An iterative algorithm for interactive multiobjective programming

A new iterative algorithm for interactive multiobjective programming is proposed. The algorithm is based on the Lagrange multiplier technique of generating noninferior solutions, and it is shown to converge under certain conditions. It reduces a complex multiobjective problem into a sequence of two-objective problems which the decision maker can handle more easily. The number of two-objective problems with which the decision maker is confronted, as well as the total number of noninferior solutions that must be generated, increase more or less linearly with the number of objectives. Computational efficiency is further enhanced by avoiding the need for regression. The decision maker interacts with the model directly in the functional space, and he is not required to translate his judgment of relative worth into numbers. Due to the iterative nature of the algorithm, the decision maker can articulate his preferences in a progressive manner. Furthermore, he may modify his attitude at any stage of the computation, based on partial results, without adversely affecting the quality of the solution. An example problem previously solved by other methods, including the surrogate worth trade-off approach, is used to illustrate the new algorithm.