Directed search domain: A method for even generation of the Pareto frontier in multiobjective optimization

Engineering Optimization

Volumn 43, Issue 5, 2011, Pages 467-484

  Erfani, Tohid ^a   Utyuzhnikov, Sergei V ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

directed search domain; multiobjective optimization; Pareto set; Pareto solution

Indexed keywords

CLASSICAL APPROACH; DECISION MAKERS; DIRECTED SEARCH DOMAIN; ENGINEERING DESIGN; OPTIMAL SOLUTIONS; PARETO FRONTIERS; PARETO OPTIMAL SOLUTIONS; PARETO SET; PARETO SOLUTION; REAL-WORLD DESIGNS; TEST CASE;

ALGORITHMS; DESIGN; OPTIMAL SYSTEMS; PARETO PRINCIPLE;

MULTIOBJECTIVE OPTIMIZATION;

EID: 79957496570     PISSN: 0305215X     EISSN: 10290273     Source Type: Journal    
DOI: 10.1080/0305215X.2010.497185     Document Type: Article

References (26)

1. Athan, T. and Papalambros, P., 1996. A note on weighted criteria methods for compromise solutions in multi-objective optimization. Engineering Optimization, 27 (2), 155-176. (Pubitemid 126633948)
2. Das, I., 1999. An improved technique for choosing parameters for Pareto surface generation using normal-boundary intersection. In: Proceedings of the third world congress of structural and multidisciplinary optimization (WCSMO-3), 17-21 May 1999, University of Buffalo, Amherst, NY. Berlin: Springer.
3. Das, I. and Dennis, J., 1997. A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems. Structural and Multidisciplinary Optimization, 14 (1), 63-69. (Pubitemid 127676980)
4. Das, I. and Dennis, J., 1998. Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal on Optimization, 8, 631.
5. Deb, K., 2001. Multi-objective optimization using evolutionary algorithms. NewYork:Wiley.
6. Deb, K., et al., 2005. Scalable test problems for evolutionary multi-objective optimization. Evolutionary Multiobjective Optimization. Theoretical Advances and Applications. Berlin: Springer, 105-145.
7. Fantini, P., 2007. Effective multiobjective MDO for conceptual design -an aircraft design perspective. Thesis (PhD). Cranfield University, UK.
8. Hoffman, K. and Kunze, R., 2002. Linear algebra. Englewood Cliffs, NJ: Prentice Hall.
9. Koski, J., 1985. Defectiveness of weighting method in multicriterion optimization of structures. Communications in Applied Numerical Methods, 1 (6), 333-337. (Pubitemid 16590380)
10. Messac,A., 1996. Physical programming: Effective optimization for computational design. AIAA Journal, 34 (1), 149-158. (Pubitemid 126499205)
11. Messac, A., 2000. From dubious construction of objective functions to the application of physical programming. AIAA Journal, 38 (1), 155-163. (Pubitemid 32212303)
12. Messac, A., Ismail-Yahaya, A., and Mattson, C., 2003. The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization, 25 (2), 86-98.
13. Messac, A. and Mattson, C., 2002. Generating well-distributed sets of Pareto points for engineering design using physical programming. Optimization and Engineering, 3 (4), 431-450.
14. Messac, A. and Mattson, C., 2004. Normal constraint method with guarantee of even representation of complete Pareto frontier. AIAA Journal, 42 (10), 2101-2111.
15. Messac,A., Puemi-Sukam, C., and Melachrinoudis, E., 2000a.Aggregate objective functions and Pareto frontiers: Required relationships and practical implications. Optimization and Engineering, 1 (2), 171-188.
16. Messac, A., et al., 2000b. Ability of objective functions to generate points on nonconvex Pareto frontiers. AIAA Journal, 38 (6), 1084-1091.
17. Michalewicz, Z., 1996. Genetic algorithms + data structures = evolution programs. Berlin: Springer-Verlag.
18. Miettinen, K., 1999. Nonlinear multiobjective optimization. Berlin: Springer-Verlag.
19. Sanchis, J., et al., 2008. A new perspective on multiobjective optimization by enhanced normalized normal constraint method. Structural and Multidisciplinary Optimization, 36 (5), 537-546.
20. Shukla, P. and Deb, K., 2007. On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods. European Journal of Operational Research, 181 (3), 1630-1652. (Pubitemid 46498551)
21. Steuer, R., 1986. Multiple criteria optimization: Theory, computation, and application. NewYork:Wiley.
22. Tanaka, M., et al., 1995. GA-based decision support system for multicriteria optimization. In: Proceedings of the IEEE international conference on systems, man and cybernetics: Intelligent systems for the 21st century, Vol. 2. 22-25 October, Vancouver, Canada. NewYork: IEEE Press.
23. Utyuzhnikov, S., 2010. Multi-objective optimization: Quasi-even generation of Pareto frontier and its local approximation. In: J.Varela and S. Acuna, eds. Handbook of optimization theory: Decision analysis and application. NewYork: Nova Science.
24. Utyuzhnikov, S., Fantini, P., and Guenov, M., 2005. Numerical method for generating the entire Pareto frontier in multiobjective optimization. Proceedings of Eurogen'2005, 12-14 September 2005, Munich, Germany.
25. Utyuzhnikov, S., Fantini, P., and Guenov, M., 2009. A method for generating a well-distributed Pareto set in nonlinear multiobjective optimization. Journal of Computational and Applied Mathematics, 223 (2), 820-841.
26. Vincent, T. and Grantham,W., 1981. Optimality in parametric systems. NewYork:Wiley.