Abstract
Innovization (innovation through optimization) is a relatively new concept in the field of multi-objective engineering design optimization. It involves the use of Pareto-optimal solutions of a problem to unveil hidden mathematical relationships between variables, objectives and constraint functions. The obtained relationships can be thought of as essential properties that make a feasible solution Pareto-optimal. This paper proposes two major extensions to innovization, namely higher-level innovization and lower-level innovization. While the former deals with the discovery of common features among solutions from different Pareto-optimal fronts, the latter concerns features commonly occurring among solutions that belong to a specified (or preferred) part of the Pareto-optimal front. The knowledge of such lower-level information is extremely beneficial to a decision maker, since it focuses on a preferred set of designs. On the other hand, higher-level innovization reveals interesting knowledge about the general problem structure. Neither of these crucial aspects concerning multi-objective designs has been addressed before, to the authors’ knowledge. We develop methodologies for handling both levels of innovization by extending the authors’ earlier automated innovization algorithm and apply them to two well-known engineering design problems. Results demonstrate that the proposed methodologies are generic and are ready to be applied to other engineering design problems.
Similar content being viewed by others
Notes
Refer to [11] for further details.
References
Ali, M., Khompatraporn, C., Zabinsky, Z.: A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems. J. Glob. Optim. 31(4), 635–672 (2005)
Bandaru, S., Deb, K.: Automated innovization for simultaneous discovery of multiple rules in bi-objective problems. In: Proceedings of the 6th International Conference on Evolutionary Multi-Criterion Optimization, EMO’11, pp. 1–15. Springer, Berlin, Heidelberg (2011)
Bandaru, S., Deb, K.: Towards automating the discovery of certain innovative design principles through a clustering-based optimization technique. Eng. Optim. 43(9), 911–941 (2011)
Bandaru, S., Tutum, C., Deb, K., Hattel, J.: Higher-level innovization: A case study from friction stir welding process optimization. In: 2011 IEEE Congress on Evolutionary Computation (IEEE-CEC), pp. 2782–2789 (2011)
Branke, J., Deb, K., Dierolf, H., Osswald, M.: Finding knees in multi-objective optimization. In: Parallel Problem Solving from Nature-PPSN VIII, pp. 722–731. Springer (2004)
Deb, K.: Unveiling innovative design principles by means of multiple conflicting objectives. Eng. Optim. 35(5), 445–470 (2003)
Deb, K., Agarwal, S., Pratap, A., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Deb, K., Datta, R.: Hybrid evolutionary multi-objective optimization and analysis of machining operations. Eng. Optim. 44(6), 685–706 (2012)
Deb, K., Gupta, S.: Understanding knee points in bicriteria problems and their implications as preferred solution principles. Eng. Optim. 43(11), 1175–1204 (2011)
Deb, K., Gupta, S., Daum, D., Branke, J., Mall, A., Padmanabhan, D.: Reliability-based optimization using evolutionary algorithms. IEEE Trans. Evol. Comput. 13(5), 1054–1074 (2009)
Deb, K., Srinivasan, A.: Innovization: Innovating design principles through optimization. In: GECCO ’06—Proceedings of the 8th annual conference on genetic and evolutionary computation, pp. 1629–1636. ACM, New York (2006)
Deb, K., Sundar, J.: Reference point based multi-objective optimization using evolutionary algorithms. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, GECCO ’06, pp. 635–642. ACM, New York, NY, USA (2006)
Gil, C., Márquez, A., Banos, R., Montoya, M., Gómez, J.: A hybrid method for solving multi-objective global optimization problems. J. Glob. Optim. 38(2), 265–281 (2007)
Karasakal, E., Nadirler, D.: An interactive solution approach for a bi-objective semi-desirable location problem. J. Glob. Optim. 42(2), 177–199 (2008)
Newman, M.: Power laws, Pareto distributions and Zipf’s law. Contemp. Phys. 46(5), 323–351 (2005)
Oei, C.K., Goldberg, D.E., Chang, S.J.: Tournament selection, niching, and the preservation of diversity. IlliGAL Report No. 91011. University of Illinois at Urbana-Champaign, Urbana, IL (1991)
Quiza Sardiñas, R., Rivas Santana, M., Alfonso Brindis, E.: Genetic algorithm-based multi-objective optimization of cutting parameters in turning processes. Eng. Appl. Artif. Intell. 19(2), 127–133 (2006)
Witting, K., Ober-Blöbaum, S., Dellnitz, M.: A variational approach to define robustness for parametric multiobjective optimization problems. J. Glob. Optim. (2012). doi:10.1007/s10898-012-9972-6
Acknowledgments
Authors were extremely motivated by the comments made on an earlier version of this work by the participants of the MCDM-2011 conference in Jyväskylä, Finland and judging the work as one of the best presented papers. Authors acknowledge the financial support provided by Michigan State University, East Lansing, for their visits which made this work possible.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bandaru, S., Deb, K. Higher and lower-level knowledge discovery from Pareto-optimal sets. J Glob Optim 57, 281–298 (2013). https://doi.org/10.1007/s10898-012-0026-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-012-0026-x