Cellz: A simple dynamical game for testing evolutionary algorithms Simon M. Lucas Department of Computer Science University of Essex Colchester, Essex CO4 3SQ sml@essex.ac.uk Abstract— The game of Cellz has been designed as a test bed for evolutionary algorithms. The game has a minimal set of rules that nonetheless offer the possibility for complex behaviour to emerge. Computationally, the game is cheap to simulate, which leads to rapid runs of evolutionary algorithms. A key feature of the game is the cell division process, which can lead to evolution in situ without reference to any externally defined fitness function. This paper describes the rationale behind the development of Cellz, the rules of the game and the software interfaces for the cell controllers. The randomness in the game initialisation leads to extremely noisy fitness functions, which adds to the challenge of evolving high-performance controllers. Initial results demonstrate that an evolved perceptron-type controller can achieve mediocre performance on the single-species game. I. I NTRODUCTION When solving a problem with an evolutionary algorithm, arguably the central question is which space to perform the evolutionary search in. For example, standard genetic program- ming searches the space of programs specified as expression trees. Another common space to choose is that of feed-forward neural networks, since these are known to be capable of representing any functional mapping. Therefore, one approach to evolutionary computing is to choose a sufficiently general solution space, and search in this space for solutions to any given problem. On the other hand, intuition suggests that choosing an overly-general space will impede progress towards an acceptable solution, since the size of the space will be much larger than necessary (though note that the evolvability [9], [2] of solutions to a particular problem in a particular space can be more important than the size of the space. Evidence can be found for this in many problem domains, one example being the learning of deterministic finite automata (DFA). Some of the best results for this have been obtained using a simple random hill-climber operating in a cut-down DFA space [18], which gives significantly better performance than more complex genetic programming [4] or cellular en- coding [6] approaches to the problem. The advantage of choosing a problem-specific space to search in is that the learning algorithm only has to learn to solve the problem instance, it does not have to learn to represent solutions to the problem in general. When trying to evolve a competitive game player, however, the appropriate space in which to search is usually far from ap- parent. An overly general space can make the search problem too hard, while an overly simple space runs the risk of being unable to represent good solutions. Cellz provides a simple dynamic environment in which controllers based on different representations and search spaces can compete against each other. A well designed game should have simple rules yet be diffi- cult to master. Cellz has been designed with this in mind. The aim of the game is for a species of cell to eat food, multiply, and collectively attain as much mass as possible within a specified time limit. Cellz is based on a simple continuous 2D physics model simulated in discrete time. The adoption of a continuous state space means that conventional discrete space search procedures such as minimax cannot directly be applied. Furthermore, the way the cells smoothly accelerate and move in chaotic patterns makes the game interesting to observe. The game can involve any number of species, though this paper focusses mostly on the simpler single species game. A. Related Games Cellz has been inspired by many previous games and a- life simulations. Braitenberg’s vehicles [5] demonstrated how interesting and apparently intentional behaviour could arise from very simple circuits when placed in certain environments. Conway’s game of life [14] demonstrated how complex patterns of activity could arise in a grid of very simple cellular automata. Recent work related to this has been done by Miller [20] on evolving automata rules that would generate some desired simple pattern, such as a French flag. In cellular automata work, however, while the rule-set may be evolved, the automata themselves are connected in a fixed topology. The cells in Cellz on the other hand, are free to move. It would be an interesting challenge to get the cells in the game of Cellz to evolve movement rules with the aim of forming particular patterns, but this is not explored in this paper. The simulated version of RoboCup [3] soccer provides an environment in which controllers can be evolved [19]. Russell Abbot 1 has developed also developed a version of football called billiard soccer. This version is based on a simple physics model like Cellz, and this also provides an interesting test-bed for evolving controllers. Abbott’s billiard soccer is built on top 1 Posting to Genetic Programming email list, and personal communication.