Access the full text.
Sign up today, get DeepDyve free for 14 days.
Perepelitsa (1969)
The finding of the minima Hamiltonian directed circuit in a graph with the weighted edges In All - Union Conference on Theoretical Cybernetics Problems Math Inst Siberian Branch of USSR Acad Sei pp inProc, 58
Burkard (1982)
Efficiency and optimality in minisum minimax programming problems / OperRes Soc, 14
Burkard (1981)
A relationship between optimality and efficiency in multicriteria programming problems ComputOper Res, 21
Dauer (1980)
An equivalence result for solutions of multiobjective linear programs ComputOper Res, 20
Hansen (1980)
Bicriterial path problems Lect Notes EconMath Syst, 49
Emelichev (1991)
On the unsolvability of vector problems on graphs by algorithms of linear convolution In VI Tiraspol Symposium on General Topology and its Applications Moldavian Univ pp inProc, 63
Emelichev (1989)
On some algorithmical problems of multicriteria optimization on graphs / and Math inPhys, 32
Kravtsov (1990)
The problems of polyhedral combinatorics in transportation problems with exclusions No inCybernetics, 79
Slominski (1982)
Probabilistic analysis of combinatorial algorithms A bibliography with selected annota - tionsComputing, 30
Timofeev (1919)
Minimax two - connected subgraphs and the bottleneck travelling - salesman problem No inCybernetics, 53
Gimadi (1974)
On statistically efficient algorithms for some extremal problems of graph theory In Third All - Union Conference on Problems of Theoretical Cybernetics Math Inst Siberian Branch of USSR Acad Sei pp inProc, 40
V. Emelichev, V. Perepelitsa (1992)
On cardinality of the set of alternatives in discrete many-criterion problems, 2
Kravtsov (1989)
On solution of combinatorial optimization problems with minimax criteria No inCybernetics, 22
Emelichev (1989)
The review of some discrete multicriteria optimization problems In Seminar on Discrete Optimization and its Applications Moscow Univ pp inProc, 45
Sergienko (1987)
To the problem of finding the sets of alternatives in discrete multicriteria problems No inCybernetics, 36
Emelichev (1992)
On cardinality of the set of alternatives in discrete many - criterion problems Discrete MathAppl, 34
Izermann (1979)
The enumeration of all efficient solutions for a linear multiple - objective transportation problem Naval Res Logistics Quart The analysis of a class of integer multicriteria problems / and Math inPhys, 26
Wald (1939)
Contributions to the theory of statistical estimation and testing hypothesis Ann StatistMath, 17
Sergienko (1988)
On a class of multicriteria problems of integer programming In Intern Yalta Conf Glushkov Cybern Inst pp inProc, 80
Emelichev (1984)
On a dass of multicriteria problems on graphs and hypergraphs No inCybernetics, 116
Kochkarov (1982)
Multicriteria problem of covering a graph by paths of given lengths In Problems of Operations Research Minsk pp in inMath, 68
-- This review contains the results which concern the estimates of the computational complexity of combinatorial problems of vector optimization, the solvability of these problems in the class of algorithms of linear convolution, and the accuracy evaluation of fast algorithms of finding the set of alternatives in typical cases. The discrete, multicriteria problems considered here include polynomially solvable, polynomially reducible to the NP class, and intractable problems, i.e., they cover the main part of the scale of estimates of the computational complexity. 1. FORMULATION OF THE PROBLEMS A mathematical setting of any multicriteria problem presupposed that a set X = {x} of admissible solutions (AS's) is given and a multiobjective function (MF) F(x) = (ii(*), F2(x), . . . , FN(x)) (1.1) is defined on this set. For definiteness, we assume that all the criteria of this MF should be minimized, i.e., fXaO-nnin, i/ = l,...,7V. (1.2) An admissible solution (further the word admissible will be omitted) G X is said to be a Pareto optimal solution or a Pareto optimum (PO) if there is no x" £ X such that F(x~) < F(x)9 F(x*) £ F(x) (see [1]). The symbol X denotes the Pareto set consisting of
Discrete Mathematics and Applications – de Gruyter
Published: Jan 1, 1994
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.