A class of practical interactive branch and bound algorithms for multicriteria integer programming

A practical interactive solution approach to multicriteria integer programming problems is developed. The problem is solved by a branch-and-bound method that employs the Zionts and Wallenius procedure [23] for solving the multicriteria linear programming problem. The development of algorithms for multicriteria decision problems itself is a multicriteria problem, which involves the simultaneous minimization of the number of questions asked of the decision maker and the solution time. Two branch-and-bound algorithms that follow different search strategies to meet different levels of these criteria have been developed. Further, two families of hybrid algorithms that incorporate a combination of the strategies of the two algorithms have also been developed. Strategies for the exploration of the decision-maker's preference structure are discussed. Computational experience with the algorithms is presented. The class of algorithms represents a collection of viable solution strategies applicable to a variety of decision-making styles.