An interactive approximation algorithm for multi-objective integer programs - Lokman, Banu; Köksalan, Murat; Korhonen, Pekka J.; Wallenius, Jyrki (Computers & operations research, 2018)
•An interactive algorithm for multi-objective integer programs is developed.•The algorithm finds the most preferred point at a desired level of accuracy.•The decision maker is assumed to have an underlying quasiconcave value function.•Extensive computational experiments show the algorithm works very well. We develop an interactive algorithm that approximates the most preferred solution for any multi-objective integer program with a desired level of accuracy, provided that the decision maker's (DM's) preferences are consistent with a nondecreasing quasiconcave value function. Using pairwise comparisons of the DM, we construct convex cones and eliminate the inferior regions that are close to being dominated by the cones in addition to the regions dominated by the cones. The algorithm allows the DM to change the desired level of accuracy during the solution process. We test the performance of the algorithm on a set of multi-objective combinatorial optimization problems. It performs very well in terms of the quality of the solution found, the solution time, and the required preference information.