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Competitive Coevolution through Evolutionary Complexification
 Journal of Artificial Intelligence Research
, 2002
"... Two major goals in machine learning are the discovery of complex multidimensional solutions and continual improvement of existing solutions. In this paper, we argue that complexification, i.e. the incremental elaboration of solutions through adding new structure, achieves both these goals. We demons ..."
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Cited by 204 (72 self)
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Two major goals in machine learning are the discovery of complex multidimensional solutions and continual improvement of existing solutions. In this paper, we argue that complexification, i.e. the incremental elaboration of solutions through adding new structure, achieves both these goals. We demonstrate the power of complexification through the NeuroEvolution of Augmenting Topologies (NEAT) method, which evolves increasingly complex neural network architectures. NEAT is applied to an openended coevolutionary robot duel domain where robot controllers compete head to head. Because the robot duel domain supports a wide range of sophisticated strategies, and because coevolution benefits from an escalating arms race, it serves as a suitable testbed for observing the effect of evolving increasingly complex controllers. The result is an arms race of increasingly sophisticated strategies. When compared to the evolution of networks with fixed structure, complexifying networks discover significantly more sophisticated strategies. The results suggest that in order to realize the full potential of evolution, and search in general, solutions must be allowed to complexify as well as optimize.
Ideal Evaluation from Coevolution
 Evolutionary Computation
, 2004
"... In many problems of interest, performance can be evaluated using tests, such as examples in concept learning, test points in function approximation, and opponents in gameplaying. Evaluation on all tests is often infeasible. Identification of an accurate evaluation or fitness function is a difficult ..."
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Cited by 68 (6 self)
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In many problems of interest, performance can be evaluated using tests, such as examples in concept learning, test points in function approximation, and opponents in gameplaying. Evaluation on all tests is often infeasible. Identification of an accurate evaluation or fitness function is a difficult problem in itself, and approximations are likely to introduce human biases into the search process. Coevolution evolves the set of tests used for evaluation, but has so far often led to inaccurate evaluation. We show that for any set of learners, a Complete Evaluation Set can be determined that provides ideal evaluation as specified by Evolutionary MultiObjective Optimization. This provides a principled approach to evaluation in coevolution, and thereby brings automatic ideal evaluation within reach. The Complete Evaluation Set is of manageable size, and progress towards it can be accurately measured. Based on this observation, an algorithm named DELPHI is developed. The algorithm is tested on problems likely to permit progress on only a subset of the underlying objectives. Where all comparison methods result in overspecialization, the proposed method and a variant achieve sustained progress in all underlying objectives. These findings demonstrate that ideal evaluation may be approximated by practical algorithms, and that accurate evaluation for testbased problems is possible even when the underlying objectives of a problem are unknown.
Pareto coevolution: Using performance against coevolved opponents in a game as dimensions for Pareto selection
 Proceedings of the Genetic and Evolutionary Computation Conference, GECCO2001
, 2001
"... When using an automatic discovery method to nd a good strategy in a game, we hope to nd one that performs well against a wide variety of opponents. An appealing notion in the use of evolutionary algorithms to coevolve strategies is that the population represents a set of dierent strategies ag ..."
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Cited by 45 (3 self)
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When using an automatic discovery method to nd a good strategy in a game, we hope to nd one that performs well against a wide variety of opponents. An appealing notion in the use of evolutionary algorithms to coevolve strategies is that the population represents a set of dierent strategies against which a player must do well. Implicit here is the idea that dierent players represent dierent \dimensions" of the domain, and being a robust player means being good in many (preferably all) dimensions of the game. Pareto coevolution makes this idea of \players as dimensions" explicit. By explicitly treating each player as a dimension, or objective, we may then use established multiobjective optimization techniques to nd robust strategies. In this paper, we apply Pareto coevolution to Texas Hold'em poker, a complex realworld game of imperfect information. The performance of our Pareto coevolution algorithm is compared with that of a conventional genetic algorithm and shown to be promising. 1
A Mathematical Framework for the Study of Coevolution
 Foundations of Genetic Algorithms 7
, 2003
"... Despite achieving compelling results in engineering and optimization problems, coevolutionary algorithms remain difficult to understand, with most knowledge to date coming from practical successes and failures, not from theoretical understanding. Thus, explaining why coevolution succeeds is still ..."
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Cited by 36 (11 self)
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Despite achieving compelling results in engineering and optimization problems, coevolutionary algorithms remain difficult to understand, with most knowledge to date coming from practical successes and failures, not from theoretical understanding. Thus, explaining why coevolution succeeds is still more art than science. In this paper, we present a theoretical framework for studying coevolution based on the mathematics of ordered sets.
The Dominance Tournament Method of Monitoring Progress in Coevolution
, 2002
"... In competitive coevolution, the goal is to establish an "arms race" that will lead to increasingly sophisticated strategies. The existing methods for monitoring progress in coevolution are designed to demonstrate that the arms race indeed occurred. However, two issues remain: (1) How can p ..."
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Cited by 32 (5 self)
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In competitive coevolution, the goal is to establish an "arms race" that will lead to increasingly sophisticated strategies. The existing methods for monitoring progress in coevolution are designed to demonstrate that the arms race indeed occurred. However, two issues remain: (1) How can progress be monitored efficiently so that every generation champion does not need to be compared to every other generation champion? (2) How can a monitoring method determine whether strictly more sophisticated strategies are discovered as the evolution progresses? We introduce a new method for tracking progress, the dominance tournament, which provides an answer to both questions. The dominance tournament shows how different coevolution runs continue to innovate for different periods of time, reveals the precise generation in each run where stagnation occurs, and identifies the best individuals found during the runs. Such differences are difficult to detect using standard techniques but are clearly distinguished in a dominance tournament, which makes this method a highly useful tool in understanding progress in coevolution.
On identifying global optima in cooperative coevolution
 In GECCO 2005: Proceedings of the 2005 conference on Genetic and evolutionary computation
, 2005
"... When applied to optimization problems, Cooperative Coevolutionary Algorithms (CCEA) have been observed to exhibit a behavior called relative overgeneralization. Roughly, they tend to identify local optima with large basins of attraction which may or may not correspond to global optima. A question wh ..."
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Cited by 32 (4 self)
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When applied to optimization problems, Cooperative Coevolutionary Algorithms (CCEA) have been observed to exhibit a behavior called relative overgeneralization. Roughly, they tend to identify local optima with large basins of attraction which may or may not correspond to global optima. A question which arises is whether one can modify the algorithm to promote the discovery of global optima. We argue that a mechanism from Pareto coevolution can achieve this end. We observe that in CCEAs candidate individuals from one population are used as tests or measurements of individuals in other populations; by treating individuals as tests in this way, a finergrained comparison can be made among candidate individuals. This finergrained view permits an algorithm to see when two candidates are differently capable, even when one’s evident value is higher than the other’s. By modifying an existing CCEA to compare individuals using Pareto dominance we have produced an algorithm which reliably finds global optima. We demonstrate the algorithm on two Maximum of Two Quadratics problems and discuss why it works.
Ordertheoretic Analysis of Coevolution Problems: Coevolutionary Statics
 IN PROCEEDINGS OF THE GECCO2002 WORKSHOP ON COEVOLUTION: UNDERSTANDING COEVOLUTION
, 2002
"... We present an ordertheoretic framework for analyzing coevolution problems. The framework focuses attention on the underlying problem definition, or statics of coevolution, as opposed to the dynamics of search algorithms. We define a notion of solution for coevolution which generalizes similar ..."
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Cited by 25 (7 self)
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We present an ordertheoretic framework for analyzing coevolution problems. The framework focuses attention on the underlying problem definition, or statics of coevolution, as opposed to the dynamics of search algorithms. We define a notion of solution for coevolution which generalizes similar solution concepts in GA function optimization and MOO. We then define the ideal test set, a potentially small set of tests which allow us to find the solution set of a problem. One feature of the ideal test set is that we are able to categorize problems by considering its cardinality. We
Representation development from ParetoCoevolution
 in: Genetic and Evolutionary Computation Conference, GECCO 2003, 2003
"... Abstract. Genetic algorithms generally use a fixed problem representation that maps variables of the search space to variables of the problem, and operators of variation that are fixed over time. This limits their scalability on nonseparable problems. To address this issue, methods have been propos ..."
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Cited by 23 (4 self)
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Abstract. Genetic algorithms generally use a fixed problem representation that maps variables of the search space to variables of the problem, and operators of variation that are fixed over time. This limits their scalability on nonseparable problems. To address this issue, methods have been proposed that coevolve explicitly represented modules. An open question is how modules in such coevolutionary setups should be evaluated. Recently, Paretocoevolution has provided a theoretical basis for evaluation in coevolution. We define a notion of functional modularity, and objectives for module evaluation based on ParetoCoevolution. It is shown that optimization of these objectives maximizes functional modularity. The resulting evaluation method is developed into an algorithm for variable length, open ended development of representations called DevRep. DevRep successfully identifies large partial solutions and greatly outperforms fixed length and variable length genetic algorithms on several test problems, including the 1024bit HierarchicalXOR problem.
managed challenge’ alleviates disengagement in coevolutionary system identification
 GECCO 2005: Proceedings of the 2005 conference on Genetic and evolutionary computation
, 2005
"... In previous papers we have described a coevolutionary algorithm (EEA), the estimationexploration algorithm, that infers the hidden inner structure of systems using minimal testing. In this paper we introduce the concept of ‘managed challenge ’ to alleviate the problem of disengagement in this and ..."
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Cited by 20 (5 self)
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In previous papers we have described a coevolutionary algorithm (EEA), the estimationexploration algorithm, that infers the hidden inner structure of systems using minimal testing. In this paper we introduce the concept of ‘managed challenge ’ to alleviate the problem of disengagement in this and other coevolutionary algorithms. A known problem in coevolutionary dynamics occurs when one population systematically outperforms the other, resulting in a loss of selection pressure for both populations. In system identification (which deals with determining the inner structure of a system using only input/output data), multiple trials (a test that causes the system to produce some output) on the system to be identified must be performed. When such trials are costly, this disengagement results in wasted data that is not utilized by the evolutionary process. Here we propose that data from futile interactions should be stored during disengagement and automatically reintroduced later, when the population reengages: we refer to this as the test bank. We demonstrate that the advantage of the test bank is twofold: it allows for the discovery of more accurate models, and it reduces the amount of required training data for both parametric identification – parameterizing inner structure – and symbolic identification – approximating inner structure using symbolic equations – of nonlinear systems.