and that this process produces a hierarchy of equivalent search spaces.

Emergence of genomic self-similarity in location independent representations

A key property for predicting the effectiveness of stochastic search techniques, including evolutionary algorithms, is the existence of a positive correlation between the form and the quality of candidate solutions. In this paper we show that when the ordering of genomic symbols in a genetic algorithm is completely independent of the fitness function and therefore free to evolve along with the candidate solutions it encodes, the resulting genomes self-organize into self-similar structures that favor this key stochastic search property.

On the performance effects of unbiased module encapsulation

A recent theoretical investigation of modular representations shows that certain modularizations can introduce a distance bias into a landscape. This was a static analysis, and empirical investigations were used to connect formal results to performance. Here we replace this experimentation with an introductory runtime analysis of performance. We study a base-line, unbiased modularization that makes use of a complete module set (CMS), with special focus on strings that grow logarithmically with the problem size. We learn that even unbiased modularizations can have profound effects on problem performance. Our (1+1) CMS-EA optimizes a generalized OneMax problem in Ω(n2) time, provably worse than a (1+1) EA. More generally, our (1+1) CMS-EA optimizes a particular class of concatenated functions in O(2lm k n) time, where lm is the length of module strings and k is the number of module positions, when the modularization is aligned with the problem separability. We compare our results to known results for traditional EAs, and develop new intuition about modular encapsulation. We observe that search in the CMS-EA is essentially conducted at two levels (intra- and extra-module) and use this observation to construct a module trap, requiring super-polynomial time for our CMS-EA and O(n ln n) for the analogous EA.

Analyzing the effects of module encapsulation on search space bias

Modularity is thought to improve the evolvability of biological systems [18, 22]. Recent studies in the field of evolutionary computation show that the use of modularity improves performance and scalability of evolutionary algorithms for certain applications. [5, 12, 15, 16, 17]. The effects of introducing modularity to evolutionary search, however, are not well understood. This paper focuses on analyzing the effects of modularity on evolutionary computation. In particular, we analyze the effects of modular representations on the search space bias.

On favoring positive correlations between form and quality of candidate solutions via the emergence of genomic self-similarity

A key property for the effectiveness of stochastic search techniques, including evolutionary algorithms, is the existence of a positive correlation between the form and the quality of candidate solutions. In this paper, we show that when the ordering of genomic symbols in a genetic algorithm is completely independent of the fitness function and therefore free to evolve along the candidate solutions it encodes, the resulting genomes self-organize into self-similar structures that favor this key stochastic search property.

Role of entrepreneurial support for networking in innovation ecosystems: an agent based approach

Entrepreneurial support organizations are among the most successful approaches for economic growth. There are multiple dimensions of entrepreneurial support activities such as resource provision, funding or networking support. In this paper, we present an approach for the assessment and analysis of entrepreneurial support for networking and its effects on global innovation ecosystems. The innovation ecosystem in our approach is modeled as a complex adaptive network by using an agent-based modeling methodology with a focus on entrepreneurial support organizations. A portion of the economic entities in this ecosystem is provided with entrepreneurial support of different types to assess their effects. The results highlight the positive impact of networking support on the innovation ecosystem.

On location independent representations and self-organization

We study the self-organization of genomic symbols on a genetic algorithm with a location independent representation—the Proportional Genetic Algorithm (PGA) [2]. Self-organization of genomic symbols is possible because location independent representations ensure the absence of selective pressure for a particular order. We hypothesize that self-similarity emerges because self-similar genomes are more robust with respect to crossover and mutation and because it favors positive correlations between the form and quality of candidate solutions.