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Introduction

  • Michael Z. ZgurovskyEmail author
  • Alexander A. Pavlov
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 173)

Abstract

We formulate the research problems which are a generalization of our earlier results in the field of intractable combinatorial optimization problems. On the basis of these problems, we have created a hierarchical model of planning and decision making for objects with a network representation of technological processes and limited resources (Chap.  9). We say that the problem is intractable if it is NP-hard (NP-hard in the strong sense) or such for which an exact polynomial time solution algorithm has not been yet obtained. To solve such problems efficiently, we developed a methodology of PSC-algorithms construction meaning the algorithms which necessarily include the following: sufficient conditions (signs) of a feasible solution optimality, verification of which can be implemented only at the stage of a feasible solution construction by a polynomial algorithm (the first polynomial component of the PSC-algorithm). The second polynomial component of the PSC-algorithm is an approximation algorithm with polynomial complexity. For NP-hard (NP-hard in the strong sense) combinatorial optimization problems, a PSC-algorithm may include an exact algorithm for its solving in case if sufficient conditions were found, satisfying of which during this algorithm execution turns it into a polynomial complexity algorithm (Chaps.  4 and  5). We also give a brief overview of the monograph’s chapters content.

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Authors and Affiliations

  1. 1.Kyiv Polytechnic InstituteNational Technical University of UkraineKyivUkraine
  2. 2.Faculty of Informatics and Computer ScienceNational Technical University of UkraineKyivUkraine

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