Evolvability in Optimization Problems:
Towards more Efficient Evolutionary Algorithms
Jorge Tavares
INRIA Lille - Nord Europe Research Centre
jorge.tavares@ieee.org
http://jorgetavares.wordpress.com

Overview
• Fundamental issues
• Hows and Whys
• Case Studies
• Insights for more efficient
algorithms

Motivation
• Combinatorial Optimization Problems are a class of problems with high
practical importance but difficult to solve.
• Evolutionary algorithms integrate a set of techniques that proved to be an
efficient and robust paradigm for complex problem solving.
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Motivation
• Combinatorial Optimization Problems are a class of problems with high
practical importance but difficult to solve.
• Evolutionary algorithms integrate a set of techniques that proved to be an
efficient and robust paradigm for complex problem solving.
• The representation of candidate solutions for a given problem is one of the
fundamental questions.
3

Motivation
• Combinatorial Optimization Problems are a class of problems with high
practical importance but difficult to solve.
• Evolutionary algorithms integrate a set of techniques that proved to be an
efficient and robust paradigm for complex problem solving.
• The representation of candidate solutions for a given problem is one of the
fundamental questions.
• It is important to understand the role of representation and the interplay with
heuristics and local methods.
3

Genetic Representations
• It’s important to distinguish
between genotypes and
phenotypes.
4

Genetic Representations
• It’s important to distinguish
between genotypes and
phenotypes.
• Genotype: representation
manipulated by the evolutionary
algorithm's components.
4

Genetic Representations
• It’s important to distinguish
between genotypes and
phenotypes.
• Genotype: representation
manipulated by the evolutionary
algorithm's components.
• Phenotype: a candidate solution to
a given problem.
4

Genetic Representations
• It’s important to distinguish
between genotypes and
phenotypes.
Solution's
Phenotype Fitness Function
• Genotype: representation Quality
manipulated by the evolutionary
algorithm's components. Mapping Function
Genotype Genetic Operators
• Phenotype: a candidate solution to
a given problem.
• Important: the mapping between
these two entities
4

Genetic Representations
• Interdependencies between
operators and representations can
not be neglected.
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Genetic Representations
• Interdependencies between
operators and representations can
not be neglected.
• In a direct representation the
genotype is the same as the Individual Genetic Operators
phenotype. Genetic operators are
directly applied to the phenotype.
5

Genetic Representations
• Interdependencies between
operators and representations can
not be neglected.
• In a direct representation the
genotype is the same as the Individual Genetic Operators
phenotype. Genetic operators are
directly applied to the phenotype.
• A representation is indirect if the Phenotype
genotype and the phenotype are
different. Genetic operators are Mapping Function
applied to the genotype. Genotype Genetic Operators
5

Heuristics
• Heuristic: any method specifically
developed for application with
representations which are simple in
nature.
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Heuristics
• Heuristic: any method specifically
developed for application with
representations which are simple in
nature.
• Applied at three different levels:
mapping function, genetic
operators and on the structure.
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Heuristics
• Heuristic: any method specifically
developed for application with
representations which are simple in
nature.
Phenotype
Heuristics
• Applied at three different levels:
mapping function, genetic Mapping Function
operators and on the structure.
Genotype Genetic Operators
• Heuristic bias: the influence of the
heuristic on the efficiency of the
representation.
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Overview
• Fundamental issues
• Hows and Whys
• Case Studies
• Insights for more efficient
algorithms

How to perform Analysis?
• In the past years, some tools have been used with this aim in mind, from
empirical methods to theory-based analysis.
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How to perform Analysis?
• In the past years, some tools have been used with this aim in mind, from
empirical methods to theory-based analysis.
• Fitness landscape analysis:
‣ the characteristics of the search space can be helpful to identify a
search strategy that is likely to improve the algorithm performance
8

How to perform Analysis?
• In the past years, some tools have been used with this aim in mind, from
empirical methods to theory-based analysis.
• Fitness landscape analysis:
‣ the characteristics of the search space can be helpful to identify a
search strategy that is likely to improve the algorithm performance
• Empirical Analysis of Representation Properties:
‣ measurement and quantification of essential aspects for evolutionary
search allowing an inexpensive pre-evaluation of an algorithm
8

Landscape Analysis
• Evolutionary search can be represented by three spaces:
‣ the search space
‣ the phenotype space
‣ the fitness space
• Fitness landscapes describe the relation between the search and the fitness
space.
9

Fitness Distance Correlation
• One way to measure problem difficulty is determining how close is the
relation between fitness value and distance to the nearest optimum.
• The search should be easy, for selection-based algorithms, when fitness
increases as the distance to the optimum decreases. This indicates the
existence of a path via solutions with increasing fitness values.
• Measure:
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Auto-Correlation
• The structure of a fitness landscape can be examined by measuring the
degree of correlation between points on the landscape. The degree depends
on the difference between the fitness values of the points.
• Smoother landscapes are highly correlated, making the search for an
evolutionary algorithm easier. If the difference of fitness values is higher, the
landscape is less correlated, which implies a rugged landscape, thus being
harder to search in it.
• Measure:
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Representations Properties
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Representations Properties
• Locality:
‣ Small steps in the search space cause small phenotypic changes.
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Representations Properties
• Locality:
‣ Small steps in the search space cause small phenotypic changes.
• Heritability:
‣ The ability of crossover operators to produce offspring that combine
meaningful features of their parents.
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Representations Properties
• Locality:
‣ Small steps in the search space cause small phenotypic changes.
• Heritability:
‣ The ability of crossover operators to produce offspring that combine
meaningful features of their parents.
• Heuristic Bias:
‣ Phenotypes with higher probability to be created without selection
pressure, induced by heuristics or problem specific operators.
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Mutation Innovation
• The distance between the individuals involved in a mutation is used to predict
the effect of the application this operator.
• MI illustrates how much innovation the mutation operator introduces, i.e., it
aims to determine how much this operator modifies the semantic properties
of an individual.
• Measure:
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Crossover Innovation
• It measures the ability of this operator to create descendants that are different
from their parents, i.e., the phenotypic distance between a child and its
phenotypical closer parent.
• Similar parents tend to create descendants that are also close to both of
them. On the contrary, dissimilar parents tend to originate larger crossover
innovations.
• Measure:
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Other Measures
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Other Measures
• Heritability:
‣ Crossover Loss: measures the total size of phenotypic substructures in
an offspring that is not inherited from either of the parents but newly
introduced.
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Other Measures
• Heritability:
‣ Crossover Loss: measures the total size of phenotypic substructures in
an offspring that is not inherited from either of the parents but newly
introduced.
• Heuristic Bias:
‣ Bias in the encodings: mean and standard deviaton of each individual
to the best known solution.
‣ Bias in the operators: mean and standard deviation on a evolutionary
run without selection.
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Overview
• Fundamental issues
• Hows and Whys
• Case Studies
• Insights for more efficient
algorithms

Landscape Analysis: Golomb Rulers
• A Golomb Ruler is defined as a ruler that has marks unevenly spaced at
integer locations where the distance between any two marks is unique.
• Unlike usual rulers, they have the ability to measure more discrete measures
than the number of marks they possess.
• Golomb Rulers are not redundant since they do not measure the same
distance twice.
• An Optimal Golomb Ruler (OGR) is defined as the shortest length ruler for a
given number of marks.
• There may exist multiple different OGRs for a specific number of marks.
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Landscape Analysis: Golomb Rulers
• An example:
• Representations: binary, integer, permutation, random-key
• Operators: flip (for all mutation variants), shift, 1-point cx, uniform cx
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Landscape Analysis: Golomb Rulers
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Fitness Distance Correlation: Mutation
Binary with Flip Binary with Shift Integer
Permutation Random-key Incomplete Permutation
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Fitness Distance Correlation: Crossover
Binary with 1Pt CX Integer with 1Pt CX Permutation with 1Pt CX Random-key with 1Pt CX
Binary with Uniform CX Integer with Uniform CX Permutation with Uniform CX Random-key with Uniform CX
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Fitness Distance Correlation: adding Heuristics
Binary + Flip + Correction Binary + Flip + Insertion Binary + Flip + Correction + Insertion
Binary + Shift + Correction Binary + Shift + Insertion Binary + Shift + Correction + Insertion
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Inc. Permutation + Heuristic Permutation + Heuristic Random-key + Heuristic

Locality Analysis: Protein-Ligand Docking
• Protein-ligand docking is an energy minimization search problem with the aim
to find the best ligand conformation and orientation relative to the active site
of a target protein.
• The docking problem can be very difficult since the relative orientation and
conformations of the two molecules must be considered.
• Typically, the receptor (usually a protein) is fixed in a three-dimensional
coordinate system. By contrast, the ligand can be repositioned and rotated.
23

Locality Analysis: Evolutionary Model
• Auto-Dock: this approach is a conformational search method which uses an
approximate physical model to evaluate possible protein-ligand
conformations.
• It incorporates flexibility by allowing the ligand to change its conformation
during the docking simulation.
• A genotype is encoded by a vector of real-valued numbers which represent
the ligand’s translation and orientation. Cartesian coordinates represent the
ligand translation, three variables in the vector, whereas four variables
defining a quaternion represent the ligand orientation. For each flexible
torsion angle one variable is used.
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Locality Analysis: Evolutionary Model
• The phenotype of a candidate solution is composed of the atomic
coordinates that represent the three-dimensional structure of the ligand.
• The atomic structure of the ligand is built from the translation and orientation
coordinates in the ligand crystal structure with the application of the torsion
angles.
• Since the encoding is a real-valued vector, mutation is performed by using
evolutionary strategies based operators:
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Locality: the effect of Mutation
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Locality: the effect of Mutation
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Locality: the effect of Mutation
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Locality: the effect of Mutation
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Locality: the impact of Local Search
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Locality: the impact of Local Search
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Locality: the impact of Local Search
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Overview
• Fundamental issues
• Hows and Whys
• Case Studies
• Insights for more efficient
algorithms

Understanding Algorithms
• The analysis of adding heuristics and local improvement techniques; although
in general the addition of these type of mechanisms provide a better
performance, this is not always true.
• Is important for an operator to induce strong locality to obtain good
optimization results.
• It provides hints on how future genetic operators, representations, heuristics
and local search methods can be developed.
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The Generic Evolutionary Algorithm
• Organization of the Evolution engine:
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Example: Evolving Operators
• Evolution by means of Genetic Programing, or similar techniques, of genetic
operators for a specific problem.
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Example: Evolving Operators
• Evolution by means of Genetic Programing, or similar techniques, of genetic
operators for a specific problem.
• The operators are evolved according to:
➡ The degree of representation properties induced by the operator, e.g.,
we want a locally-strong operator.
➡ How an operator can navigate more smoothly on a landscape.
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Evolution and Self-Organization
• With these elements, it will be possible to provide a framework dedicated to
the evolution of genetic representations and other evolutionary components.
• Understanding the effects of a representation and operators when solving a
problem is important so that new and more efficient encodings can be
developed to the problem being solved.
• Using representation properties and the effects of genetic operators, as well
other components, to guide the algorithm in the search for its own
configuration.
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Questions?
jorge.tavares@ieee.org
http://jorgetavares.wordpress.com
Images by Penousal Machado, University of Coimbra
http://eden.dei.uc.pt/~machado