A flexible method for nonlinear multicriteria decision-making problems

An iterative and interactive approach to formulating and solving multicriteria decision-making problems is proposed in which the modeling and the solution phases are not strictly separated but overlap. At each iteration, the decision-maker is allowed to designate criterion functions as objective functions or as constraints or as something in between. The algorithm guarantees all intermediate solutions to be efficient and the final solution to be a most preferred solution. While the algorithm does not provide information about the marginal rates of substitution among the objective functions at a solution point as given by other methods, the marginal substitution rates are obtained by comparing two objectives at a time. The algorithm can also be used to solve linear multicriteria decision-making problems. However, since the surrogate function is nonlinear, the procedure introduces nonlinearities into the problems and may not be as computationally efficient as some of the other available algorithms. The algorithm is illustrated using a specific problem in water resources management