Final Compromise Solution Selection from Pareto Surface through Clustering-based Methodology
DOI:
https://doi.org/10.5890/JVTSD.2026.06.006Abstract
Final compromise solution selection from a Pareto surface using a clustering-based methodology is presented in this paper. The Pareto surface is generated through multi-objective optimization of an aero engine rotor system with the response at critical speed due to unbalance of the rotor, the response during turning maneuvering of the aircraft and the weight of the shaft of the rotor system as objectives under critical speed constraint. Clustering is carried out in both the design and the objective space and an indirect mapping between the two spaces is created. Literature survey has shown that the application of the clustering-based methodology for the final compromise solution is limited to the Pareto front generated by two objective optimization. Present work introduces the clustering-based methodology for the final compromise solution to the Pareto surface generated from three objective optimization. Utopia point methodology used for arriving at the final compromise solution requires three separate single objective optimizations to identify the Utopia point. This step is eliminated by introducing the clustering-based methodology. The improvement in objective values are found to be same, as compared to the initial design, for the final compromise solution obtained through both the selection methodologies. Time consumed for the final compromise solution selection is reduced by 1/4${}^{\rm th}$ in comparison to the Utopia point methodology by using the proposed methodology.References
[1] Rao, S.S. (2019), Engineering optimization: theory and practice, John Wiley & Sons.
[2] Chankong, V. and Haimes, Y.Y. (2008), Multiobjective decision making: theory and methodology, Courier Dover Publications.
[3] Gen, M. and Cheng, R. (2000), Genetic algorithms and engineering optimization, John Wiley & Sons, USA.
[4] Konak, A., Coit, D.W., and Smith, A.E. (2006), Multi-objective optimization using genetic algorithms: a tutorial, Reliability Engineering & System Safety, 91(9), 992-1007.
[5] Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002), A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6(2), 182-197.
[6] Cormack, R.M. (1971), A review of classification, Journal of the Royal Statistical Society Series A, 134(3), 321-367.
[7] Nilsson, N.J. (2014), Principles of artificial intelligence, Morgan Kaufmann.
[8] Alpaydin, E. (2020), Introduction to machine learning, MIT Press.
[9] Benson, H.P. and Sayin, S. (1997), Towards finding global representations of the efficient set in multiple objective mathematical programming, Naval Research Logistics, 44, 47-67.
[10] Jain, A.K. and Dubes, R.C. (1988), Algorithms for clustering data, Prentice-Hall, Englewood Cliffs, NJ.
[11] Mattson, C.A., Mullur, A.A., and Messac, A. (2004), Smart pareto filter: obtaining a minimal representation of multiobjective design space, Engineering Optimization, 36(6), 721-740.
[12] Forgey, E. (1965), Cluster analysis of multivariate data: efficiency vs. interpretability of classification, Biometrics, 21(3), 768-769.
[13] Joseph Shibu, K., Shankar, K., Kanna Babu, Ch., and Deogaonkar, G.K. (2021), Multi-objective optimization of a maneuvering small aircraft turbine engine rotor system, Journal of Intelligent and Robotic Systems, 103, 60.
[14] Joseph Shibu, K., Shankar, K., Kanna Babu, Ch., and Deogaonkar, G.K. (2020), Three-objective optimization of aircraft secondary power system rotor dynamics, Mechanics Based Design of Structures and Machines, 1-17.
[15] Srinivas, N. and Deb, K. (1994), Multiobjective optimization using nondominated sorting in genetic algorithms, Evolutionary Computation, 2, 221-248.
[16] Arora, J.S. (2004), Introduction to optimum design, Elsevier.
[17] Jiang, S.Y. and Xum, Y.M. (2004), An efficient clustering algorithm, International Conference on Machine Learning and Cybernetics, 3, 1513-1518.
[18] Milligan, G.W. and Cooper, M.C. (1988), A study of standardization of variables in cluster analysis, Journal of Classification, 5(2), 181-204.
[19] Calinski, T. and Harabasz, J. (1974), A dendrite method for clustering, Communications in Statistics, 3(1), 1-27.
[20] Lowry, J.T. (1999), Performance of light aircraft, American Institute of Aeronautics and Astronautics.
[21] Coombes, M., Chen, W.H., and Render, P. (2014), Reachability analysis of landing sites for forced landing of a UAS, Journal of Intelligent & Robotic Systems, 73(1-4), 635-653.
[22] Hou, L., Chen, Y., Cao, Q., and Zhang, Z. (2015), Turning maneuver caused response in an aircraft rotor-ball bearing system, Nonlinear Dynamics, 79(1), 229-240.
Article Metrics
Usage tracking begins September 1, 2026.