A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One
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Schultz_A general.pdf
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Author(s)
Mittal, Shashi, Ph. D. Massachusetts Institute of Technology
Schulz, Andreas S
Date Issued
February 2013
Journal
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
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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DOI of Published Version
https://doi.org/10.1287/opre.1120.1093
