On combinatorial vector optimization problems
Copyright policy )On combinatorial vector optimization problems
Summary: A class of combinatorial optimization problems with several criteria of the form MINMAX and MINSUM in arbitrary combinations is investigated. A class of vector optimization problems is formulated in terms of systems of subsets. It contains optimization problems on graphs and Boolean programming. It is proved that finding a complete set of alternatives for such problems can be of exponential complexity. New results concerning the existence of statistically efficient algorithms for these problems are obtained. For the case of two criteria (when at least one of them is MINIMAX) polynomial algorithms are proposed which find a complete set of alternatives for the problem on paths, matchings, spanning trees, and for the integer transportation problem.
vector optimization, Combinatorial optimization, paths, integer transportation problem, matchings, spanning trees, Multi-objective and goal programming
vector optimization, Combinatorial optimization, paths, integer transportation problem, matchings, spanning trees, Multi-objective and goal programming
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