A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One

• Published in: Operations research Vol. 61; no. 2; pp. 386 - 397
• Main Authors: Mittal, Shashi, Schulz, Andreas S.
• Format: Journal Article
• Language: English
• Published: Linthicum INFORMS 01-03-2013; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Analysis; analysis of algorithms; Approximation; Combinatorial optimization; Customers; Design optimization; Hierarchies; Job shops; Linear transformations; Management science; METHODS; networks/graphs; Objective functions; Operations research; Optimization; Optimization algorithms; Pareto optimum; Polynomials; Problem solving; Production scheduling; Scheduling; Studies; United States
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1120.1093

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.