New approaches to multi-objective optimization

نویسندگان

  • Fabrizio Grandoni
  • R. Ravi
  • Mohit Singh
  • Rico Zenklusen
چکیده

A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Many classical optimization problems, such as maximum spanning tree and forest, shortest path, maximumweight (perfect) matching, maximum weight independent set (basis) in a matroid or in the intersection of two matroids, become NP-hard even with one budget constraint. Still, for most of these problems efficient deterministic and randomized approximation schemes are known. Not much is known however about the case of two or more budgets: filling this gap, at least partially, is the main goal of this paper. In more detail, we obtain the following main results: Using iterative rounding for the first time in multi-objective optimization, we obtain multi-criteria PTASs (which slightly violate the budget constraints) for spanning tree, matroid basis, and bipartite matching with k = O(1) budget constraints. We present a simple mechanism to transform multicriteria approximation schemes into pure approximation schemes for problems whose A preliminary version of many results in this paper appeared in ESA’09 [17] and ESA’10 [18]. F. Grandoni IDSIA, University of Italian Switzerland, Manno, Switzerland e-mail: [email protected] R. Ravi Tepper School of Business, Carnegie Mellon University, Pittsburgh, USA e-mail: [email protected] M. Singh School of Computer Science, McGill University, Montreal, Canada e-mail: [email protected] R. Zenklusen (B) Institute for Operations Research (IFOR), Department of Mathematics, ETH, Zurich, Switzerland e-mail: [email protected]

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عنوان ژورنال:
  • Math. Program.

دوره 146  شماره 

صفحات  -

تاریخ انتشار 2014