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Ontology type: schema:Chapter     


Chapter Info

DATE

2019

AUTHORS

Michael Z. Zgurovsky , Alexander A. Pavlov

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. More... »

PAGES

1-14

References to SciGraph publications

Book

TITLE

Combinatorial Optimization Problems in Planning and Decision Making

ISBN

978-3-319-98976-1
978-3-319-98977-8

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-98977-8_1

DOI

http://dx.doi.org/10.1007/978-3-319-98977-8_1

DIMENSIONS

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49 schema:description 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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