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

doi:10.1016/S0305-0548(98)00108-7

Computers & Operations Research

Volume 26, Issue 13, November 1999, Pages 1311-1321

https://doi.org/10.1016/S0305-0548(98)00108-7 Get rights and content

Abstract

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 (IWTP) of Steuer and Choo (An interactive weighted Tchebycheff procedure for multiple objective programming. Mathematical Programming 1983;26:326–44) 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 (RLTP) 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.

Scope and purpose

Interactive multiple objective decision making procedures are concerned with helping decision makers search for improved solutions to problems involving multiple, often conflicting, objectives. Several refinements of an existing procedure are proposed and tested. These refinements are shown to increase the flexibility of the decision making process, while maintaining the quality of the solutions generated. Without increasing information processing requirements, they give decision makers the option of exercising more control and direction over the interactive solution process, if they choose to do so.

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