Search

Modularity is a system property of many natural and artificial adaptive systems. Evolutionary algorithms designed to produce modular solutions have increased convergence rates and improved generalization ability; however, their performance can be impacted if the task is inherently nonmodular. Previously, we have shown that some design variables can influence whether the task on the remaining variables is inherently modular. We investigate the possibility of exploiting that dependence to simplify optimization and arrive at a general design pattern that we use to show that evolutionary search can seek such modularity-inducing design variable values, thus easing subsequent search for highly fit, modular organization within the remaining design variables. We investigate this approach with embodied agents in which evolutionary discovery of morphology enables subsequent discovery of highly fit, modular controllers and show that it benefits from biasing search toward modular controllers and setting the mutation rate for control policies higher than that for morphology. This work also reinforces our previous finding that the relationship between modularity and evolvability that is well-studied in nonembodied systems can, under certain conditions, be generalized to include embodied systems as well and provides a practical approach to satisfying the conditions in question.

Due to the large number of evaluations required, evolutionary robotics experiments are generally conducted in simulated environments. One way to increase the generality of a robot's behavior is to evolve it in multiple environments. These environment spaces can be defined by the number of free parameters (f) and the number of variations each free parameter can take (n). Each environment space then has nf individual environments. For a robot to be fit in the environment space it must perform well in each of the nf environments. Thus the number of environments grows exponentially as n and f are increased. To mitigate the problem of having to evolve a robot in each environment in the space we introduce the concept of ecological modularity. Ecological modularity is here defined as the robot's modularity with respect to free parameters in the its environment space. We show that if a robot is modular along m of the free parameters in its environment space, it only needs to be evolved in nf-m+1 environments to be fit in all of the nf environments. This work thus presents a heretofore unknown relationship between the modularity of an agent and its ability to generalize evolved behaviors in new environments.

Due to the large number of evaluations required, evolutionary robotics experiments are generally conducted in simulated environments. One way to increase the generality of a robot’s behavior is to evolve it in multiple environments. These environment spaces can be defined by the number of free parameters (f) and the number of variations each free parameter can take (n). Each environment space then has \(n^f\) individual environments. For a robot to be fit in the environment space it must perform well in each of the \(n^f\) environments. Thus the number of environments grows exponentially as n and f are increased. To mitigate the problem of having to evolve a robot in each environment in the space we introduce the concept of ecological modularity. Ecological modularity is here defined as the robot’s modularity with respect to free parameters in its environment space. We show that if a robot is modular along m of the free parameters in its environment space, it only needs to be evolved in \(n^{f-m+1}\) environments to be fit in all of the \(n^f\) environments. This work thus presents a heretofore unknown relationship between the modularity of an agent and its ability to generalize evolved behaviors in new environments.

In evolutionary robotics, populations of robots are typically trained in simulation before one or more of them are instantiated as physical robots. However, in order to evolve robust behavior, each robot must be evaluated in multiple environments. If an environment is characterized by $f$ free parameters, each of which can take one of $n_p$ features, each robot must be evaluated in all $n_p^f$ environments to ensure robustness. Here we show that, if the robots are constrained to have modular morphologies and controllers, they only need to be evaluated in $n_p$ environments to reach the same level of robustness. This becomes possible because the robots evolve such that each module of the morphology allows the controller to independently recognize a familiar percept in the environment, and each percept corresponds to one of the environmental free parameters. When exposed to a new environment, the robot perceives it as a novel combination of familiar percepts which it can solve without requiring further training. A non-modular morphology and controller however perceives the same environment as a completely novel environment, requiring further training. This acceleration in evolvability -- the rate of the evolution of adaptive and robust behavior -- suggests that evolutionary robotics may become a scalable approach for automatically creating complex autonomous machines, if the evolution of neural and morphological modularity is taken into account.

Random recombination in evolutionary algorithms can be counterproductive in systems that evolve increasing modularity, because such operators do not preserve community structures during their development. Partly because of this, methods have been proposed that derandomize recombination by placing potential crossover locations under evolutionary control. Since crossover is likely to be particularly useful when genetic material that generates incipient phenotype modules is recombined, there may be an advantage to seeking such modularity directly in the phenotype and probabilistically focusing recombination at such "hotspot" locations. Here we show that such phenotypically-aware crossover operators can outcompete random or evolved crossover points as the size of the system being evolved grows. As this crossover operator can be viewed as epigenetic, and as epigenetic processes seem to be common in biological systems, other such epigenetic mechanisms may further improve future evolutionary algorithms.

A network is structurally modular if it can be divided into tightly connected groups which are weakly connected or disconnected from each other. Such networks are known to be capable of fast evolutionary adaptation, which makes modularity a highly desired property of networks involved in evolutionary computation. Modularity is known to correlate positively with another network parameter, sparsity. Based on this relationship, we hypothesize that starting evolution with a population of sparse networks should increase the modularity of the evolved networks. We find that this technique can enhance the performance of an existing technique for modularity evolution, multiobjective performance-connection cost (P&CC) optimization, and enable a multiobjective algorithm which maximizes performance and minimizes time since last mutation to produce modular solutions almost as efficiently as the P&CC optimization does.

Although recent work has demonstrated that modularity can increase evolvability in non-embodied systems, it remains to be seen how the morphologies of embodied agents influences the ability of an evolutionary algorithm to find useful and modular controllers for them. We hypothesize that a modular control system may enable different parts of a robot's body to sense and react to stimuli independently, enabling it to correctly recognize a seemingly novel environment as, in fact, a composition of familiar percepts and thus respond appropriately without need of further evolution. Here we provide evidence that supports this hypothesis: We found that such robots can indeed be evolved if (1) the robot's morphology is evolved along with its controller, (2) the fitness function selects for the desired behavior and (3) also selects for conservative and robust behavior. In addition, we show that if constraints (1) and (3) are relaxed, or structural modularity is selected for directly, the robots have too little or too much modularity and lower evolvability. Thus, we demonstrate a previously unknown relationship between modularity and embodied cognition: evolving morphology and control such that robots exhibit conservative behavior indirectly selects for appropriate modularity and, thus, increased evolvability.