SPECIALSESSIONSMODEL REDUCTION IN MULTI-OBJECTIVE
AND ROBUST DESIGN OPTIMIZATION
Liqiang Hou, Tapabrata Ray, Edmondo Minisci

Optimizations of Expensive Numerical Model
For many complex real-world design optimization problems, the numerical model in thedesign can be computational expensive , e.g. for the design optimization with
Computational Fluid Dynamics (CFD), it may take hours for the computationally expensivemodel to evaluate an engineering design.
To tackle the issues due to expensive numerical model in the design, the low fidelity andcheap model can be used to guide the search. The low fidelity model can be the first orderapproximation to the expensive model, or th numerical model with coarse meshes. Anothermethod is to use the surrogate, e.g. Kriging/Co-Kriging to reduce the cost.
Such methods works well in a series of test functions. However, one needs numbers ofsample data to train the surrogate and the number of samples increases exponentially withnumber of design variables. One also need some extra sample points as the infill points toupdate the surrogate during the optimization. Therefore, the number of design variables ofsurrogate assisted optimization is strictly limited. In most of the literatures on surrogate
assisted MOO, the number of design variables are no more than 10.

Optimization under Uncertainty
In preliminary design, one also needs to analyze the impacts due to uncertainties. The
uncertainties can be either aleatory or epistemic uncertainties. As for the aleatory
uncertainties, their distribution information can be known and given prior to the design
optimization. One can use the model, such as Gaussian distribution function to model theuncertainty impacts. However, such information can not be available for the epistemic
uncertainties, particularly in the preliminary design. In this case, information of theuncertainties are given in some other forms, e.g. Basic Probability Assignment (BPA)structure. Two measures of the evidence, belief and plausibility can be used to measure theuncertain impacts. The belief measures the minimum or necessary support whereas
plausibility reflects the maximum or potential support for that hypothesis.

Special Session Chair
Ke Tang · ketang@ustc.edu.chn

IEEE Conference on Evolutionary Computation
Donostia – San Sebastián, June 8-5
www.cec2017.org · info@cec2017.org

SPECIALSESSIONS

To evaluate uncertain impacts, one needs to explore the uncertainty space and design
space. The cost can be huge and soon becomes prohibitive if numbers of uncertainties anddesign variables are involved. This lead to another problem: evidence approximation in thedesign optimization.

Model Reduction in Multi-objective Optimization and Robust Design
Optimization
The design optimization under uncertainty are commonly found in many practicalproblems, particularly in aerospace engineering design. With model reduction, e.g. Proper
Orthogonal Decomposition (POD, also called Principal Components Analysis, PCA) basedmodel reduction, expenses of searching process can be greatly reduced. Take the standard
ZDT series test functions for example, it takes around 20 iterations for the MOO with POD
model reduction to search the true Pareto front.
The model reduction can also be used in surrogate assisted optimization and evidenceapproximation. With model reduction, surrogate and evidence computation can beconstructed on a reduced data set, thus the sample size can be greatly reduced.
The optimization with model reduction shows advantages over conventional MOOs andcan be potentially extended to the scenarios such as optimization problems with manyobjectives. However, to implement successfully the methods in design optimization withexpensive model under uncertainty, a series of issues such as evidence approximation,model fidelity management, optimization algorithm and the strategy to integrate them, etc.
should be resolved. We therefore propose the special issue on Model Reduction in Multiobjective and Robust Optimization.

Topics•Multi-objective optimization•

Many-objective optimization•

Robust design optimization•Multi-Fidelity optimization•

Uncertainty modeling•

Parameter reduction•

Data mining in Multi-objective and Many-objective Optimization•

Model fidelity management•

Surrogate of expensive model•

Model reduction in Multi-objective and Many-objective Optimization•

Infill strategy of surrogate

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SPECIALSESSIONS•Surrogate assisted optimization•

Evidence approximation of epistemic uncertainty•

Multi-objective robust optimization under uncertainty•

Applications of design optimization with model reduction, particularly the aerospaceengineering design•

Preliminary space mission design under uncertainty•Multi-objective optimization in preliminary space mission design

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