Some experiments in Tchebycheff-based approaches for interactive multiple objective decision making

Tchebycheff metric based approaches have become popular for sampling the set of nondominated solutions in an interactive search for a most preferred solution in multiple objective decision making situations. These approaches systematically reduce the set of nondominated solutions which remain available for identification and selection from one iteration to the next. The interactive weighted Tchebycheff procedure of Steuer and Choo is a weight space reduction method. An alternative approach to reducing the set of nondominated solutions within a Tchebycheff framework is proposed and compared to the IWTP. This approach uses reservation levels based upon decision maker responses for objective space reduction. This reservation level driven Tchebycheff procedure is shown to be more flexible than the original IWTP, while producing solutions of similar high quality. Several issues related to the basic Tchebycheff framework in addition to the type of reduction factor employed are explored. They include (1) the rate of reduction of the nondominated solution space, (2) the impact of allowing decision makers to retain more than just a single solution as more or most preferred at intermediate iterations of the procedure, and (3) the robustness of the procedure, if decision makers should happen to specify their preference information incorrectly.