Finding preferred solutions under weighted Tchebycheff preference functions for multi-objective integer programs - Karakaya, G.; Köksalan, M. (European journal of operational research, 2023)
•Considers weighted Tchebycheff preference functions.•Develops an interactive algorithm that finds the most preferred solution.•Exploits the characteristics of Tchebycheff functions in the search process.•Quickly converges to the most preferred solution. Many interactive approaches in multi-objective optimization assume the existence of an underlying preference function that represents the preferences of a decision maker (DM). In this paper, we develop the theory and an exact algorithm that guarantees finding the most preferred solution of a DM whose preferences are consistent with a Tchebycheff function for multi-objective integer programs. The algorithm occasionally presents pairs of solutions to the DM and asks which one is preferred. It utilizes the preference information together with the properties of the Tchebycheff function to generate solutions that are candidates to be the most preferred solution. We test the performance of the algorithm on a set of three and four-objective combinatorial optimization problems.