Relationships between constrained and unconstrained multi-objective optimization and application in location theory
- 727 Downloads
This article deals with constrained multi-objective optimization problems. The main purpose of the article is to investigate relationships between constrained and unconstrained multi-objective optimization problems. Under suitable assumptions (e.g., generalized convexity assumptions) we derive a characterization of the set of (strictly, weakly) efficient solutions of a constrained multi-objective optimization problem using characterizations of the sets of (strictly, weakly) efficient solutions of unconstrained multi-objective optimization problems. We demonstrate the usefulness of the results by applying it on constrained multi-objective location problems. Using our new results we show that special classes of constrained multi-objective location problems (e.g., point-objective location problems, Weber location problems, center location problems) can be completely solved with the help of algorithms for the unconstrained case.
KeywordsMulti-objective optimization Pareto efficiency Constrained optimization Unconstrained optimization Generalized convexity Location theory Gauges
The authors wish to thank the anonymous referees for their valuable comments.
- Alzorba S, Günther C, Popovici N, Tammer C (2016) A new algorithm for solving planar multi-objective location problems involving the Manhattan norm. Optimization Online. http://www.optimization-online.org/DB_HTML/2016/01/5305.html (submitted)
- Günther C, Hillmann M, Tammer C, Winkler B (2015) Facility location optimizer (FLO)—a tool for solving location problems. http://www.project-flo.de
- Kaiser M (2015) Spatial uncertainties in continuous location problems. Dissertation, Bergische Universität WuppertalGoogle Scholar
- Nickel S (1995) Discretization of planar location problems. Shaker, AachenGoogle Scholar
- Nickel S, Puerto J, Rodríguez-Chía AM (2015) Location problems with multiple criteria. In: Laporte G, Nickel S, Saldanha da Gama F (eds) Location science. Springer, Berlin, pp 205–247Google Scholar