An interactive approach for biobjective integer programs under quasiconvex preference functions

Ozturk D. T., Koksalan M.

ANNALS OF OPERATIONS RESEARCH, vol.244, no.2, pp.677-696, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 244 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.1007/s10479-016-2149-9
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.677-696
  • Keywords: Multiobjective decision making, Combinatorial optimization, Interactive method, Biobjective traveling salesperson problem, TRAVELING SALESMAN PROBLEM, SALESPERSON PROBLEM, ASSIGNMENT PROBLEM, LOCAL SEARCH, ALGORITHMS
  • TED University Affiliated: Yes


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.