A hybrid approach based on genetic algorithms and (max, +) algebra for network applications |
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| Affiliation: | 1. INSA Lyon, 69621, France;2. Universidad de Los Andes, Mérida 5101, Venezuela;1. Economic Department, Universidad Nacional del Sur- CEDETS, UPSO. Campus Altos de Palihue, 8000 Bahía Blanca, Argentina;2. Economic Department, Universidad Nacional del Sur. Campus Altos de Palihue, 8000 Bahía Blanca, Argentina;3. Faculty of Business and Economic, Universitat Rovira i Virgili. Av. de la Universitat 1, 43204 Reus, Spain;1. School of Management, Chongqing Jiaotong University, Chongqing 400074, China;2. School of Management and Economics, University of Electronic Science & Technology, Chengdu 610054, China;3. Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200030, China;1. Department of Decision Science and Knowledge Engineering, Kharazmi University, Tehran, Iran;2. Department of Electrical Engineering, Amirkabir University of Technology, Tehran, Iran;3. Department of Maritime Engineering, Amirkabir University of Technology, Tehran, Iran;4. Department of Management, Islamic Azad University (Qazvin branch), Qazvin, Iran;1. Federal University of São Paulo - UNIFESP, Brazil;2. National Institute for Space Research - INPE, Brazil |
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| Abstract: | The following work addresses the problem of scheduling operations on a flow network, as well as alignment (path) allocation. This is a multi-objective problem, and this paper proposes a solution method through a hybrid approach based on a genetic algorithm in conjunction with (max, +) algebra. A concise system abstraction is proposed through a non-linear (max, +) model. This model describes the main optimization constraints which dictate the behavior of the mutation and crossover operations in the genetic algorithm. Additionally, each individual in the population represents the value assignment of the decision variables, which linearizes the (max, +) model. A hierarchic genetic structure is proposed for individuals such that variable dependence is modeled. For each individual, the (max, +)-linear model is solved through a matrix product which determines the daters for alignment enabling for transfer operations. The study is extendable to complex net-structured systems of different nature. |
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| Keywords: | (Max, +) algebra Genetic algorithms Artificial intelligence Flow networks System modeling |
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