Abstract
This note proposes an algorithm to generate the Pareto front of a mixed discrete multi-objective optimization problem based on the pruning of irrelevant subproblems. The knee point is introduced as a new reference point for pruning decision. The point can overcome the drawback of the existing reference point – over-pruning, and be naturally defined and used in the context of multi-objective optimization. The validity of the proposed procedure is demonstrated through case studies.
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References
Bechikh S, Said LB, Ghédira K (2011) Searching for knee regions of the Pareto front using mobile reference points. Soft Comput 15(9):1807–1823. https://doi.org/10.1007/s00500-011-0694-3
Branke J, Deb K, Dierolf H, Osswald M (2004) Finding knees in multi-objective optimization. In: parallel problem solving from nature (PPSN) 2004 - Lecture notes in Computer Science Vol 3242, pp 722–731
Das I (1999) On characterizing the ‘knee’ of the Pareto curve based on normal-boundary intersection. Struct Optim 18(2):107–115
Das I, Dennis JE (1998) Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multi-criteria optimization problems. Soc Ind Appl Math J Optim 8(3):631–657
Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Chichester
Deb K, Gupta S (2010) Towards a link between knee solutions and preferred solution methodologies. In: Panigrahi B, Das S, Suganthan P, Dash S (eds) Swarm, evolutionary, and memetic computing (SEMCCO) 2010 – Lecture notes in computer science Vol 6466, pp 182-189
Hong S, Ahn J, Choi HL (2015) Pruning-based Pareto front generation for mixed-discrete bi-objective optimization. Struct Multidiscip Optim 51(1):193–198
Hwang C, Masud A (2012) Multiple objective decision making - methods and applications: a state-of-the-art survey. Springer, Berlin
Kim IY, de Weck O (2006) Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation. Struct Multidiscip Optim 31(2):105–116
MathWorks (2007) Global optimization toolbox: gamultiobj. Retrieved December 27, 2017 (https://kr.mathworks.com/help/gads/gamultiobj.html)
Mela K, Koski J, Silvennoinen R (2007) Algorithm for generating the Pareto optimal set of multiobjective nonlinear mixed-integer optimization problems. In: 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference. Structures, structural dynamics, and materials and co-located conferences. AIAA, Honolulu, Hawaii
Rachmawati L, Srinivasan D (2009) Multiobjective evolutionary algorithm with controllable focus on the knees of the Pareto front. IEEE Trans Evol Comput 13(4):810–824
Shukla PK (2007) On the normal boundary intersection method for generation of efficient front. In: Shi Y, van Albada GD, Dongarra J, Sloot PMA (eds) Computational science – ICCS 2007. ICCS 2007. Lecture notes in computer science, vol 4487. Springer, Berlin
Sudeng S, Wattanapongsakorn N (2015) Finding knee solutions in multi-objective optimization using extended angle dominance approach. In: Information science and applications. Lecture notes in Electrical Engineering Vol 339, pp 673–679
Zhang WH, Gao T (2006) A min-max method with adaptive weightings for uniformly spaced Pareto optimum points. Comput Struct 84(28):1760–1769
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Lee, J., Lee, SI., Ahn, J. et al. Pareto front generation with knee-point based pruning for mixed discrete multi-objective optimization. Struct Multidisc Optim 58, 823–830 (2018). https://doi.org/10.1007/s00158-018-1926-2
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DOI: https://doi.org/10.1007/s00158-018-1926-2