An interactive weight space reduction procedure for nonlinear multiple objective mathematical programming

To make a decision that is defined by multiple, conflicting objectives it is necessary to know the relative importance of the different objectives. In this paper we present an interactive method and the underlying theory for solving multiple objective mathematical programming problems defined by a convex feasible region and concave, continuously differentiable objective functions. The relative importance of the different objectives for a decision maker is elicited by using binary comparisons of objective function vectors. The method is cognitively easy to use and in test problems has rapidly converged to an optimal solution.