Results

Interesting results were obtained in both problems where we studied the representa- tions for shapes. This is particularly important in our context of situated embodied self-organized intelligence that is in the very focus of this thesis. Even though combining evolution of robot morphology with controllers is beyond the scope of this thesis, representing the shapes is very central to the main theme.

Topological Optimum Design

For all three shapes, 8x8, 16x16, and 32x32, both of the new representations (polygon holes, and polygon-holes with repetitions, labeled modular ) outperformed both the original Voronoi and rectangle-holes representations as expected – the advantage of a much stronger flexibility of polygonal shapes, where sides are not necessarily aligned

Figure 5.12: Best individual fitness with standard deviations (average of 20 different random 3D models 20x20x5) for layer 4. Steady-state selection is compared to both roulette-wheel selection (left) and multiple-deme with 5 populations of 1/5 size of population size of steady-state GA and 10 individuals migrating after each generation (right). Both comparisons show that the steady-state GA performs better.

with the grid, outweighs the disadvantage of larger search space. See Figure 5.13 for visualization of partial results and Figure 5.14, Figure 5.15, and Figure 5.16 for plots of fitness average from 20 runs for different shapes. The difference between the polygonal holes and modular representations is not very significant at the sample shapes that were used in the experiments. Our results suggest that evolution of shapes requires a richer set of operators and richer representations, which better adapt to specific details and features of the evolved shape in a particular design problem. However, attention needs to be paid to avoid too large search spaces, or redundant options which can hinder the progress of the evolutionary design runs.

LEGO Brick Layout

We have successfully evolved simple test shapes with direct genotype representation consisting of ten layers with 20x20 square profile. See Figure 5.17 for an example evolved layout of the first two layers. We studied the performance of the algorithm depending on the number of populations and the number of migrating individuals. We found that in our case, multiple-deme GA did not outperform single-population steady-state GA. See [Petroviˇc, 2001a] for more details, where we also proposed extensions of the direct representation with indirect features. This was taken further in the cooperation with the group at Maersk institute in Odense, and an improved result was obtained with a representation where the bricks could be placed with repetition. The genotype was extended with the number of placements and a relative displacement between the repetitions. The Figure 5.19 plots average of best fitness from 20 runs and shows that the representation with indirect features outperforms the direct representation. The functionality of the algorithm has been verified on evolving larger structures, examples of a hollow cyllinder and a Chinese bridge are shown at Figure 5.18. The challenge of deciding a good genotype representation of shapes is an important one. Using indirect representations can have several strong

5.5 Evolution of Shape and Form 115

Figure 5.13: Example runs of 16x16 shape (see Figure 5.10): Top-left: Voronoi representation after 100 generations with fitness around 1.7 (fitness is minimized), top-right: Rectangles representation after 150 generations with fitness around 0.082, bottom-left: Holes representations after generation 150 with fitness around 0.02, and bottom-right: Holes with repetitions representation after 120 generations with fitness around 0.16.

Figure 5.14: Best fitness (average of 20 runs) for the four different representations, 8x8 shape.

Figure 5.15: Best fitness (average of 20 runs) for the four different representations, 16x16 shape.

Figure 5.16: Best fitness (average of 20 runs) for the four different representations, 32x32 shape.

5.5 Evolution of Shape and Form 117

Figure 5.17: The first two layers evolved with steady-state GA. Notice the low number of edges common in both layers, which makes the layout more stable.

Figure 5.18: Shapes with evolved brick layouts, from [Na, 2002].

Figure 5.19: Comparison of the performance of the improved GA that has features of indirect representations (repetitive brick placements), [Na, 2002].

advantages:

• Information can be compressed – it is not required to create one-to-one blueprint of the whole shape in the genotype. This allows for coping with the curse of dimensionality.

• Indirect representations can focus on details, which are important and need to be described with finer resolution, while covering larger plain areas with several bits of the genotype.

• The internal structures, symmetries, repetitions, and modularities of shapes can be exploited only using indirect representations.

• Indirect representations are better prone to local optima: small modifications in the genotype can represent large changes in the target shape, and thus bring a locally converged population to a new promising areas.

• Indirect representations are more likely to create shapes with higher aesthetic value due to the symmetries and regularities.

• Shapes created using indirect representations can be easier to analyze by analytical methods thanks to higher uniformity of their structure.

5.6

Chapter Summary

• The robots that we work with throughout the whole thesis are educational robotics sets.

• We find it important to understand how these are used for their original purpose in order to understand their potential.

• It allows us to make contributions in that area as well as create links with our field, Evolutionary Robotics.

• In addition, we work with a robotics educational platform of drawing robots, and see its functionality being extended to research platform.

• On the tasks of evolving 3D structures from LEGO bricks and 2D topological optimum design, we study the role of representations in evolutionary design. Indirect representations have important properties that make them more suitable for evolutionary design. The evolutionary design is important for Evo- lutionary Robotics that should ultimately involve evolving robot morphologies.

Chapter 6

Comparison of FSA and GP-tree

Representations

6.1

Introduction and Aims

Some of our experiments in this thesis are based on augmented finite-state automata (FSA) used as behavior arbitration in behavior-based mobile robot controllers. Our aim is to design these controllers by the means of evolutionary computation. The main motivation for choosing the state-based representations is their structural similarity to the structure of the robot controller tasks: the robot performing some activity is always in some state while it reactively responds with immediate actions or it proceeds to other states also as a response to environmental percepts – thus the activity of a robotic agent can be modeled by a state diagram accurately. We believe that state-diagram formalisms can in fact steer controllers themselves and be the back-bone of their internal architecture. Secondly, we believe that the state automata are easier to understand, analyze, and verify than other representations, for example neural networks. Thirdly, we believe that state automata are more amenable to incremental construction of the controller, because adding new func- tionality involves adding new states and transitions, and making relatively small changes to the previous states and transitions. On the contrary, neural network architectures often need to be dramatically modified, unless some modular approach is used. However, research in modular neural approaches is still in its very early stages. For an example, see the work of the group at university in Essex [Baldassarre, 2001], or a little bit older overview in [Ronco and Gawthrop, 1995].

While the focus of the experimental work in the following chapters of this thesis lies in the issues of incremental evolution and evolving the arbitration itself, this preliminary study pays attention to evaluating the performance of the state- based representations as such. The purpose is to analyze the performance of the state-based representations and compare it to the performance of the GP- tree representation. See section 2.10 for an overview on FSA as a genotype representation. We study the performance on several artificial tasks of various kinds with the intention to understand the set of tasks, where the state-representation might outperform the GP-tree representation, but also to identify the tasks, where

the state-representations are less efficient. For the purposes of performing these experiments, we have designed a package for evolutionary computation experiments for educational programming environment Imagine Logo [Kalaˇs and Hruˇseck´a, 2004] that has an interface to control both simulated and real robots [Petroviˇc et al., 2006], see section 5.4 on Evolve with Imagine1.