An interactive approach for biobjective integer programs under quasiconvex preference functions

作者：Ozturk Diclehan Tezcaner^*; Koksalan Murat

来源：Annals of Operations Research, 2016, 244(2): 677-696.

DOI：10.1007/s10479-016-2149-9

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

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.

• 出版日期2016-9