Unveiling evolutionary algorithm representation with DU maps

Evolutionary algorithms (EAs) have proven to be effective in tackling problems in many different domains. However, users are often required to spend a significant amount of effort in fine-tuning the EA parameters in order to make the algorithm work. In principle, visualization tools may be of great help in this laborious task, but current visualization tools are either EA-specific, and hence hardly available to all users, or too general to convey detailed information. In this work, we study the Diversity and Usage map (DU map), a compact visualization for analyzing a key component of every EA, the representation of solutions. In a single heat map, the DU map visualizes for entire runs how diverse the genotype is across the population and to which degree each gene in the genotype contributes to the solution. We demonstrate the generality of the DU map concept by applying it to six EAs that use different representations (bit and integer strings, trees, ensembles of trees, and neural networks). We present the results of an online user study about the usability of the DU map which confirm the suitability of the proposed tool and provide important insights on our design choices. By providing a visualization tool that can be easily tailored by specifying the diversity (D) and usage (U) functions, the DU map aims at being a powerful analysis tool for EAs practitioners, making EAs more transparent and hence lowering the barrier for their use

Multi-level diversity promotion strategies for Grammar-guided Genetic Programming

Grammar-guided Genetic Programming (G3P) is a family of Evolutionary Algorithms that can evolve programs in any language described by a context-free grammar. The most widespread members of this family are based on an indirect representation: a sequence of bits or integers (the genotype) is transformed into a string of the language (the phenotype) by means of a mapping function, and eventually into a fitness value. Unfortunately, the flexibility brought by this mapping is also likely to introduce non-locality phenomena, reduce diversity, and hamper the effectiveness of the algorithm. In this paper, we experimentally characterize how population diversity, measured at different levels, varies for four popular G3P approaches. We then propose two strategies for promoting diversity which are general, independent both from the specific problem being tackled and from the other components of the Evolutionary Algorithm, such as genotype-phenotype mapping, selection criteria, and genetic operators. We experimentally demonstrate their efficacy in a wide range of conditions and from different points of view. The results also confirm the preponderant importance of the phenotype-level analyses in diversity promotion

Weighted Hierarchical Grammatical Evolution

Grammatical evolution (GE) is one of the most widespread techniques in evolutionary computation. Genotypes in GE are bit strings while phenotypes are strings, of a language defined by a user-provided context-free grammar. In this paper, we propose a novel procedure for mapping genotypes to phenotypes that we call weighted hierarchical GE (WHGE). WHGE imposes a form of hierarchy on the genotype and encodes grammar symbols with a varying number of bits based on the relative expressive power of those symbols. WHGE does not impose any constraint on the overall GE framework, in particular, WHGE may handle recursive grammars, uses the classical genetic operators, and does not need to define any bound in advance on the size of phenotypes. We assessed experimentally our proposal in depth on a set of challenging and carefully selected benchmarks, comparing the results of the standard GE framework as well as two of the most significant enhancements proposed in the literature: 1) position-independent GE and 2) structured GE. Our results show that WHGE delivers very good results in terms of fitness as well as in terms of the properties of the genotype-phenotype mapping procedure

Landing gear Patent

Vertically descending flight vehicle landing gear for rough terrai

Designing automatically a representation for grammatical evolution

A long-standing problem in Evolutionary Computation consists in how to choose an appropriate representation for the solutions. In this work we investigate the feasibility of synthesizing a representation automatically, for the large class of problems whose solution spaces can be defined by a context-free grammar. We propose a framework based on a form of meta-evolution in which individuals are candidate representations expressed with an ad hoc language that we have developed to this purpose. Individuals compete and evolve according to an evolutionary search aimed at optimizing such representation properties as redundancy, uniformity of redundancy, and locality. We assessed experimentally three variants of our framework on established benchmark problems and compared the resulting representations to human-designed representations commonly used (e.g., classical Grammatical Evolution). The results are promising as the evolved representations indeed exhibit better properties than the human-designed ones. Furthermore, the evolved representations compare favorably with the human-designed baselines in search effectiveness as well. Specifically, we select a best evolved representation as the representation with best search effectiveness on a set of learning problems and assess its effectiveness on a separate set of challenging validation problems. For each of the three proposed variants of our framework, the best evolved representation exhibits an average fitness rank on the set of validation problems that is better than the average fitness rank of the human-designed baselines on the same problems

On the Automatic Design of a Representation for Grammar-Based Genetic Programming

A long-standing problem in Evolutionary Computation consists in how to choose an appropriate representation for the solutions. In this work we investigate the feasibility of synthesizing a representation automatically, for the large class of problems whose solution spaces can be defined by a context-free grammar. We propose a framework based on a form of meta-evolution in which individuals are candidate representations expressed with an ad hoc language that we have developed to this purpose. Individuals compete and evolve according to an evolutionary search aimed at optimizing such representation properties as redundancy, locality, uniformity of redundancy. We assessed experimentally three variants of our framework on established benchmark problems and compared the resulting representations to human-designed representations commonly used (e.g., classical Grammatical Evolution). The results are promising in the sense that the evolved representations indeed exhibit better properties than the human-designed ones. Furthermore, while those improved properties do not result in a systematic improvement of search effectiveness, some of the evolved representations do improve search effectiveness over the human-designed baseline

Valuing the Goodness of Earth

Though John Chrysostom, Augustine, and Thomas Aquinas, when reflecting on the creation story, valued all types of creatures, living and non-living, intrinsically for their unique goodness and instrumentally for the sustenance they provide to others, they valued most highly their complex interrelation in the physical world

Use of Special Function in the Production of Heat in a Cylinder

We have considered the application of H-function, generalized hypergeometric function and Gauss's hypergeometric function in solving the fundamental differential equation of diffusion of heat in a cylinder. A few known results have also been derived as particular cases