Multi-objective optimization over convex disjunctive feasible sets using reference points |
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| Institution: | 1. State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China;2. Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, China;3. School of Basic Medicine, Capital Medical University, Beijing 100069, China;4. School of Printing and Packaging Engineering, Beijing, Institute of Graphic Communication, Beijing 102600, China;1. Área de Ornitología, Colección Científica, Museo de Historia Natural (MUSA), Universidad Nacional de San Agustín de Arequipa, Av. Alcides Carrión s/n, Arequipa, Peru;2. Grupo de Investigaciones en Biología de la Conservación, Laboratorio Ecotono, INIBIOMA, Universidad Nacional del Comahue - CONICET, Quintral 1250 (R8400FRF), San Carlos de Bariloche, Argentina;3. Centro de Ornitología y Biodiversidad, CORBIDI, Calle Santa Rita Of. 202, Urb. Huertos de San Antonio, Surco, Lima 15023, Peru;4. Servicio Nacional de Áreas Naturales Protegidas por el Estado (SERNANP), Calle Diecisiete 355, Urb. El Palomar, San Isidro, Lima, Peru;5. Programa de Desarrollo Productivo Agrario Rural–AGRO RURAL, Av. República de Chile 350, Jesús María, Lima, Peru |
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| Abstract: | In this paper we consider the Multiple Objective Optimization Problem (MOOP), where concave functions are to be maximized over a feasible set represented as a union of compact convex sets. To solve this problem we consider two auxiliary scalar optimization problems which use reference points. The first one contains only continuous variables, it has higher dimensionality, however it is convex. The second scalar problem is a mixed integer programming problem. The solutions of both scalar problems determine nondominated points. Some other properties of these problems are also discussed. |
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