Aspiration-based search algorithm for multiple objective linear programming problems: Theory and comparative tests

Aspiration-based search algorithm for multiple objective linear programming problems: Theory and comparative tests

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Article ID: iaor19983029
Country: United States
Volume: 43
Issue: 8
Start Page Number: 1047
End Page Number: 1059
Publication Date: Aug 1997
Journal: Management Science
Authors: , ,
Keywords: decision theory: multiple criteria, programming: linear
Abstract:

We develop an interactive method for multiple objective linear programming based on aspiration levels of a decision maker. The method assumes an unknown pseudoconcave preference structure of a decision maker throughout the decision process, and the decision maker's ability to select a preferred solution from p + 1 alternatives, where p is the number of objectives. In addition to presenting the supporting theory and algorithm, we perform a comparative study using a fictitious decision maker, comparing our approach to those of Steuer and Choo, and Reeves and Franz. All three methods are interactive. During an iteration, each method presents several solution alternatives to the decision maker simultaneously. Our approach utilizes a Tchebycheff function that facilitates attainment of an optimum at a nonextreme point solution. The statistics collected in the comparative study provide insights into the nature of the algorithms and the behavior of the solution techniques with different categories of problem structure and different underlying utility functions.

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