Companies daily need to optimize their products, hence optimization plays a significant role in today's design cycle. Problems related to one or more than one objective, originate in several disciplines; typically using a single optimization technology is not sufficient to deal with real-life problems, particularly when the design concerns complex and expensive products. Therefore, engineers are frequently asked to solve problems with several conflicting objective functions. The multiobjective optimization approach provides a set of non-dominant designs (Pareto optimality) where a further improvement for one objective is at the expense of all the others: this allows designers to choose the best solution for each scenario. Solving real-world multiobjective problems is not simple, engineers must address problems connected to the non-linearity of the functions, complexity of the physics and the computational cost that snowballs as the number of parameters increases. Moreover, the coupling between disciplines for design a product can be really challenging, involving several complicating factors, such as the limitation on the computational resources, and even a lack of communication between different departments. This tutorial is a survey on methodologies to approach design optimization process, a set of best practices intended for rapid delivery of high-quality products, with a specific focus on the numerical algorithms and post-processing used for selecting optimal design configurations.

1. Multiobjective Optimization for
Innovation in Engineering Design
Silvia Poles, M. Margonari, G. Borzi
EnginSoft S.p.A.
mail: s.poles@enginsoft.it
LION 5 - Jan 17-21, 2011, Rome, Italy

2. OUR MISSION
EnginSoft is a consulting company operating
in the field of Computer-Aided-Engineering
(CAE).
Our mission is to spread the culture of
digital technologies within both
production and research contexts. We
pursue this challenge by offering
engineering consulting services, world-
class CAE software, dedicated training
courses and by promoting
conferences, collaborations with research
institutes, and publishing activity.
We propose us as key partner in Design Process Innovation

3. History and business
HISTORY:
Private company, founded in 1984 on the basis of other activities/structures operating
since 1973
ACTIVITIES:
- Leading group in Italy for CAE/iDP.
- Supply of software, services, consultancy, training.
- Participation in industrial research projects (EU or national funding).
- MIUR – acknowledged research centre for CAE/iDP technology transfer.
OFFICES
IN ITALY:
Trento,
Bergamo,
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Florence,
Mesagne (BR)

4. The International EnginSoft Network
EnginSoft proposes itself as partner for
the introduction of virtual prototyping into
businesses, also on a European and
International level, through a network of
new companies.
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GREAT BRITAIN | SPAIN | GREECE | TURKEY | PORTUGAL | USA
Official network website: www.enginsoft.com

5. MACRO-ACTIVITIES and FIGURES
ENGINEERING ACTIVITIES
SOFTWARE AND KNOWLEDGE
1700 consultancy services TRANSFER
succesfully carried out
with over 80 expert engineers More than 1000 software licenses in Italy
TRAINING AND METHODOLOGICAL
SUPPORT RESEARCH PROJECTS
An offer of more than 100 courses per Participation in over 30 research
year and a portal for on-line training projects with public co-funding
EnginSoft S.p.A. Company Profile
5

6. Innovation in Engineering Design

7. Obstacles to innovation
While it is simplistic to claim that all organizations are dealing with the same
obstacles, there are repeating themes that we have noticed during the past years:
• Lack of a shared vision, purpose and/or strategy
• Short-term thinking
• Inadequate understanding of customers
• Lack of key competencies
• Costs
• …

8. Steps in product innovation
There are two parallel paths involved in the process:
• the idea generation, product design and detail engineering;
• market research and marketing analysis.
Technical
Idea Commercializ NEW
implementa ation
Screening PRODUCT
tion

9. An unsupervised text classification method implemented in
Scilab
IDEA SCREENING

10. Strategy Canvas
• The strategy canvas is both a diagnostic and an action framework for building a
compelling blue ocean strategy.
• It captures the current state of play in the known market space.
• This allows you to understand where the competition is currently investing,
the factors the industry currently competes on in products, service, and
delivery, and what customers receive from the existing competitive offerings
on the market.
Citation: Blue Ocean Strategy.
Harvard Business School Press. 2005.

11. Strategy Canvas Example
US Wine Industry in the late 1990s
High
Premium Wines
Budget Wines
Low
Price Above-the-line Vineyard prestige Wine
marketing range
Use of enological Aging Wine complexity
terminology and distinctions quality
in wine communication

12. Eliminate-Reduce-Raise-Create Grid
Case Study Yellow Tail
Eliminate Raise
Enological Terminology Price versus budget wines
Aging qualities Retail stores involvement
Above-the-line Marketing
Reduce Create
Wine complexity Easy drinking
Wine range Ease of selection
Vineyard prestige Fun and adventure

13. A New Value Curve –
Strategy Canvas of Yellow Tail
High
Premium Wines
[yellow tail]
Budget Wines
CREATE
RAISE
Low
REDUCE
Price Above-the-line Vineyard Wine Ease of
ELIMINATE
marketing prestige range selection
Use of enological Aging Wine Easy Fun and
terminology and quality complexity drinking adventure
distinctions in wine
communication

14. Text Mining
• Text mining is a relatively new research
field whose main concern is to develop
effective procedures able to extract
meaningful information from a collection
of text documents.
• A reliable document classification strategy
can help in information retrieval.
• The subject is undoubtedly challenging for
researchers who have to consider different
and problematic aspects coming out when
working with text documents and natural
language.
14

15. A text classification using Self Organizing Maps
• Many mathematical frames have been
developed for the text classification: Bayes
classifiers, supervised and unsupervised neural
networks, learning vector machines and
clustering techniques.
• We use an unsupervised self organizing map
(SOM) as a tool to discover possible clusters of
documents
• Such maps allow a 2D representation of
multivariate datasets, preserving the original
topology.

16. The Problem
• Our personal interest for these techniques was
born reading the EnginSoft newsletters.
• A typical newsletter issue usually has many
contributions: case studies, interviews,
corporate and software news, …
• A series of questions came out:
– can we have a deeper insight into our
community?
– Can we imagine a new categorization based on
other criteria?
– Can we discover categories without knowing
them a-priori?

17. Stem
• It easy to understand that one of the difficulties that can arise when managing
text is that we could consider as “different” words which conceptually can
have the same meaning.
optimization, optimizing, optimized, optimizes, optimisation, optimality.
• It is clear that a good preprocessing of a text document should recognize that
different words can be grouped under a common root (also known as stem)

18. Collect & Managing
• Scilab has been used to collect and manage all the stems
• A criterion to judge the importance of a stem in a document is needed.
• We decided to adopt the tf_idf coefficient (term frequency – inverse document
frequency) which takes into account the relative frequency of a stem in a
document and the frequency of the stem within the corpus.
w is the word,
tf _ idf w, d tfw,d * idf w d is the document
n_ij is the number of time the word i appears in
nw , d the document j
tfw,d N
nw , k N is the total number of document
k 1 C is the entire corpus
N
idf w ln
1 nw , C

19. Counting stems
A matrix representation of the non-zeros tf-idf coefficients within the corpus.
The matrix rows collect the text files sorted in the same order as they are
processed, the columns collect the stems added to the dictionary in the
same order as they appear while processing the files.

20. Training the SOM
• We submitted the dataset with the tf-idf coefficients and ran a SOM training.
• To avoid stems with high and low values, we keep only those belonging to the
range 0.1-0.8 probability. The extremes are cancelled out from the dataset,
ensuring a more robust training.
• The dictionary decreases from 7000 to 5000 stems which are considered to be
enough to describe the corpus, keeping quite common words and preserving
the peculiarities of documents.

21. D-Matrix
• The white diamonds give
evidence of the number of
files pertaining to the neuron.
• The colormap represents the
mean distance between a
neuron’s prototype and the
prototypes of the neighbor
neurons. Two groups of
documents (blue portions)
can be detected.

22. The stems
My boss
contributions to
the company
Newsletter
My contributions
to the company
Newsletter
For each neuron the first two stems with the highest tf-idf are
reported. This highlights the main subject discussed by articles falling
in the neurons.

23. Results of text mining
• With this analysis we identify the most important “stems” and their frequency
and distribution.
• This is very similar to analyze web pages, blogs, … to indentify the factors the
industry currently competes on in products, and what customers receive from
the existing competitive offerings on the market.
• For any factor we can identify the importance and fill up the strategy canvas
and create our new IDEA

24. TECHNICAL IMPLEMENTATION

25. What is optimization?
Selection of the best option from a range of possible
choices.
What makes it a complex task?
The potentially huge number of options to be tested
What qualifies as an optimization technique?
The search strategy

26. Optimization Problem
Mathematical formulation
max f1 x1 ,  , xn , f 2 x1 ,  , xn ,  , f k x1 ,  , xn
gi x 0
gj x 0
subject t o
gl x 0
x S
Note : When k>1 and the functions
are in contrast, we speak about
multi-objective optimization.

27. Math and Real world
There is a huge difference between mathematical optimization and
optimization in the real-world applications
Ideal function in
the mathematical
world
Rugged hill in the
experimental
world

28. Variables
Variables:
Variables are the free parameters, quantities that the designer can control
Continuous variables:
• point coordinates
• process variables
Discrete variables:
• components from a
catalogue
• number of components

29. Objectives
Objectives are the response parameters, i.e. the quantities that the designer wish to
be MAX or MIN
MAX MIN
efficiency cost
performance weight
... …
Note : A MAX problem can always be transformed into a MIN problem.

30. Why Multiobjective optimization
• Most design or problem solving
activities are multiobjective by
nature
• Problems usually involve multiple
conflicting objectives that should
be considered simultaeously

31. Pareto dominance
• Pareto Dominance:
• Design a dominates Design b if:
– [f1(a) >= f1(b) and f2(a) >= f2(b)...and fn(a) >= fn(b)]
– and [f1(a) > f1(b) or f2(a) > f2(b)...or fn(a) > fn(b)]
• In the Pareto frontier none of the components can be improved without
deterioration of at least one of the other component.
• Pareto dominance for one objective coincides with a classical optimization
approach
• Pareto dominance defines a group of efficient solutions: in case of n objectives,
the group of efficient solutions contains at Max ∞(n-1) points

32. Pareto dominance
A dominates B if and only if:
[ f1(a) >= f1(b) and f2(a) >= f2(b)... and fn(a) >= fn(b) ]
and
[ f1(a) > f1(b) or f2(a) > f2(b)... or fn(a) > fn(b) ]
f1
Red dots are all efficient
solutions
f2

33. Pareto Dominated Points
• Rapidly decreasing probability of
having a dominated solution in a
randomly generated dataset
• Rapidly increasing search effort for
when the number of objective is large
• Fortunately, in real-case applications
the number of dimensions can
collapse
m
( 1) k 1 m
k 1 kn 1 k
r Where m is number of points and n is number of
m objectives

34. Weighted Function
Weighted Function:
• n objectives can be added in a single objective using
weights:
– F(x) = w1*Obj1+w2*Obj2+…+wn*Objn...
• Pro:
• simple formulation
• Cons:
• weights are problem-dependent and must be
empirically defined
• weights are connected to objectives values and
might lose significance for different objectives
values

35. Why is the Weighting Method Ineffective
• Although this type of scalarization is widely used in many practical problems, it has
a serious drawback: it cannot provide solutions for non-convex cases
• Depending on the structure of the problem, the linearly weighted sum can not
necessarily provide a solution that the Decision Maker (DM) desires
• The DMs tend to misunderstand that a desirable solution can be obtained by
adjusting the weights but there is no positive correlation between the weights and
the value of functions

36. Example
min y1 f1 ( x), y2 f 2 ( x), y3 f 3 ( x) Suppose the DM want
x to reduce more y1 and
2 even a bit y2
s.t. yi 1 1
i 1, 2,3
The minimum of the linearly weighted
sum with all the weights equal to 1 is y1, y2 , y3 1 1/ 3,1 1/ 3,1 1/ 3
given by:
The DM changes the weights: y1, y2 , y3 1 10/ 105,1 2 / 105,1 1/ 105
1 , 2 , 3 10,2,1
The value of y2 is worse than before,
despite the weights given by the DM

37. Why is the Weighting Method Ineffective
• Someone might suspect that this is due to a missing
normalization of the weights!
• Normalization of the weights do not solve the problem
• It is usually very difficult to adjust the weights to
obtain a solution as the DM wants.

38. Maximize a Mathematical function
Maximize:
F1 ( x, y) [1 ( A1 B1 )2 ( A2 B2 )2 ]
2
Ai (ai , j sin( j) bi , j cos( j ))
j 1
2
Bi (ai , j sin( j ) bi , j cos( j ))
j 1
0.5 1.0 2.0 1.5
a b 1.0 2.0
1.5 2.0 1.0 0.5
( x, y) [ , ]

39. Mathematical functions
Maximize:
F2 ( x, y) [( x 3) 2 ( y 1) 2 ]
x, y [ , ]

40. Weighted Sum
Weighted Sum:
• F= (1-k)*F1+k*F2
• The parameter k is varied from 0 to 1
with a step of 0.1
• The weighted sum goes progressively
from F1 to F2
• The red zones indicate higher values for
the weighted sum

41. Pareto Frontier
Two variables, two
objectives, infinite
efficient solutions in two
regions not connected in
the variables definition
domain.
F2
F1

42. General Remarks
Facing a design problem:
• Rarely is there a clearly identified and unique objective
• There is a vague distinction between constraints and objectives
• Even if algorithms and numerical optimization theories exists in the
academic world since many years, the practical impact until today was
negligible and limited to very specific applications:
• It is necessary to:
• extend the concept of mathematical optimization to several
objectives
• have “robust” tools to explore the entire design configuration
space

43. Evolution & Optimization
• Evolutionary algorithms are direct
global search methods based the model
of organic evolution.
• Metaheuristics methods are a new type
of methods that have been developed
since 1980.
• These methods have the ability to solve
even difficult optimization problems in
the best way possible. This is an
important group of methods that has
significantly contributed to the renewal
of multiobjective optimization.

44. EA advantages
• Evolutionary algorithms (EAs) do not need derivatives information
• EAs are simple to implement
• EAs are flexible, may be applied to several different problems
• EAs are scalable to high-dimensional optimization problems
• EAs may deal with continuous, discrete and binary variables
• Always converge to a good enough solution in successive, self-
contained stages
• Robust against noisy objective functions
• Can be easily parallelized
• Shortcomings
– Slow convergence (but metamodeling may help!)

45. History
DARWIN in the wind tunnel!
The first real-case
application of
Evolution Strategy
methods used by
Prof. Rechenberg
Number of possible
adjustments
515 = 345 025 251

46. What companies really like of EAs
• EAs find a set of solutions which lie on the trade-off (Pareto frontier)
– Putting the preferences after optimization
– Much better understanding of the problem
– Better choices
f1
Engineers may choose
between solutions
f2

47. Evolutionary Optimization of Yagi-Uda Antennas

48. The Problem
• The Yagi antenna evolved as a special configuration of an endfire array
• It is a traveling wave antenna with a surface wave that propagates along the
array with a phase velocity slightly less than that of the free space
• It consists of a single driven element and a number of parasitic elements made
up of a reflector and a set of directors

49. Optimization
• The Yagi configuration has not been
amenable to theoretical analysis since it
is an array of elements of different
lengths with non-uniform spacing and
thus cannot be treated using
conventional array theory
• The Yagi-Uda antennas are known to be
difficult to optimize due to their
sensitivity at high gain and the inclusion
of numerous parasitic elements
• Over the years the performance of Yagi
antennas has been improved very
slowly

50. Antenna Parameters
• Parameters:
– Lenght for each element
– Spacing between elements
– Diameter of the wire
• With N elements, we have 2N parameters

51. Software used
• The original Numerical Electromagnetics Code (NEC)
has been developed at the Lawerence Livermore
Laboratory.
• The code has always been a "card image/batch run“
• SCILAB (www.scilab.org)

52. 4nec2 project
4nec2 is a completely free
Nec2 windows based tool for
creating, viewing, optimizing
and checking 2D and 3D style
antenna geometry structures
and generate, display and/or
compare near/far-field
radiation patterns for both the
starting and experienced
antenna modeler.
Antenna geometry edit in 4nec2.

53. Antenna Card
• An antenna described to NEC is
given in two parts, a structure
and a sequence of controls.
• The structure is simply a
numerical description of where
any part of the antenna is
located, and how the wires are
connected up. Thanks to the
old fashioned structure card
style input, it is very easy to
automatically change the
geometry.

54. Problem Setup - SCILAB
• Scilab is an interactive platform
for numerical computation
providing a powerful
computing environment for
engineering and scientific
applications.
• Scilab is a free software!
• A set of modules are available,
we will use OPTIMIZATION
tools.

55. Antenna Card
wire X,Y,Z start point X,Y,Z end point radius
CM NEC 2 elements
CE
GW 15 10 0.0000 -0.2500 0.0000 0.0000 0.2500 0.0000 1.e-3
GW 20 42 2.0000 -2.0000 0.0000 2.0000 2.0000 0.0000 1.e-3
GE 0
EX 0 15 5 0 1.0000 0 Means of excitation
GN -1
FR 0 1 0 0 299.8 0 Frequency (MHz)
RP 0 37 73 1003 -180 0 5 5
Optimization
Parameters
Radiation Pattern

56. Define Parameters
Parameters Lower Upper Step Goal Expression
bound bound
MaxGain Maximize(min(gain))
Lengths 0.1λ 1.5 λ 0.01
MinVSWR Mimize(max(VSWR))
Separations 0.05λ 0.75λ 0.01
Radius 2mm 6mm 1mm
The VSWR, or Standing Wave
Ratio, of an antenna is a
Frequency 219MHz 251MHz 16
measure of how efficiently
your antenna is radiating the
energy it produces when you
transmit.

57. Let SCILAB find the best solutions
• Several different optimization methods are
available (evolutionary and gradient
based)
• In this example we use an evolutionary
algorithm because this class of methods
are able to effectively search large space
• We can even approach the problem as a
multiobjective optimization problem
where we want to maximize the gain and
minimize the Voltage Standing Wave Ratio
(VSWR) without any weighting function.

58. Output Results
……..
- - - POWER BUDGET - - -
INPUT POWER = 4.4745E-03 WATTS
RADIATED POWER= 4.4745E-03 WATTS
STRUCTURE LOSS= 0.0000E+00 WATTS
NETWORK LOSS = 0.0000E+00 WATTS
EFFICIENCY = 100.00 PERCENT
- - - RADIATION PATTERNS - - -
- - ANGLES - - - POWER GAINS - - - - POLARIZATION - - - - - - E(THETA) - - - - - - E(PHI) - - -
THETA PHI VERT. HOR. TOTAL AXIAL TILT SENSE MAGNITUDE PHASE MAGNITUDE
PHASE
DEGREES DEGREES DB DB DB RATIO DEG. VOLTS/M DEGREES VOLTS/M
DEGREES
-180.00 0.00 -999.99 1.78 1.78 0.00000 -90.00 LINEAR 0.00000E+00 0.00 6.35890E-01 -120.91
-175.00 0.00 -999.99 2.24 2.24 0.00000 -90.00 LINEAR 0.00000E+00 0.00 6.70390E-01 -119.64
-170.00 0.00 -999.99 2.61 2.61 0.00000 -90.00 LINEAR 0.00000E+00 0.00 6.99122E-01 -121.61
-165.00 0.00 -999.99 2.54 2.54 0.00000 -90.00 LINEAR 0.00000E+00 0.00 6.93579E-01 -124.59
……...

59. Results
• Preparation time: 1 h
• Running time on a laptop: few hours
• Number of runs: 1000
• Initial design: Lowest gain 2.20 dB, Highest VSWR 13.43
• Some Pareto Solutions:
ID Gain VSWR
681 7.66 1.39
818 7.94 1.38
820 8.57 1.86
763 8.62 2.54

60. Results
Initial
points
VSWR
Gain

61. VSWR
From 13.43
to 1.38
-90%
Gain
From
2.20dB to
7.94dB
+261%

62. Conclusions
• Boost your creativity with SCILAB
• Push the limits of product innovation with open source
software
• No limits in the number of available licenses
• Option for parallel computing

63. References
• Kim and Mauborgne. Blue Ocean Strategy. Harvard Business School Press. 2005.
• Electromagnetic Optimization by Genetic Algorithms, Y.Rahmat-Samii and E. Michielssen,
eds.,Wiley,1999
• Evolutionary Optimization of Yagi-Uda Antennas, Lohn, J. D. Kraus, W. F. Linden, D. S. Colombano,
S. P., LECTURE NOTES IN COMPUTER SCIENCE, 2001, ISSU 2210, pages 236-243, Springer-Verlag;
1999
• Design of Yagi-Uda antennas using comprehensive learning particle swarm optimisation, Baskar,
S. Alphones, A. Suganthan, P.N. Liang, J.J. Sch. of Electr. & Electron. Eng., Nanyang Technol.
Univ., Singapore, in: Microwaves, Antennas and Propagation Proceedings,Oct. 2005, Volume: 152-
5, pages: 340- 346
• Single and Multi-objective design of Yagi-Uda Antennas using Computational Intelligence,
Neelakantam V. Venkatarayalu and Tapabrata Ray., in Proceedings of the 2003 Congress on
Evolutionary Computation, Volume 2, pp. 1237--1242, IEEE Press, Canberra, Australia, December
2003 .

64. THANK YOU FOR YOUR KIND
ATTENTION!
s.poles@enginsoft.it