Using aspiration levels in an interactive interior multiobjective linear programming algorithm |
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| Institution: | 1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247 667, INDIA;2. School of Mathematics, Thapar University, Patiala-147 004, INDIA;1. Dipartimento di Ingegneria dell’Informazione, University of Pisa, Largo Lucio Lazzarino, Pisa 1 - 56122, Italy;2. Dipartimento di Informatica, University of Pisa, Largo Bruno Pontecorvo, Pisa 3 - 56127, Italy;3. Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, University of Calabria, Via P. Bucci, 42-C, - 87036 Rende (CS), Italy;4. Department of Software and High Performance Computing, Lobachevsky University, pr. Gagarina, 23, - 603950 Nizhni Novgorod, Russia;1. Key Laboratory of Advanced Control of Iron and Steel Process (Ministry of Education), School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;2. Department of Management Science, Lancaster University Management School, Bailrigg, Lancaster LA1 4YX, United Kingdom;1. College of Environment and Safety, Taiyuan University of Science and Technology, Taiyuan, Shanxi 030024, China;2. School of Life Science, Shanxi Datong University, Datong, Shanxi 037009, China;3. Shanxi Land Consolidation Center, Taiyuan, Shanxi 030024, China |
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| Abstract: | In this paper, we propose the use of an interior-point linear programming algorithm for multiple objective linear programming (MOLP) problems. At each iteration, a Decision Maker (DM) is asked to specify aspiration levels for the various objectives, and an achievement scalarizing function is applied to project aspiration levels onto the nondominated set. The interior-point algorithm is used to find an interior solution path from a starting solution to a nondominated solution corresponding to the optimum of the achievement scalarizing function. The proposed approach allows the DM to re-specify aspiration levels during the solution process and thus steer the interior solution path toward different areas in objective space. We illustrate the use of the approach with a numerical example. |
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