EVEN GENERATION of PARETO SET in MULTIOBJECTIVE OPTIMIZATION

 

The Directed Search Domain (DSD) approach has been developed to generate a well distributed Pareto set. The method proved to be quite universal. 

 

Fig8a

Fig8b

Physical Programming Approach

DSD Method

 

 

1.   Utyuzhnikov, S.V., Guenov, M.D., and Fantini, P., “Numerical method for generating the entire Pareto frontier in multiobjective optimization”, Proceedings of EUROGEN 2005, Munich, September 12-14, 2005 (ISBN: 3-00-017534-2).

 

2.   Guenov, M.D., Utyuzhnikov, S.V., and Fantini, P., “Application of the modified physical programming method to generating the entire Pareto frontier in multiobjective optimization”,  Proceedings of EUROGEN 2005, Munich, September 12-14, 2005 (ISBN: 3-00-017534-2).

 

3.   Utyuzhnikov, S V, Fantini P, Guenov M., "A Method for Generating a Well-Distributed Pareto Set in Nonlinear Multiobjective Optimization", J. Computational and Applied Mathematics, 2009, 223 (2): 820-841.

 

4.   Utyuzhnikov, S.V., “Multi-Objective Optimization: Quasi-Even Generation of Pareto Frontier and its Local Approximation”, in “Handbook of Optimization Theory: Decision Analysis and Application”, Eds: Varela, J., Acuna, S., Nova Science Publishers, NY, ISBN: 978-1-60876-500-3, 2010.

 

5.   Erfani, T., and Utyuzhnikov, S.V., “Directed Search Domain: a method for even generation of Pareto frontier in Multiobjective Optimization”, J. Engineering Optimization, 2011, 43 (5): 467-484.

 

6.   Wang, K., Utyuzhnikov, S.V., “An extension of the Directed Search Domain algorithm to bilevel optimization”, J. Engineering Optimization, 2017, 49 (8): 1420-1440.

 

7.   Wang, K., Utyuzhnikov, S.V., "A modified rotation strategy for directed search domain algorithm in multiobjective engineering optimization", J. Structural and Multidisciplinary Optimization, 2018, 57 (2): 877-890.

 

 

Sensitivity Analysis is considered in

 

1.   Utyuzhnikov, S.V., Maginot, J., and Guenov, M.D., “Local Pareto approximation for multi-objective optimization”, J. of Engineering Optimization, 2008, 40 (9): 821-847.

For the first time, the linear and quadratic approximations of a smooth enough Pareto surface have been obtained. It has been proven that the linear approximation known in the literature is not applicable in the general n-dimensional case.

 

Robust design in MOO under uncertainties is considered in

1.    Erfani, T., and Utyuzhnikov, S.V., “Control of robust design in multiobjective optimization under uncertainties”, J. Structural and Multidisciplinary Optimization, 2012, 45 (2): 247-256.

In this paper, trade-off between robustness and Pareto optimality is addressed.

 

Ranking in MOO

1.  Jaini, N.I., Utyuzhnikov, S.V., “Trade-off Ranking Method for Multi-Criteria Decision Analysis”, J. Multi-Criteria Decision Analysis, 2017, 24 (3-4): 121-132.