Fundamenta Informaticae - Volume 166, issue 2

Authors: Abu Arqub, Omar

Article Type: Research Article

Abstract: The object of this article is to present the computational solution of the time-fractional Schrödinger equation subject to given constraint condition based on the generalized Taylor series formula in the Caputo sense. The algorithm methodology is based on construct a multiple fractional power series solution in the form of a rabidly convergent series with minimum size of calculations using symbolic computation software. The proposed technique is fully compatible with the complexity of this problem and obtained results are highly encouraging. Efficacious computational experiments are provided to guarantee the procedure and to illustrate the theoretical statements of the present algorithm in …order to show its potentiality, generality, and superiority for solving such fractional equation. Graphical results and numerical comparisons are presented and discussed quantitatively to illustrate the solution. Show more

Keywords: Fractional Schrödinger equation, Multiple fractional power series, Residual power series method, Numerical algorithm, Symbolic computations

DOI: 10.3233/FI-2019-1795

Citation: Fundamenta Informaticae, vol. 166, no. 2, pp. 87-110, 2019

Authors: Abu Arqub, Omar

Article Type: Research Article

Abstract: The aim of this article is to introduce the reproducing kernel algorithm for obtaining the numerical solutions of fractional order systems of Dirichlet function types. The algorithm provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n -term of exact solutions, numerical solutions of linear and nonlinear time-fractional equations of homogeneous and nonhomogeneous function type are studied from mathematical viewpoint. Convergence analysis, error estimations, and error bounds for the present algorithm are also discussed. The dynamical properties of these numerical solutions are discussed and the profiles of several representative numerical solutions are …illustrated. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to such systems compared with other numerical methods. Show more

Keywords: Reproducing kernel theory, Boundary value problems, Numerical algorithm, Fractional order system, Dirichlet function types, Comparative analysis

DOI: 10.3233/FI-2019-1796

Citation: Fundamenta Informaticae, vol. 166, no. 2, pp. 111-137, 2019

Authors: Bistarelli, Stefano | Santini, Francesco | Torroni, Paolo

Article Type: Other

DOI: 10.3233/FI-2019-1797

Citation: Fundamenta Informaticae, vol. 166, no. 2, pp. 139-140, 2019

Authors: Fitzgerald, Tadhg | O’Sullivan, Barry

Article Type: Research Article

Abstract: Many modern combinatorial solvers have a variety of parameters through which a user can customise their behaviour. Algorithm configuration is the process of selecting good values for these parameters in order to improve performance. Time and again algorithm configuration has been shown to significantly improve the performance of many algorithms for solving challenging computational problems. Automated systems for tuning parameters regularly out-perform human experts, sometimes but orders of magnitude. Online algorithm configurators, such as ReACTR, are able to tune a solver online without incurring costly offline training. As such ReACTR’s main focus is on runtime minimisation while solving combinatorial …problems. To do this ReACTR adopts a one-pass methodology where each instance in a stream of instances to be solved is considered only as it arrives. As such ReACTR’s performance is sensitive to the order in which instances arrive. It is still not understood which instance orderings positively or negatively effect the performance of ReACTR. This paper investigates the effect of instance ordering and grouping by empirically evaluating different instance orderings based on difficulty and feature values. Though the end use is generally unable to control the order in which instances arrive it is important to understand which orderings impact Re- ACTR’s performance and to what extent. This study also has practical benefit as such orderings can occur organically. For example as business grows the problems it may encounter, such as routing or scheduling, often grow in size and difficulty. ReACTR’s performance also depends strongly configuration selection procedure used. This component controls which configurations are selected to run in parallel from the internal configuration pool. This paper evaluates various ranking mechanisms and different ways of combining them to better understand how the candidate selection procedure affects realtime algorithm configuration. We show that certain selection procedures are superior to others and that the order which instances arrive in determines which selection procedure performs best. We find that both instance order and grouping can significantly affect the overall solving time of the online automatic algorithm configurator ReACTR. One of the more surprising discoveries is that having groupings of similar instances can actually negatively impact on the overall performance of the configurator. In particular we show that orderings based on nearly any instance feature values can lead to significant reductions in total runtime over random instance orderings. In addition, certain candidate selection procedures are more suited to certain orderings than others and selecting the correct one can show a marked improvement in solving times. Show more

Keywords: Constraint Satisfaction, Boolean Satisfiability, Algorithm Configuration

DOI: 10.3233/FI-2019-1798

Citation: Fundamenta Informaticae, vol. 166, no. 2, pp. 141-166, 2019

Authors: Koutras, Costas D. | Moyzes, Christos | Rantsoudis, Christos

Article Type: Research Article

Abstract: Default conditionals are statements that express a condition of normality , in the form ‘if φ then normally ψ ’ and are of primary importance in Knowledge Representation. There exist modal approaches to the construction of conditional logics of normality. Most of them are built on notions of preference among possible worlds, corresponding to the semantic intuition that φ ⇒ ψ is true in a situation if in the most preferred (most ‘normal’) situations in which φ is true, ψ is also true. It has been noticed that there exist natural epistemic readings of a default conditional, but this …direction has not been thoroughly explored. A statement of the form ‘something known to be a bird, that can be consistently believed to fly, does fly’ involves well-known epistemic attitudes and allows the possibility of defining defaults within the rich framework of Epistemic Logic. We pursue this direction here and proceed to define conditionals within KBE , a recently introduced S4.2 -based modal logic of knowledge , belief and estimation . In this logic, knowledge is a normal S4 operator, belief is a normal KD45 operator and estimation is a non-normal operator interpreted as a ‘majority’ quantifier over the set of epistemically alternative situations. We define and explore various conditionals using the epistemic operators of KBE , capturing φ ⇒ ψ in various ways, including ‘according to the agent’s knowledge, an estimation that φ is true implies the estimation that (φ∧ψ) is true ’ or ‘if φ is known and there is no reason to believe ¬ψ then ψ can be plausibly inferred ’. Overall, we define here three nonmonotonic default conditionals, one conditional satisfying monotonicity (strengthening the antecedent ) and two nonmonotonic conditionals that do not satisfy the ubiquitous axiom ID (reflexivity ). Our project provides concrete evidence that the machinery of epistemic logic can be exploited for the study of default conditionals. Show more

Keywords: Default reasoning, Conditional logic, Epistemic logic

DOI: 10.3233/FI-2019-1799

Citation: Fundamenta Informaticae, vol. 166, no. 2, pp. 167-197, 2019