An Interactive Reference Direction Algorithm For Solving Multi-Objective Convex Nonlinear Integer Programming Problems

We present a learning-oriented interactive reference direction algorithm for solving multi-objective convex nonlinear integer programming problems. At each iteration the decision-maker (DM) sets his/her preferences as aspiration levels of the objective functions. The modified aspiration point and the solution found at the previous iteration define the reference direction. Based on the reference direction, we formulate a mixed-integer scalarizing problem with specific properties. By solving this problem approximately, we find one or more integer solutions located close to the efficient surface. At some iteration (usually at the last iteration), the DM may want to solve the scalarizing problem to obtain an exact (weak) efficient solution. Based on the proposed algorithm, we have developed a research-decision support system that includes one exact and one heuristic algorithm. Using this system, we illustrate the proposed algorithm with an example, and report some computational results.