A reference direction approach to multiple objective quadratic-linear programming |
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| Institution: | 1. Systems Realization Laboratory, The University of Oklahoma, Room 219-C, 202 W. Boyd Street, Norman, Oklahoma, 73019, USA;2. Institute for Industrial Engineering, Beijing Institute of Technology, 5 S. Zhongguancun St., Bejing, 100081, China;1. Non-traditional Security Center of Huazhong University of Science and Technology, Wuhan 430074, China;2. College of Public Administration, Huazhong University of Science and Technology, Wuhan 430074, China;1. Department of Geology, Faculty of Sciences, Ferdowsi University of Mashhad, Mashhad, Iran;2. Department of Biology, Faculty of Sciences, Ferdowsi University of Mashhad, Mashhad, Iran |
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| Abstract: | In this paper, we propose an interactive procedure for solving multiple criteria problems with one quadratic objective, several linear objectives, and a set of linear constraints. The procedure is based on the use of reference directions and weighted sums. Reference directions for the linear functions, and weighted sums for combining the quadratic function with the linear ones are used as parameters to implement the free search of nondominated solutions. The idea leads to the parametric linear complementarity problem formulation. An approach to deal with this type of problems is given as well. The approach is illustrated with a numerical example. |
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