A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One
Author(s)
Mittal, Shashi, Ph. D. Massachusetts Institute of Technology; Schulz, Andreas S
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In this paper, we present a general framework for designing approximation schemes for combinatorial optimization problems in which the objective function is a combination of more than one function. Examples of such problems include those in which the objective function is a product or ratio of two linear functions, parallel machine scheduling problems with the makespan objective, robust versions of weighted multiobjective optimization problems, and assortment optimization problems with logit choice models. The main idea behind our approximation schemes is the construction of an approximate Pareto-optimal frontier of the functions that constitute the given objective. Using this idea, we give the first fully polynomial-time approximation schemes for the max-min resource allocation problem with a fixed number of agents, combinatorial optimization problems in which the objective function is the sum of a fixed number of ratios of linear functions, or the product of a fixed number of linear functions, and assortment optimization problems with logit choice model.
Date issued
2013-02Department
Massachusetts Institute of Technology. Operations Research Center; Sloan School of ManagementJournal
Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Mittal, Shashi, and Andreas S. Schulz. “A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One.” Operations Research 61, no. 2 (April 2013): 386–97.
Version: Original manuscript
ISSN
0030-364X
1526-5463