Introducing Reference Point Using g-Dominance in Optimum Design Considering Uncertainties: An Application in Structural Engineering

Considering uncertainties in engineering optimum design is often a requirement. Here, the use of the deterministic optimum design as the reference point in g-dominance is proposed. The multiobjective optimum robust design in a structural engineering test case where uncertainties in the external loads are taken into account is proposed as application, where the simultaneous minimization of the constrained weight average and the standard deviation of the constraints violation are the objective functions. Results include a comparison between both non-dominated sorting genetic algorithm II (NSGA-II) and strength Pareto evolutionary algorithm (SPEA2), including S-metric (hypervolume) statistical comparisons with and without the g-dominance approach. The methodology is capable to provide robust optimum structural frame designs successfully.

[1]  Vijitashwa Pandey.  Structures and Infrastructures Series , 2011 .

[2]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[3]  G. Winter,et al.  Optimising frame structures by different strategies of genetic algorithms , 2001 .

[4]  Luis F. Gonzalez,et al.  Robust design optimisation using multi-objectiveevolutionary algorithms , 2008 .

[5]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[6]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[7]  Dan Frangopol.  Structural Design Optimization Considering Uncertainties: Structures & Infrastructures Book , Vol. 1, Series, Series Editor: Dan M. Frangopol , 2008 .

[8]  Tomasz Arciszewski,et al.  Evolutionary computation and structural design: A survey of the state-of-the-art , 2005 .

[9]  Carlos M. Fonseca,et al.  An Improved Dimension-Sweep Algorithm for the Hypervolume Indicator , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[10]  J. Hammersley,et al.  Monte Carlo Methods , 1965 .

[11]  Carlos A. Coello Coello,et al.  g-dominance: Reference point based dominance for multiobjective metaheuristics , 2009, Eur. J. Oper. Res..

[12]  Lothar Thiele,et al.  A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers , 2006 .

[13]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO '06.

[14]  Thomas Bäck,et al.  Parallel Problem Solving from Nature — PPSN V , 1998, Lecture Notes in Computer Science.

[15]  Manolis Papadrakakis,et al.  Robust seismic design optimization of steel structures , 2007 .

[16]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

[17]  Manolis Papadrakakis,et al.  Structural design optimization considering uncertainties , 2008 .

[18]  Kim Fung Man,et al.  Multiobjective Optimization , 2011, IEEE Microwave Magazine.

[19]  Jürgen Branke,et al.  Consideration of Partial User Preferences in Evolutionary Multiobjective Optimization , 2008, Multiobjective Optimization.

[20]  David Greiner,et al.  Gray Coding in Evolutionary Multicriteria Optimization: Application in Frame Structural Optimum Design , 2005, EMO.