# Finding representations for an unconstrained bi-objective combinatorial optimization problem

Finding representations for an unconstrained bi-objective combinatorial optimization problem Typically, multi-objective optimization problems give rise to a large number of optimal solutions. However, this information can be overwhelming to a decision maker. This article introduces a technique to find a representative subset of optimal solutions, of a given bounded cardinality for an unconstrained bi-objective combinatorial optimization problem in terms of $$\epsilon$$ ϵ -indicator. This technique extends the Nemhauser–Ullman algorithm for the knapsack problem and allows to find a representative subset in a single run. We present a discussion on the representation quality achieved by this technique, both from a theoretical and numerical perspective, with respect to an optimal representation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Optimization Letters Springer Journals

# Finding representations for an unconstrained bi-objective combinatorial optimization problem

, Volume 12 (2) – Mar 24, 2017
14 pages

/lp/springer_journal/finding-representations-for-an-unconstrained-bi-objective-8V4LNhd7D9
Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Optimization; Operations Research/Decision Theory; Computational Intelligence; Numerical and Computational Physics, Simulation
ISSN
1862-4472
eISSN
1862-4480
D.O.I.
10.1007/s11590-017-1129-6
Publisher site
See Article on Publisher Site

### Abstract

Typically, multi-objective optimization problems give rise to a large number of optimal solutions. However, this information can be overwhelming to a decision maker. This article introduces a technique to find a representative subset of optimal solutions, of a given bounded cardinality for an unconstrained bi-objective combinatorial optimization problem in terms of $$\epsilon$$ ϵ -indicator. This technique extends the Nemhauser–Ullman algorithm for the knapsack problem and allows to find a representative subset in a single run. We present a discussion on the representation quality achieved by this technique, both from a theoretical and numerical perspective, with respect to an optimal representation.

### Journal

Published: Mar 24, 2017

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