Introduction to combinatorial theory
Introduction to combinatorial theory
Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
Adaptive Penalties for Evolutionary Graph Coloring
AE '97 Selected Papers from the Third European Conference on Artificial Evolution
| Hi-index | 0.00 |
Ramsey Theory studies the existence of highly regular patterns within a large system or a set of randomly selected points or numbers. The role of Ramsey Numbers is to quantify some of the general existential theorems in Ramsey Theory. Attempting to find Ramsey Numbers has been an arduous task that is too often unfruitful. Only a handful of specific numbers are known. Genetic Algorithms (GA), which are based on the idea of optimizing by simulating the natural processes of evolution, have proven successful in solving complex problems that are not easily solved through conventional methods. However, premature convergence is an inherent characteristic of traditional GAs that makes them incapable of searching numerous points in a problem domain. Parallel GA (PGA) is an extension of the classical GA that takes advantage of a GA's inherent parallelism to improve its time performance and reduce the likelihood of premature convergence. A cgGA (Coarse-Grain GA) maintains a number of independent populations and allows for the occasional interchange of individuals. In this manner, a cgGA increases the diversity of search paths and helps to stop premature convergence to nonoptimal solutions. Given this motivation, a tool was developed, called SIPAGAR (Simulated Parallel Genetic Algorithm for finding Ramsey Numbers), that allows us to verify and validate the superior performance of cgGAs over traditional GAs applied to the problem of improving the bounds of classical Ramsey Numbers. Significant differences between the simulated cgGA and traditional GA were observed in both the premature convergence rate and the quality of the results. This leads us to the conclusion that future cgGA-based attempts to improve the bounds of Ramsey Numbers will probably be more promising than those based on traditional GAs.