An efficient multi-objective optimization approach based on the micro genetic algorithm and its application
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An efficient multi-objective optimization approach based on the micro genetic algorithm and its application G. P. Liu • X. Han • C. Jiang
Received: 22 March 2011 / Accepted: 19 October 2011 / Published online: 6 November 2011 Springer Science+Business Media, B.V. 2011
Abstract In this paper, an efficient multi-objective optimization approach based on the micro genetic algorithm is suggested to solving the multi-objective optimization problems. An external elite archive is used to store Pareto-optimal solutions found in the evolutionary process. A non-dominated sorting is employed to classify the combinational population of the evolutionary population and the external elite population into several different non-dominated levels. Once the evolutionary population converges, an exploratory operator will be performed to explore more non-dominated solutions, and a restart strategy will be subsequently adopted. Simulation results for several difficult test functions indicate that the present method has higher efficiency and better convergence near the globally Pareto-optimal set for all test functions, and a better spread of solutions for some test functions compared to NSGAII. Eventually, this approach is applied to the structural optimization of a composite laminated plate for maximum stiffness in thickness direction and minimum mass.
G. P. Liu (&) X. Han C. Jiang State Key Laboratory of Advanced Design Manufacturing for Vehicle Body, College of Mechanical and Automotive Engineering, Hunan University, Changsha 410082, People’s Republic of China e-mail: [email protected]
Keywords Multi-objective optimization Micro genetic algorithm Non-dominated sorting Laminated plates
1 Introduction Many engineering optimization problems involve multiple objectives. There often exist a number of optimal solutions, no solutions from which can be said to be better than any other without any further information. These solutions are known as Paretooptimal solutions or non-dominated solutions. Classical optimization methods convert multiple objectives into a single by the information about the relative preference vector of objectives. Apparently, these methods only find one particular Pareto-optimal solution at a time and they have to be applied many times for finding multiple solutions. Genetic algorithms (GAs) seem to be particularly suited for solving multi-objective optimization problems for their natural ability of finding multiple optimal solutions in one single simulation run. Since the mid-1980s, GAs have been developed to find the Pareto-optimal solutions. The first evolutionary multi-objective optimization algorithm was proposed by Schaffer (1984). After that, many different multi-objective genetic algorithms were proposed, among which, Fonseca and Fleming’s multi-objective GA (MOGA) (Fonseca and Fleming 1993), Srinivas and Deb’s non-dominated sorting GA (NSGA)
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(Srinivas and Deb 1994), Horn, Nafploitis and Goldberg’s niched Pareto-GA (NPGA) (Horn et al. 1994), Zitzler and Thiele’s strength Pareto evolutionar
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