Using Co-solvability to Model and Exploit Synergetic Effects in Evolution

We introduce, analyze, and experimentally verify the concept of co-solvability, meant as the ability of a solution maintained by an evolutionary run to solve (correctly process) a pair of fitness cases (tests). The method based on this concept can be considered as a second-order implicit fitness sharing, where solutions compete for the rewards granted for solving pairs of tests, rather than single tests. We prove that co-solvability fitness function is by definition synergistic and imposes selection pressure which is qualitatively different from that induced by standard fitness function or implicit fitness sharing. The results of experimental verification on eight genetic programming tasks demonstrate that evolutionary runs driven by the proposed fitness function usually converge faster to global optima than other methods

Lexicase selection in Learning Classifier Systems

The lexicase parent selection method selects parents by considering performance on individual data points in random order instead of using a fitness function based on an aggregated data accuracy. While the method has demonstrated promise in genetic programming and more recently in genetic algorithms, its applications in other forms of evolutionary machine learning have not been explored. In this paper, we investigate the use of lexicase parent selection in Learning Classifier Systems (LCS) and study its effect on classification problems in a supervised setting. We further introduce a new variant of lexicase selection, called batch-lexicase selection, which allows for the tuning of selection pressure. We compare the two lexicase selection methods with tournament and fitness proportionate selection methods on binary classification problems. We show that batch-lexicase selection results in the creation of more generic rules which is favorable for generalization on future data. We further show that batch-lexicase selection results in better generalization in situations of partial or missing data.Comment: Genetic and Evolutionary Computation Conference, 201

General Program Synthesis from Examples Using Genetic Programming with Parent Selection Based on Random Lexicographic Orderings of Test Cases

Software developers routinely create tests before writing code, to ensure that their programs fulfill their requirements. Instead of having human programmers write the code to meet these tests, automatic program synthesis systems can create programs to meet specifications without human intervention, only requiring examples of desired behavior. In the long-term, we envision using genetic programming to synthesize large pieces of software. This dissertation takes steps toward this goal by investigating the ability of genetic programming to solve introductory computer science programming problems. We present a suite of 29 benchmark problems intended to test general program synthesis systems, which we systematically selected from sources of introductory computer science programming problems. This suite is suitable for experiments with any program synthesis system driven by input/output examples. Unlike existing benchmarks that concentrate on constrained problem domains such as list manipulation, symbolic regression, or boolean functions, this suite contains general programming problems that require a range of programming constructs, such as multiple data types and data structures, control flow statements, and I/O. The problems encompass a range of difficulties and requirements as necessary to thoroughly assess the capabilities of a program synthesis system. Besides describing the specifications for each problem, we make recommendations for experimental protocols and statistical methods to use with the problems. This dissertation\u27s second contribution is an investigation of behavior-based parent selection in genetic programming, concentrating on a new method called lexicase selection. Most parent selection techniques aggregate errors from test cases to compute a single scalar fitness value; lexicase selection instead treats test cases separately, never comparing error values of different test cases. This property allows it to select parents that specialize on some test cases even if they perform poorly on others. We compare lexicase selection to other parent selection techniques on our benchmark suite, showing better performance for lexicase selection. After observing that lexicase selection increases exploration of the search space while also increasing exploitation of promising programs, we conduct a range of experiments to identify which characteristics of lexicase selection influence its utility

Mathematical Economics

This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

The Thirteenth Annual Conference YUCOMAT 2011: Programme and the Book of Abstracts

The First Conference on materials science and engineering, including physics, physical chemistry, condensed matter chemistry, and technology in general, was held in September 1995, in Herceg Novi. An initiative to establish Yugoslav Materials Research Society was born at the conference and, similar to other MR societies in the world, the programme was made and objectives determined. The Yugoslav Materials Research Society (Yu-MRS), a nongovernment and non-profit scientific association, was founded in 1997 to promote multidisciplinary goal-oriented research in materials science and engineering. The main task and objective of the Society has been to encourage creativity in materials research and engineering to reach a harmonic coordination between achievements in this field in our country and analogous activities in the world with an aim to include our country into global international projects. Until 2003, Conferences were held every second year and then they grew into Annual Conferences that were traditionally held in Herceg Novi in September of every year. In 2007 Yu-MRS formed two new MRS: MRS-Serbia (official successor of Yu-MRS) and MRS-Montenegro (in founding). In 2008, MRS – Serbia became a member of FEMS (Federation of European Materials Societies)