Abstract
Interactive methods for solving the discrete multi-objective programming problems are proposed and examined in this paper.
The ε constrained method is first investigated to see how it works for finding all non-inferior solutions in the discrete vector optimization problem. Then a new type of the maximum component minimization method is presented. The method differs from the conventional one in the sense that instead of assigning the weighting coefficients of the objective functions the goal values of the objective functions are introduced as the parameters to find the non-inferior solutions.
Two interactive algorithms are proposed in this paper to select the decision-maker's preferred solution among all the non-inferior solutions. The first algorithm, which is only good for the two objective functions problem, utilizes the dichotomous method to find the best parameter values in the ε constrained method. The second algorithm, which is good for the more than three objective functions problem, utilizes the pattern search method for the search in the parameter space in the maximum component minimization method.
The both algorithms require the decision-maker only to do the pairwise comparisons of the non-inferior solutions in the objective function space. To verify the practical usefulness of the proposed two methods, several computational experiments are conducted on the illustrative examples.
