LandscapeEC: Adding Geographical Structure to Cellular Evolutionary Algorithms Lucas Ellgren and Nicholas Freitag McPhee Division of Science and Mathematics University of Minnesota, Morris Morris, MN 562367 ellgr001@morris.umn.edu mcphee@morris.umn.edu Abstract Evolutionary computation is a field of Computer Science in which possible solu- tions to a problem are represented as individuals and undergo the basic principles of recombination and mutation to evolve an optimal or near-optimal solution to a prob- lem. In this paper we introduce LandscapeEC, a new type of evolutionary algorithm (EA) that introduces the concept of geography to more effectively evolve solutions to problems. In cellular EAs, individuals are placed in cells on a grid, and can only reproduce with nearby individuals. LandscapeEC is a type of cellular EA which uses geography to add a landscape to the grid. In real-world biology, organisms in different locations must adapt to different conditions (e.g., higher temperatures, less rainfall) in order to survive. In LandscapeEC, geography introduces restrictions that individuals must meet in order to live in each cell. These restrictions are usually sub-problems derived from the chosen problem. By arranging these restrictions in the landscape, we can encourage individuals to gradually make their way across various sub-problems of roughly increasing difficulty of survival, drawing closer to a full solution as they do. Here we present the results of experiments with several different kinds of geogra- phy, including flat geography, gradient geography and fractal geography, all applied to square 2-D grids. Flat geography is essentially the same as traditional cellular EAs; individuals do not need to meet any restrictions to live. Gradient geography creates a smooth gradient of cells that gradually increase in difficulty as they move closer and closer to the center of the grid. Fractal geography is similar to gradient geogra- phy, but the gradient is generated using fractals with random noise to create a rough, unsymmetrical landscape. In this initial study we used 3-SAT as our test problem, as it is an NP-complete optimization problem which can be easily broken down into sub-problems. Our com- parison of these different kinds of geography will determine if adding geography to cellular EAs will increase their effectiveness, efficiency and ability to maintain a di- verse population. 1