New algorithmic approaches for interactive multiple objective decision-making

In this dissertation, three interactive algorithms for different multiple objective decision making problems are presented. The common property of these algorithms is that they all search through the set of efficient solutions for a most preferred solution of the decision maker. The first algorithm is for solving the multiple objective linear programming problem. It is a line search algorithm that requires tradeoff information from the decision maker to find a feasible direction of increase. The algorithm generates an efficient feasible direction that is at least as good as the feasible direction of increase specified by the decision maker and moves in that direction. Iterations go on until there is no feasible direction of increase. The second algorithm is for bicriterion convex programming problems. The algorithm reduces the set of nondominated solutions based on the responses of the decision maker, utilizing the golden section search method over the interval of nondominance of one of the objective functions. The decision maker is required to make a preference comparison between two nondominated solutions at each iteration. The third algorithm is for bicriterion nonconvex mixed integer programming problems. This algorithm uses a branch and bound search. In the algorithm, branching corresponds to dividing the subset of nondominated solutions considered at a node into two subsets. The incumbent solution is updated based on the preference of the decision maker between two nondominated solutions. Fathoming decisions are based on the decision maker's preference between the incumbent solution and the ideal solution of the node in consideration.