An interactive approach for biobjective integer programs under quasiconvex preference functions

Date

2016-09-01

Author

Ozturk, Diclehan Tezcaner
Köksalan, Mustafa Murat

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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We develop an interactive algorithm for biobjective integer programs that finds the most preferred solution of a decision maker whose preferences are consistent with a quasiconvex preference function to be minimized. During the algorithm, preference information is elicited from the decision maker. Based on this preference information and the properties of the underlying quasiconvex preference function, the algorithm reduces the search region and converges to the most preferred solution progressively. Finding the most preferred solution requires searching both supported and unsupported nondominated points, where the latter is harder. We develop theory to further restrict the region where unsupported nondominated points may lie. We demonstrate the algorithm on the generalized biobjective traveling salesperson problem where there are multiple efficient edges between node pairs and show its performance on a number of randomly generated instances.

Subject Keywords

Biobjective traveling salesperson problem, Interactive method, Combinatorial optimization, Multiobjective decision making

URI

https://hdl.handle.net/11511/56920

Collections

Department of Industrial Engineering, Article