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NAFEMS World Congress 2015 | 21-24 June | San Diego | California | USA
Multi-Strategy Intelligent Optimization
Algorithm For Computationally
Expensive CAE Simulation
S. Costanzo, Z. Xue, M. Engel,
S. Parashar, C. Chuang

Goal
• Reduce number of evaluations
• Solve a complex constrained MDO problem
• Handle computationally expensive CAE
simulations
• Case study:
–MDO of Ford Taurus 2001

MDO Ford Taurus 2001
Our target was to improve the baseline design of
the 2001 Ford Taurus model based on the
National Crash Analysis Center (NCAC) criteria.
Disciplines considered:
• safety (subdivided into Full Frontal and 40%
offset impact)
• NVH (noise, vibration & harshness)

MDO Problem Description

For a vehicle model with over a million elements a
single design evaluation takes about 5 hours on
32-CPUs HPC clusters.
The challenge

Software Platform
is an integration platform for multi-objective and multi-
disciplinary optimization. It provides a seamless coupling with
third party engineering tools, enables the automation of the design
simulation process, and facilitates analytic decision making.

Optimization Workflow
Problem: identify most appropriate algorithm

Algorithm suite
Taking into account a subset of available
optimization algorithm categories:
• Gradient-Based
• Heuristic
• Multi-Strategy

Algorithm suite
• Gradient-Based
• Heuristic
• Multi-Strategy
Main focus: few number of evaluations.

Algorithm suite
• Gradient-Based
• Heuristic
• Multi-Strategy
Main focus: few number of evaluation.

Heuristics: Genetic Approach
• Well known algorithms, recognized in
literature
• Allow for parallel computing
• High robustness and design space
exploration capabilities
• Elitism allows the GA to focus on the best
solutions and explore the most interesting
regions

Heuristic: Genetic Approach
MOGA-II
Multi-objective Genetic Algorithm II is an
improved version of MOGA developed by C.
Poloni, that uses a smart multi-search
elitism for robustness and a directional
crossover for fast convergence.

Heuristic: Genetic Approach
NSGA-II
Non-dominated Sorting Genetic Algorithm is
a well-known multi-objective optimization
algorithm developed by K. Deb,
implementing a fast and clever elitism and
non-dominated sorting.

Multi-Strategy Approach
• Combine heuristics with other techniques:
– Local search for refinement
– response surfaces to speed up convergence
• Suitable for MDO problems where
correlations between disciplines may
require different optimization techniques
to achieve the best results

FAST
Automatic iterative algorithm focused on the
exploration, exploitation and validation cycle.
Fast optimizer uses different internal
adaptive Response Surface Metamodels to
speed up the optimization process.

HYBRID
Combines a genetic algorithm and a
gradient-based SQP local search algorithm
within a steady-state evolution scheme,
which can keep the computational resources
saturated with concurrent design
evaluations.

pilOPT
Exploits the advantages of local and global
search algorithms while automatically
adjusting the ratio between different
optimization strategies based on their
performance. It also uses Response
Surfaces to speed up the optimization.

Preliminary Benchmark
• Comparison based on a limited number of
evaluations
• Mathematical test functions from literature
– Michalewicz test library
– Zitzler benchmark library
• Target:
Find the most appropriate strategy for the Ford
Taurus model optimization

Preliminary Benchmark: T01
Objective Function:
Constraints: Bounds:

Preliminary Benchmark: T01

Preliminary Benchmark: ZDT2
Objective Functions:
Bounds:

Preliminary Benchmark: ZDT2

Inverted Generational Distance
•

Preliminary Benchmark
• Multi-strategy algorithms outperform GA
on short runs
• All candidate algorithms have shown
remarkable results on a long run
• Accordingly, we decided that we could
afford three short optimizations

Application Test
• Also in this case only default algorithm
parameter settings were used
• Maximum number of evaluations for each
algorithm was set to 400
• In spite of the use of significant parallel
computing resources, one whole run took more
than three days

HYBRID

FAST

pilOPT

Conclusions
• Good validation for multi-strategy algorithms on
a complex MDO problems
• The baseline design weight has been
successfully reduced with all algorithms
• The best result has been obtained with pilOPT,
with 13.72% weight reduction
• The remarkable performance indicates great
potential for intelligent multi-strategy algorithms

Future Work
• Single-parameter multi-strategy algorithm
• Improve automatic controls in pilOPT
• Increase number of available internal algorithms
• Find other complex MDO cases where intelligent
algorithms could be effectively applied

Thank you for your attention

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Multi strategy intelligent optimization algorithm for computationally expensive cae

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