Interactive stability cutting-plane algorithm for multiobjective nonlinear programming problems

In this paper, we introduce an interactive stability cutting-plane algorithm for determining a best-compromise solution to a multiobjective nonlinear programming problems in situations with an implicitly defined utility function. The method is called “interactive stability cutting-plane compromise programming (ISCPCP)”. The cutting-planes which I am going to derive, are based on suitable pairwise trade-offs between the objective functions, as prescribed by the decision maker (DM) at each iterate generated by the algorithm. This algorithm requires no line searches, and generates iterates that are all contained in the efficient frontier. This feature facilitates the preference judgment of the decision maker, and permits an analyst to terminate short of optimality with an efficient near-optimal solution. Also, we investigate the stability of its efficient solutions which are obtained by using this algorithm. An illustrating example is presented to clarify this algorithm.