The paper presents a survey of analysis of different types of stability in vector (multiple-criteria) combinatorial problem with the parametrized optimality principle. Formulas of “stability sphere” radius are given along with qualitative characteristics of stability.

Stability of Discrete Vector Problems with the Parametric Principle of Optimality

Properties of three computational forms of r-algorithms differentiated by their complexities (number of calculations per iteration) are considered. The results on convergence of the limit variants of r-algorithms for smooth functions and r μ (α)-algorithm for nondifferentiable functions are presented. A variant of r(α)-algorithms with a constant coefficient of space dilation α and adaptive step adjustment along the normalized anti-subgradient in the transformed space of variables is discussed. Octave-functions ralgb5 and ralgb4 of r(α)-algorithms with adaptive step adjustment are described. The results of computational experiments for substantially ravine piecewise quadratic function and ravine quadratic and piecewise linear functions are presented.

Shor’s r-Algorithms: Theory and Practice

In the 1970–1980s, V. K. Leont’ev and E. N. Gordeev proposed and studied an approach to the analysis of the stability of solutions. In a number of subsequent articles, this approach was developed and the stability of solutions was analyzed on its basis. The approach itself is of a rather general nature but was originally connected with the discrete optimization problems. Later similar results, although in different terms, were published for various classes of problems. We demonstrate the proximity of approaches both on the level of statements of problems and the interpretation of results.

Comparison of three approaches to studying stability of solutions to problems of discrete optimization and computational geometry

In this paper the primary components of a Decision Support System (DSS) for on line control of various activities of a Computer Integrated Manufacturing System (CIMS) will be delineated More specifically, the interrelationships among various decision making components of such a system will be discussed

Components of a decision support system for computer integrated manufacturing

Program package for solving large-scale production and transportation planning problems (PLANNER)

Construction of optimal programmed paths for the motion of a robotic manipulator

The paper describes the features of the DISNEL package for interactive solution of a wide range of discrete and nonlinear optimization problems of ES computers.

V. I. Artemenko

Papers

Construction of optimal programmed paths for the motion of a robotic manipulator

Program package for solving large-scale production and transportation planning problems (PLANNER)

Disnel: An application package for solving discrete and nonlinear optimization problems

The software package DISPRO-3: Objectives, classes of problems, systemic and algorithmic support

Formalization and solution of a special class of transportation problems