Evolution Engine

Contents

• Introduction
• Selection choice of parents that will be allowed to reproduce
• Replacement choice of individuals that will survive
• Popular evolution engines all historical evolution engines are implemented in EO
• Helper classes:
• tournaments, are intensively used within selection and replacement procedures
• rate-or-number is used to decide whether to return a relative (to the current population size) or absolute number, when something should return more than one individual.
• Survive-and-die, a functor class with two populations arguments: saves some from the first in the second, and kill some others from the first. Used in replacements only.

The term evolution engine denotes the different parts of an Evolutionary Algorithm that simulate the Darwinism:

Darwinism takes place in two different phases of an EA, though in many popular variants, only one phase is activated.

Selection is the Darwinistic choice of parents that will be allowed to reproduce.
Replacement takes place after reproduction, and is the Darwinistic choice of those individuals that will survive, i.e. become the parents of the next generation.

Both selection and replacement will be discussed in turn, before some helper classes that are used within selection and replacement procedures are presented.

The replacement phase takes place after the birth of all offspring through variation operators. The idea is to close the generation loop, i.e. to end up with a population of individuals that will be the initial population of next generation. That population will be built upon the old parents and the new-born offspring. In all algorithms that come up with EO, the population size is supposed to be constant from one generation to the next one - though nothing stops you from writing an algorithm with varying population size.

Replacement: The interface

The abstract class for replacement procedures is the functor class eoReplacement, and the interface for its operator() is

which you could have guessed from the inheritance tree for class eoReplacement., as you see there that eoReplacement derives from class eoBF<eoPop<EOT>&, eoPop<EOT>&, void>.
This means that it takes 2 populations (called, for obvious anthropomorphic reasons, _parents and _offspring :-) and is free to modify both, but the resulting population should be placed in the first argument (usually called_parents) to close the loop and go to next generation.

Replacement: Instances

• eoGenerationalReplacement This is the most straightforward replacement, called generational replacement: all offspring replace all parents (used in Holland's and Goldberg's traditional GAs).  It takes no argument, and supposes that offspring and parents are of the same size (but does not check!).

 
• eoMergeReduce This is one the basic types of replacement in EO. It has two major steps, merging both populations of parents and offspring, and reducing this big population to the right size. It contains two objects of respective types eoMerge and eoReduce and you can probably guess what each of them actually does :-)

 

 

Available instances of eoMergeReduce replacement include

• eoCommaReplacement, one of the two standard strategies in Evolution Strategies, selects the best offspring. It is an eoMergeReduce(eoNoElitism, eoTruncate).
• eoPlusReplacement, the other standard Evolution Startegies replacement, where the best from offspring+parents become the next generation. It is an eoMergeReduce(eoPlus, eoTruncate).
• eoEPReplacement, used in the Evolutionary Programming historical algorithm, doing a stochastic tournament among parents + offspring. It is an eoMergeReduce(eoPlus, eoEPReduce) and its constructor requires as argument the size of the tournament (unsigned int).
• eoReduceMerge is another important type of eoReplacement: the parents are first reduced, and then merged with the offspring. Note that the parent population is reduced of the exact number of offspring.

Though not mandatory, it is implicitely assumed that few offspring have been generated. Hence, all derived replacement procedures of class eoReduceMerge are termed eoSGAxxx, as they are the ones to use in SteadyState Genetic Algorithm engine. This gives the following instances of eoReduceMerge:
•  eoSSGAWorseReplacement in which the worse parents are killed and replaced by all offsprings (no additional argument needed);
• eoSSGADetTournamentReplacement in which parents to be killed are chosen by a (reverse) determinitic tournament. Additional parameter (in the constructor) is the tournament size, an unsigned int).
• eoSSGAStochTournamentReplacement in which parents to be killed are chosen by a (reverse) stochastic tournament. Additional parameter (in the constructor) is the tournament rate, a double).
• eoSurviveAndDie is

You can add what is called weak elitism to any replacement by encapsulating it into an eoWeakElitismReplacement object. Weak elitism ensures that the overall best fitness in the population will never decrease: if the best fitness in the new population is less than the best fitness of the parent population, then the best parent is added back to the new population, replacing the worse.

Within EO, this is very easy to add:

First, declare your replacement functor (here, generational, but it can be any replacement object):
eoGenerationalReplacement<Indi> genReplace;
Then wrap the weak elitism around it:
eoWeakElitismReplacement<Indi> replace(genReplace);
and use now replace as your replacement procedure within your algorithm.

Note: of course, adding weak elitism to an elitist replacement makes no sense - but will not harm either :-)

Replacement: Test file

The file t-eoReplacement in the test directory implements all above replacmenet procedures withni a very simple and easy-to-monitor Dummy EO class.

This section will be completed soon - in the meantime just trust us that all of these are already implemented in EO (except maybe some of the last category :-) !!!!!!

The most popular evolution engines are listed below, together with the way to use them in EO. If you don't find your particuler algorithm, please send it to us, and we might include it here!

• Generational Genetic Algorihtm
• Steady-State Genetic Algorithm
• (MU+Lambda)-Evolution Strategy
• (MU,LAMBDA)-Evolution Strategy
• Evolutionary Programming
• You name it :-)

Tournaments are an easy and quick way to select individuals within a population based on simple comparisons. Though usually based on fitness comparisons, they can use any comparison operator.
In EO, there are two variants of tournaments used to select one single individual, namely Deterministic Tournament and Stochastic Tournament, that are used in selection and in replacement procedures, and a global tournament-based selection of a whole bunch of individuals, the EP Tournament. Though the single-selection tournaments can be repeated to select more than one individual, and the batch tournament selection can be used to select a single individual, both uses are probably a waste of CPU time.

• Deterministic Tournament of size T selects returns the best of T uniformly chosen individuals in the population. It is implemented in the eoDetTournamentSelect class, a sub-class of eoSelectOne, as well as in the eoDetTournamentTruncate class that repeatidly removes from the population the "winner" of the inverse tournament.  These objects use the C++ function determinitic_tournament in  selectors.h.
• Stochastic Tournament of rate R first choses two individuals from the population, and selects the best one with probability R and the worse one with probability (1-R). It is implemented in the eoStochTournamentSelect class, a sub-class of eoSelectOne, as well as in the eoStochTournamentTruncate class that repeatidly removes from the population the "winner" of the inverse tournament.  These objects use the C++ function determinitic_tournament in  selectors.h.
• EP Tournament of size T is a global tournament: it works by assigning a score to all individuals in the population the following way: starting with a score of 0, each individual I is "opposed" T times to a uniformly chosen individual. Everytime I wins, its score in incremented by 1 (and by 0.5 for every draw). The individuals are then selected deterministically based on their scores from that procedure. The EP Tournament is implemented in the  eoEPReduce truncation method used in some replacement procedures.

In replacement procedures, one frequently needs to merge two populations (computed form old parents and new-born offspring). Classes derived from the abstract class eoMerge are written for that purpose.

eoMerge: interface
The abstract class for merging procedures is the functor class eoMerge, and the interface for its operator() is

which you could have guessed from the inheritance tree for class eoMerge, as you see there that eoMerge derives from
class eoBF<const eoPop<EOT>&, eoPop<EOT>&, void>.
This means that it takes 2 populations and modifies the seond one by adding some individuals from the first one (which is supposed to remain constant).

eoMerge: instances
Available instances of eoMerge objects are eoPlus, that simply adds the parents to the offspring, or eoElitism, that adds only some of the (best) parents to the offspring. A special case of eoElistism is eoNoElitism, an eoMerge that does nothing.

The other useful component of replacement procedures, eoReduce, kills some individuals from a given population.

eoReduce: interface
The abstract class for reducing procedures is the functor class eoReduce, and the interface for its operator() is

which you could have guessed from the inheritance tree for class eoReduce, as you see there that eoReduce derives from
class eoBF<eoPop<EOT>&, unsigned int, void>.
An eoReduce shoud take a population and shrink it to the required size.

eoReduce: instances
Available instances of eoReduce are

• eoTruncate, deterministically kills the worse individuals, keeping only the required number. It starts by sorting teh populations, and hence does modify its order.
• eoLinearTruncate, deterministically kills the worse individuals, keeping only the required number. It does so by repeatedly removing the worsr individual. Hence does not modify its order, but takes longer time than eoTruncate in case of many offspring.
• eoEPReduce, uses the EP stochastic tournament to reduce the population. It requires an additinal argument, the tournament size.
• eoDetTournamentTruncate uses inverse deterministic tournament to repeatidly kill one individual until the propoer size is reached. As eoLinearTruncate, it might take some time in the case of many offspring. It requires the size of the tournament (unsigned int) as parameter in the constructor (default is 2).
• eoStochTournamentruncate  uses inverse stochastic tournament to repeatidly kill individuals from the population. It requires the rate of the tournament (double) as parameter in the constructor (default is 0.75).

Many classes in selection/replacement procedures will handle a number of individuals that may either be fixed or be a fraction of some argument-population size.
Of course, it is possible to write two different classes that will only differ by the way they compute the number of individuals they have to treat, as it is done for selectors with the two classes eoSelectPerc and eoSelectNumber (it could also have been possible to have some pure abstrat class and implement the computation of the number of individuals to treat in some derived classes).
However, rather than multiply the number of class, EO has defined a class that will handle the problem once and for all, the class eoHowMany. It receives a double, and a boolean indicating whether that double is to be treated as a rate or as an absolute (unisgned) interger.

eoHowMany: interface
The class interface for its operator() is

which you could have guessed from the inheritance tree for class eoHowMany, as you see there that eoHowMany derives from
class eoUF<unsigned int, unsigned int>.

Its constructor takes 2 argumenrts:

It is used in eoSelectMany (which supersedes eoSelectPerc and eoSelectNumber, but they are left there for tutorial reasons!) as well as in many truncation methods.