Integer Programming Approach to HP Folding

One of the most widely studied protein structure prediction models is the hydrophobic-hydrophilic (HP) model, which explains the hydrophobic interaction and tries to maximize the number of contacts among hydrophobic amino-acids. In order to find a lower bound for the number of contacts, a number of heuristics have been proposed, but finding the optimal solution is still a challenge. In this research, we focus on creating a new integer programming model which is capable to provide tractable input for mixed-integer programming solvers, is general enough and allows relaxation with provable good upper bounds. Computational experiments using benchmark problems show that our formulation achieves these goals.

Stability of an Optimal Schedule for a Job-Shop Problem with Two Jobs

The usual assumption that the processing times of the operations are known in advance is the strictest one in scheduling theory. This assumption essentially restricts practical aspects of deterministic scheduling theory since it is not valid for the most processes arising in practice. The paper is devoted to a stability analysis of an optimal schedule, which may help to extend the significance of scheduling theory for decision-making in the real-world applications. The term stability is generally used for the phase of an algorithm, at which an optimal solution of a problem has already been found, and additional calculations are performed in order to study how solution optimality depends on variation of the numerical input data.

A Mixed Integer Quadratic Programming Model for the Low Autocorrelation Binary Sequence Problem

In this paper the low autocorrelation binary sequence problem (LABSP) is modeled as a mixed integer quadratic programming (MIQP) problem and proof of the model’s validity is given. Since the MIQP model is semidefinite, general optimization solvers can be used, and converge in a finite number of iterations. The experimental results show that IQP solvers, based on this MIQP formulation, are capable of optimally solving general/skew-symmetric LABSP instances of up to 30/51 elements in a moderate time. ACM Computing Classification System (1998): G.1.6, I.2.8.

Mathematical Optimization for the Train Timetabling Problem

AMS Subj. Classification: 90C57; 90C10;

CAPS in Z(2,n)

We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.

Optimal Decision Rules in Logical Recognition Models

The task of smooth and stable decision rules construction in logical recognition models is considered. Logical regularities of classes are defined as conjunctions of one-place predicates that determine the membership of features values in an intervals of the real axis. The conjunctions are true on a special no extending subsets of reference objects of some class and are optimal. The standard approach of linear decision rules construction for given sets of logical regularities consists in realization of voting schemes. The weighting coefficients of voting procedures are done as heuristic ones or are as solutions of complex optimization task. The modifications of linear decision rules are proposed that are based on the search of maximal estimations of standard objects for their classes and use approximations of logical regularities by smooth sigmoid functions.

Solving Maximum Clique Problem for Protein Structure Similarity

Computing the similarity between two protein structures is a crucial task in molecular biology, and has been extensively investigated. Many protein structure comparison methods can be modeled as maximum weighted clique problems in specific k-partite graphs, referred here as alignment graphs. In this paper we present both a new integer programming formulation for solving such clique problems and a dedicated branch and bound algorithm for solving the maximum cardinality clique problem. Both approaches have been integrated in VAST, a software for aligning protein 3D structures largely used in the National Center for Biotechnology Information, an original clique solver which uses the well known Bron and Kerbosch algorithm (BK). Our computational results on real protein alignment instances show that our branch and bound algorithm is up to 116 times faster than BK.

A Fast Algorithm for Weber Problem on a Grid

AMS subject classification: 90B80.

Method of Linear Programming as an Idea for High School Curriculum

2010 Mathematics Subject Classification: 97D40, 97M10, 97M40, 97N60, 97N80, 97R80

Realization of an Optimal Schedule for the Two-machine Flow-Shop with Interval Job Processing Times

Non-preemptive two-machine flow-shop scheduling problem with uncertain processing times of n jobs is studied. In an uncertain version of a scheduling problem, there may not exist a unique schedule that remains optimal for all possible realizations of the job processing times. We find necessary and sufficient conditions (Theorem 1) when there exists a dominant permutation that is optimal for all possible realizations of the job processing times. Our computational studies show the percentage of the problems solvable under these conditions for the cases of randomly generated instances with n ≤ 100 . We also show how to use additional information about the processing times of the completed jobs during optimal realization of a schedule (Theorems 2 – 4). Computational studies for randomly generated instances with n ≤ 50 show the percentage of the two- machine flow-shop scheduling problems solvable under the sufficient conditions given in Theorems 2 – 4.

The Technology of Programming for a Cluster Computer by the Remote Terminal with OS Windows

The problem of preparation of a program to perform it on multiprocessor system of a cluster type is considered. When developing programs for a cluster computer the technology based on use of the remote terminal is applied. The situation when such remote terminal is the computer with operational system Windows is considered. The set of the tool means, allowing carrying out of editing program texts, compiling and starting programs on a cluster computer, is suggested. Advantage of an offered way of preparation of programs to execution is that it allows as much as possible to use practical experience of programmers used to working in OS Windows environment.

Data Flow Analysis and the Linear Programming Model

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Development of Educational Ontology for C-Programming

Development of educational ontologies is a step towards creation of sharable and reusable adaptive educational systems. Ontology as a conceptual courseware structure may work as a mind tool for effective teaching and as a visual navigation interface to the learning objects. The paper discusses an approach to the practical ontology development and presents the designed ontology for teaching/learning C programming.

Programming Paradigms in Computer Science Education

Main styles, or paradigms of programming – imperative, functional, logic, and object-oriented – are shortly described and compared, and corresponding programming techniques are outlined. Programming languages are classified in accordance with the main style and techniques supported. It is argued that profound education in computer science should include learning base programming techniques of all main programming paradigms.

Quality Assurance in Extreme Programming

Our previous research about possible quality improvements in Extreme Programming (XP) led us to a conclusion that XP supports many good engineering practices but there is still place for refinements. Our proposal was to add dedicated Quality Assurance (QA) measures, which should be sufficiently effective and at the same time simpler enough in the context of XP. This paper intends to analyze the possibilities for an effective way for applying approved quality assurance practices to XP. The last should not affect negatively to the process and in the meantime must lead to better quality assurance. We aim to make changes to XP that even if would slow down a bit the development process, will make it more suitable for widest range of projects including large and very large projects as well as life critical and highly reliable systems.