Geometric Semantic Genetic Programming

Traditional Genetic Programming (GP) searches the space of functions/programs by using search operators that manipulate their syntactic representation, regardless of their actual semantics/behaviour. Recently, semantically aware search operators have been shown to outperform purely syntactic operators. In this work, using a formal geometric view on search operators and representations, we bring the semantic approach to its extreme consequences and introduce a novel form of GP – Geometric Semantic GP (GSGP) – that searches directly the space of the underlying semantics of the programs. This perspective provides new insights on the relation between program syntax and semantics, search operators and fitness landscape, and allows for principled formal design of semantic search operators for different classes of problems. We de- rive specific forms of GSGP for a number of classic GP domains and experimentally demonstrate their superiority to conventional operators

Geometric Semantic Genetic Programming

Traditional Genetic Programming (GP) searches the space of functions/programs by using search operators that manipulate their syntactic representation, regardless of their actual semantics/behaviour. Recently, semantically aware search operators have been shown to outperform purely syntactic operators. In this work, using a formal geometric view on search operators and representations, we bring the semantic approach to its extreme consequences and introduce a novel form of GP – Geometric Semantic GP (GSGP) – that searches directly the space of the underlying semantics of the programs. This perspective provides new insights on the relation between program syntax and semantics, search operators and fitness landscape, and allows for principled formal design of semantic search operators for different classes of problems. We de- rive specific forms of GSGP for a number of classic GP domains and experimentally demonstrate their superiority to conventional operators

A Mathematical Unification of Geometric Crossovers Defined on Phenotype Space

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. This paper is motivated by the fact that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. In this paper, we study a metric transformation, the quotient metric space, that gives rise to the notion of quotient geometric crossover. This turns out to be a very versatile notion. We give many example applications of the quotient geometric crossover

Evolutionary Algorithms for Reinforcement Learning

There are two distinct approaches to solving reinforcement learning problems, namely, searching in value function space and searching in policy space. Temporal difference methods and evolutionary algorithms are well-known examples of these approaches. Kaelbling, Littman and Moore recently provided an informative survey of temporal difference methods. This article focuses on the application of evolutionary algorithms to the reinforcement learning problem, emphasizing alternative policy representations, credit assignment methods, and problem-specific genetic operators. Strengths and weaknesses of the evolutionary approach to reinforcement learning are presented, along with a survey of representative applications

Considerations for Rapidly Converging Genetic Algorithms Designed for Application to Problems with Expensive Evaluation Functions

A genetic algorithm is a technique designed to search large problem spaces using the Darwinian concepts of evolution. Solution representations are treated as living organisms. The procedure attempts to evolve increasingly superior solutions. As in natural genetics, however, there is no guarantee that the optimum organism will be produced. One of the problems in producing optimal organisms in a genetic algorithm is the difficulty of premature convergence. Premature convergence occurs when the organisms converge in similarity to a pattern which is sub-optimal, but insufficient genetic material is present to continue the search beyond this sub-optimal level, called a local maximum. The prevention of premature convergence of the organisms is crucial to the success of most genetic algorithms. In order to prevent such convergence, numerous operators have been developed and refined. All such operators, however, rely on the property of the underlying problem that the evaluation of individuals is a computationally inexpensive process. In this paper, the design of genetic algorithms which intentionally converge rapidly is addressed. The design considerations are outlined, and the concept is applied to an NP-Complete problem, known as a Crozzle, which does not have an inexpensive evaluation function. This property would normally make the Crozzle unsuitable for processing by a genetic algorithm. It is shown that a rapidly converging genetic algorithm can successfully reduce the effective complexity of the problem

A systematic review of protocol studies on conceptual design cognition: design as search and exploration

This paper reports findings from the first systematic review of protocol studies focusing specifically on conceptual design cognition, aiming to answer the following research question: What is our current understanding of the cognitive processes involved in conceptual design tasks carried out by individual designers? We reviewed 47 studies on architectural design, engineering design and product design engineering. This paper reports 24 cognitive processes investigated in a subset of 33 studies aligning with two viewpoints on the nature of designing: (V1) design as search (10 processes, 41.7%); and (V2) design as exploration (14 processes, 58.3%). Studies on search focused on solution search and problem structuring, involving: long-term memory retrieval; working memory; operators and reasoning processes. Studies on exploration investigated: co-evolutionary design; visual reasoning; cognitive actions; and unexpected discovery and situated requirements invention. Overall, considerable conceptual and terminological differences were observed among the studies. Nonetheless, a common focus on memory, semantic, associative, visual perceptual and mental imagery processes was observed to an extent. We suggest three challenges for future research to advance the field: (i) developing general models/theories; (ii) testing protocol study findings using objective methods conducive to larger samples and (iii) developing a shared ontology of cognitive processes in design

Morphological filter mean-absolute-error representation theorems and their application to optimal morphological filter design

The present thesis derives error representations and develops design methodologies for optimal mean-absolute-error (MAE) morphological-based filters. Four related morphological-based filter-types are treated. Three are translation-invariant, monotonically increasing operators, and our analysis is based on the Matheron (1975) representation. In this class we analyze conventional binary, conventional gray-scale, and computational morphological filters. The fourth filter class examined is that of binary translation invariant operators. Our analysis is based on the Banon and Barrera (1991) representation and hit-or-miss operator of Serra (1982). A starting point will be the optimal morphological filter paradigm of Dougherty (1992a,b) whose analysis de scribes the optimal filter by a system of nonlinear inequalities with no known method of solution, and thus reduces filter design to minimal search strategies. Although the search analysis is definitive, practical filter design remained elu sive because the search space can be prohibitively large if it not mitigated in some way. The present thesis extends from Dougherty\u27s starting point in several ways. Central to the thesis is the MAE analysis for the various filter settings, where in each case, a theorem is derived that expresses overall filter MAE as a sum of MAE values of individual structuring-element filters and MAE of combinations of unions (maxima) of those elements. Recursive forms of the theorems can be employed in a computer algorithm to rapidly evaluate combinations of structuring elements and search for an optimal filter basis. Although the MAE theorems provide a rapid means for examining the filter design space, the combinatoric nature of this space is, in general, too large for a exhaustive search. Another key contribution of this thesis concerns mitigation of the computational burden via design constraints. The resulting constrained filter will be suboptimal, but, if the constraints are imposed in a suitable man ner, there is little loss of filter performance in return for design tractability. Three constraint approaches developed here are (1) limiting the number of terms in the filter expansion, (2) constraining the observation window, and (3) employing structuring element libraries from which to search for an optimal basis. Another contribution of this thesis concerns the application of optimal morphological filters to image restoration. Statistical and deterministic image and degradation models for binary and low-level gray images were developed here that relate to actual problems in the optical character recognition and electronic printing fields. In the filter design process, these models are employed to generate realizations, from which we extract single-erosion and single-hit-or-miss MAE statistics. These realization-based statistics are utilized in the search for the optimal combination of structuring elements