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A k, k-ε optimality selection based multi objective genetic algorithm with applications to vehicle engineering

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Abstract

In the paper, a multi objective genetic algorithm based on the concept of k-optimality and k-ε-optimality (KEMOGA) is introduced and applied. Pareto optimality alone is not always adequate for selecting a final solution because the Pareto optimal set can be very large. The k-optimality approach and the more general k-ε-optimality method, can be used to rank the Pareto-optimal solutions. The two methods have been included into a genetic algorithm selection procedure. The k-optimality method searches for points which remain Pareto-optimal when all of the subsets of n-k objectives (n is the number of objective functions) are optimised. The k-ε approach considers not only if an objective is worse than the others but also the entity of this variation through the introduction of a vector of indifference thresholds.

The KEMOGA has been applied for the solution of two engineering problems. The selection of the stiffness and damping of a passively suspended vehicle in order to get the best compromise between discomfort, road holding and working space and a complex problem related to the optimisation of the tyre/suspension system of a sport car. The final design solution, found by means of the KEMOGA seems consistent with the solution selected by skilled suspensions specialists.

The proposed approach has been tested and validated on a complex optimization problem. The solved problem deals with the optimization of the tyre/suspension system of a sport car. The proposed approach (KEMOGA) has shown to be very effective in terms of computational efficiency and accuracy.

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References

  • Aittokoski T, Miettinen K (2010) Efficient evolutionary approach to approximate the Pareto optimal set in multiobjective optimization. Optim Methods Softw 25(6):841–858

    Article  MathSciNet  MATH  Google Scholar 

  • Benedetti A, Farina M, Gobbi M (2006) Evolutionary multiobjective industrial design: the case of a racing car tire-suspension system. IEEE Trans Evol Comput 10(3):230–244

    Article  Google Scholar 

  • Das I (1999) A preference ordering among various Pareto optimal alternatives. Struct Optim 18:30–35

    Article  Google Scholar 

  • Davis L (1990) Genetic algorithms and simulated annealing. Pitman, London

    Google Scholar 

  • Davis L (1991) The handbook of genetic algorithms. Van Nostrand Reingold, New York

    Google Scholar 

  • Deb K (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  MathSciNet  Google Scholar 

  • Di Pierro F, Khu S, Savic D (2007) An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Trans Evol Comput 11(1):17–45

    Article  Google Scholar 

  • Eschenauer HA, Schumacher A (1995) Simultaneous shape and topology optimization of structures. In: Proc of the 1st World congress of structural and multidisciplinary optimization (WCSM01). Pergamon, Elmsford, pp 177–184

    Google Scholar 

  • Farina M, Amato P (2004) A fuzzy definition of “optimality” for many-criteria optimization problems. IEEE Trans Syst Man Cybern 34(3):315–326

    Article  Google Scholar 

  • Gobbi M, Mastinu G (2001) Analytical description and optimisation of the dynamic behaviour of passively suspended road vehicles. J Sound Vib 245(3):457–481

    Article  Google Scholar 

  • Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Goldberg DE (2002) The design of innovation: lessons from and for competent genetic algorithms. Addison-Wesley, Reading

    MATH  Google Scholar 

  • Goldberg DE, Richardson J (1987) Genetic algorithms with sharing for multi-modal function optimization. In: Genetic algorithms and their applications: proceedings of the second international conference on genetic algorithms, pp 41–49

    Google Scholar 

  • Hajela P (1990) Genetic algorithms in automated structural synthesis. In: Topping BHV (ed) Optimization and artificial intelligence in civil and structural engineering. Kluwer Academic, Dordrecht, pp 639–653

    Google Scholar 

  • Hajela P (1996) Stochastic search in discrete structural optimization. C.I.S.M. Course, Udine

  • Hajela P, Lin CY (1992) Genetic search strategies in multi-criterion optimal design. Struct Optim 4:99–107

    Article  Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. The University of Michigan Press, Ann Arbor

    Google Scholar 

  • Horn J, Nafpliotis N, Goldberg DE (1994) A niched Pareto genetic algorithm for multiobjective optimization. In: Proc of the 1st IEEE conference on evolutionary computation, vol 1, pp 82–87

    Google Scholar 

  • Kamat P (1993) Structural optimization: status and promise. AIAA, Washington

    Book  Google Scholar 

  • Levi F, Gobbi M, Farina M, Mastinu G (2004) Multi-objective design and selection of one single optimal solution. In: Proceedings of IMECE 2004 ASME international mechanical engineering congress and RD&D expo, 13–19 November 2004, Anaheim, California (IMECE2004-60902), pp 841–848

    Google Scholar 

  • Mastinu G, Gobbi M, Miano C (2006) Optimal design of complex mechanical systems with applications to vehicle engineering. Springer, Berlin. ISBN:3-540-34354-7

    MATH  Google Scholar 

  • Matusov JB (1995) Multicriteria optimization and engineering. Chapman & Hall, New York

    Google Scholar 

  • Miettinen K (1999) Nonlinear multiobjective optimization. Kluwer Academic, Boston

    MATH  Google Scholar 

  • Pardalos PM, Resende M, Pardalos P (2002) Handbook of applied optimization. Oxford University Press, London

    Book  MATH  Google Scholar 

  • Pham DT, Yang Y (1993) Optimization of multi-modal discrete functions using genetic algorithms. In: Proc inst mech engrs, vol 207, pp 53–59

    Google Scholar 

  • Schäffer JD (1984) Some experiments in machine learning using vector evaluated genetic algorithms. Ph.D. Thesis, Vanderbilt University, Nashville

  • Srinivas N, Deb K (1994) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248

    Article  Google Scholar 

  • Taboadaa HA, Coitb DW (2008) Multi-objective scheduling problems: determination of pruned Pareto sets. IIE Trans 40(5):552–564. doi:10.1080/07408170701781951

    Article  Google Scholar 

  • Venkat V, Jacobson SH, Stori JA (2004) A post-optimality analysis algorithm for multi-objective optimization. Comput Optim Appl 28(3):357–372. doi:10.1023/B:COAP.0000033968.55439.8b

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mechanical Engineering, Politecnico di Milano, Via La Masa, 34, Milan, Italy

    Massimiliano Gobbi

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  1. Massimiliano Gobbi
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Correspondence to Massimiliano Gobbi.

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Gobbi, M. A k, k-ε optimality selection based multi objective genetic algorithm with applications to vehicle engineering. Optim Eng 14, 345–360 (2013). https://doi.org/10.1007/s11081-011-9185-8

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  • DOI: https://doi.org/10.1007/s11081-011-9185-8

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