Multi-scenario Multi-objective Optimization with Applications in Engineering Design

The notion of multi-scenario multi-objective optimization is proposed as a methodological framework for handling engineering design and other decision problems represented as a collection of multi-criteria optimization problems. Three specific research issues are discussed in this context, namely, the modelling of decision maker's preferences, the development of a concept of optimality, and the development of solution approaches to finding a preferred feasible solution for the overall problem. Two models of preferences that generalize the classical Pareto preference and two solution approaches to a class of multi-scenario multi-objective optimization problems are presented. Illustrative examples are included.

[1]  Vijay Kumar Singh.  Multi-Scenario Multi-Criteria Optimization in Engineering Design , 2001 .

[2]  A Gerodimos,et al.  Robust Discrete Optimization and its Applications , 1996, J. Oper. Res. Soc..

[3]  M. Wiecek.  Advances in Cone-Based Preference Modeling for Decision Making with Multiple Criteria , 2007 .

[4]  Brian J. Hunt.  Multiobjective Programming with Convex Cones: Methodology and Applications , 2004 .

[5]  Panos Y. Papalambros,et al.  Platform Selection Under Performance Loss Constraints in Optimal Design of Product Families , 2002, DAC 2002.

[6]  Massimiliano Gobbi,et al.  Symbolic multi-objective optimisation of the dynamic behaviour of actively suspended road vehicles , 2002 .

[7]  Margaret M. Wiecek,et al.  Exact generation of epsilon-efficient solutions in multiple objective programming , 2007, OR Spectr..

[8]  V. Noghin.  Relative importance of criteria: a quantitative approach , 1997 .

[9]  谷野 哲三,et al.  Multi-objective programming and goal programming : theory and applications , 2003 .

[10]  P. Yu.  Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives , 1974 .

[11]  Margaret M. Wiecek,et al.  Cones to Aid Decision Making in Multicriteria Programming , 2003 .

[12]  Panos Y. Papalambros,et al.  Platform Selection Under Performance Bounds in Optimal Design of Product Families , 2005 .

[13]  Hirotaka Nakayama,et al.  Theory of Multiobjective Optimization , 1985 .

[14]  Margaret M. Wiecek,et al.  Generating epsilon-efficient solutions in multiobjective programming , 2007, Eur. J. Oper. Res..

[15]  Margaret M. Wiecek,et al.  Modeling relative importance of design criteria with a modified pareto preference , 2007 .

[16]  Jaroslaw Sobieszczanski-Sobieski,et al.  Sensitivity analysis and multidisciplinary optimization for aircraft design - Recent advances and results , 1990 .

[17]  David Gorsich.  Automotive Research Center , 2001 .

[18]  A. M. Geoffrion.  Proper efficiency and the theory of vector maximization , 1968 .