Structural models of algorithms in problems of applied programming. I. Formal algorithmic structures

A structural approach to modelling algorithms is proposed. The concept of an algorithmic structure with operations over algorithms is introduced. Models of algorithms constructed from algorithmic structures reflect aspects of algorithm representation and execution. Examples of structural and path models of algorithms are considered. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 3–14, May-June 2009.     

I. Development of basic models

Based on the concept that task progress is the growth of developments in a structured work and activity process, mathematical models ore developed to define, identify, and follow work progress and resourco utilization patterns. These models ore developed from the Pearl-Roed Logistic function and describe operating characteristics in the micro resource allocation and control problem. The model3 are the Task Operating Characteristic (TOC) curve and the Resource Operating Characteristic (ROC) curve. A second paper extends the theoretical results and gives examples (Braswell 1971).     

Dynamical conflict models. I. Language of modeling

In this work, we present a novel paradigm for modeling and analysis of dynamical games and survey results that are most important from the point of view of this paradigm. We describe the basic qualitative characteristic features for solutions of dynamical games. The survey is primarily intended for mathematicians who use game theory in applied studies. We discuss the principles for choosing a language to describe dynamical conflicts.     

Polymorphic programming I. Another language designed on semantic principles

We wish to illustrate the potential of a thus far little explored avenue of programming language design–-namely the employment of types and routines as values in their own right within the framework of an Algol. In this first paper we pay particular attention to the development of highly orthogonal self-initializing data structures, and to the advantageous expressive power of polymorphism when combined with routine values so as to provide abstract data structures. The emphasis is on the design phase, rather than on the implementation details or precise syntactic structure of the envisaged language. A second, companion paper? discusses the design of a high-level orthogonal abstract architecture intended to support polymorphic languages in which routines are ‘first class’ values. The relationship of the abstract machine architecture to the programming language vis-a-vis the ‘semantic gap’ is then discussed from the viewpoint of compiling programs which are strongly typed while exploiting polymorphism. We feel that polymorphism is essential if truly general purpose programs, software tools, are to be written easily. The research reported herein is an effort towards realizing this goal.     

Inference of differential equation models by genetic programming

This paper describes an evolutionary method for identifying a causal model from the observed time-series data. We use a system of ordinary differential equations (ODEs) as the causal model. This approach is known to be useful for practical applications, e.g., bioinformatics, chemical reaction models, control theory, etc. To explore the search space more effectively in the course of evolution, the right-hand sides of ODEs are inferred by genetic programming (GP) and the least mean square (LMS) method is used along with the ordinary GP. We apply our method to several target tasks and empirically show how successfully GP infers the systems of ODEs. We also describe an extension of the approach to the inference of differential equation systems with transcendental functions.     

On dual dynamic programming in shape optimization of coupled models

Structural and Multidisciplinary Optimization - We propose a new method for analysis of shape optimization of coupled models. The framework of the dual dynamic programming is introduced for a...     

Structural models of algorithms in problems of applied programming. II. Structural-algorithmic approach to software simulation

Relations existing between algorithms that are variously represented and are performed on various execution units are formalized. The process of software development is considered in the context of development and transformation of models. Possible applications of the structural-algorithmic approach are analyzed in various aspects of applied programming. Problems of analyzing algorithms in the context of execution of programs on computers are formulated. Part I of this article is published in No. 3 (2009). Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 49–56, July–August 2009.     

Net models of discrete information transducers. I

Dynamic net models of a special kind — discrete process generators — are considered. Their relation to automata, Petri nets, partially commutative monoids, and the theory of traces is examined.Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 83–90, September–October, 1991.     

Generalized hidden Markov models. I. Theoretical frameworks

In this paper, we present the theoretical framework for the generalization of classical hidden Markov models using fuzzy measures and fuzzy integrals. The main characteristic of the generalization is the relaxation of the usual additivity constraint of probability measures. Fuzzy integrals are defined with respect to fuzzy measures, whose key property is monotonicity with respect to set inclusion. This property is far weaker than the usual additivity property of probability measures. As a result of the new formulation, the statistical independence assumption of the classical hidden Markov models is relaxed. Two attractive properties of this generalization are: the generalized hidden Markov model reduces to the classical hidden Markov model if we used the Choquet fuzzy integral and probability measures; and the establishment of a relation between the generalized hidden Markov model and the classical nonstationary hidden Markov model in which the transitional parameters vary with time     

Equivalent mathematical programming models of the capital budgeting problem

This paper is concerned with a capital budgeting problem where both investment and borrowing decisions are considered in imperfect capital markets. The capital budgeting problem allows for project indivisibility and lets the borrowing interest rate vary from period to period in close relation to the size of debt. Generally, a formulated model in mixed integer non-linear programming is difficult to solve since the solution space is not convex. However, characterizing the dominance properties of solutions enables the model to be solved by enumeration by virtue of special structures inherent in the model. An equivalent model is employed in order to develop the implicit enumeration algorithm which requires much less computation. Computational results for a set of example problems are also provided.     

A lambda-calculus model of programming languages—I. Simple constructs

A simple correspondence is presented between the elementary constructs of programming languages and the lambda-calculus. The correspondence is obtained by using intuitive, functional interpretations of programming language constructs, completely avoiding the notions of machine memory and address. In particular, the concepts of program variable and assignment are accounted for in terms of the concepts of mathematical variable and substitution, respectively. Lambda-expression representations are given of assignments, conditional and compound statements, input-output, and blocks. Algol 60 is used as the illustrative language.     

Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models

Two-sided assembly lines are especially used at the assembly of large-sized products, such as trucks and buses. In this type of a production line, both sides of the line are used in parallel. In practice, it may be necessary to optimize more than one conflicting objectives simultaneously to obtain effective and realistic solutions. This paper presents a mathematical model, a pre-emptive goal programming model for precise goals and a fuzzy goal programming model for imprecise goals for two-sided assembly line balancing. The mathematical model minimizes the number of mated-stations as the primary objective and it minimizes the number of stations as a secondary objective for a given cycle time. The zoning constraints are also considered in this model, and a set of test problems taken from literature is solved. The proposed goal programming models are the first multiple-criteria decision-making approaches for two-sided assembly line balancing problem with multiple objectives. The number of mated-stations, cycle time and the number of tasks assigned per station are considered as goals. An example problem is solved and a computational study is conducted to illustrate the flexibility and the efficiency of the proposed goal programming models. Based on the decision maker's preferences, the proposed models are capable of improving the value of goals.