PGAPy 1.2.1

Python wrapper for pgapack, the parallel genetic algorithm library

Author:

Ralf Schlatterbeck <[e-mail]>

News 03-2022: Attempt to make this installable on Windows. This involves some workaround in the code because the visual compiler does not support certain C99 constructs.

News 01-2022: This version wraps multiple evaluation with NSGA-III (note the additional ‘I’).

News 12-2021: This version wraps multiple evaluation values from your objective function: Now you can return more than one value to either use it for constraints (that must be fulfilled before the objective is optimized) or for multi-objective optimization with the Nondominated Sorting Genetic Algorithm V.2 (NSGA-II). You can combine both, multi-objective optimization and constraints.

News: This version wraps the Differential Evolution method (that’s quite an old method but is newly implemented in pgapack).

PGAPy is a wrapper for PGAPack, the parallel genetic algorithm library (see PGAPack Readme), a powerfull genetic algorithm library by D. Levine, Mathematics and Computer Science Division Argonne National Laboratory. The library is written in C. PGAPy wraps this library for use with Python. The original PGAPack library is already quite old but is one of the most complete and accurate (and fast, although this is not my major concern when wrapping it to python) genetic algorithm implementations out there with a lot of bells and whistles for experimentation. It also has shown a remarkably small number of bugs over the years. It supports parallel execution via the message passing interface MPI in addition to a normal “serial” version. That’s why I wanted to use it in Python, too.

To get started you need the PGAPack library, although it now comes bundled with PGApy, to install a parallel version you currently need a pre-installed PGApack compiled for the MPI library of choice. See Installation section for details.

There currently is not much documentation for PGAPy. You really, absolutely need to read the documentation that comes with PGAPack. The PGAPack user guide is now shipped together with PGAPy. It is installed together with some examples in share/pgapy, wherever the Python installer decides to place this in the final installation (usually /usr/local/share on Linux).

The original PGAPack library can still be downloaded from the PGAPack ftp site, it is written in ANSI C and therefore should run on most platforms. Note that this version is not very actively maintained. I’ve started a PGAPack fork on github where I’ve ported the library to the latest version of the MPI standard and have fixed some minor inconsistencies in the documentation. I’ve also implemented some new features (notably enhancements in selection schemes and a new replacement strategy called restricted tournament replacement and, more recently, the differential evolution strategy.)

Note: When using NSGA_III replacement for multi (or many-) objective optimization you need to either

• set reference points on the hyperplane intersecting all axes at offset 1. These reference points can be obtained with the convenience function pga.das_dennis, it creates a regular set of reference points using an algorithm originally publised by I. Das and J. E. Dennis. These points are then passed as the paramter reference_points to the PGA constructor.

  See examples/dtlz2.py for a usage example and the user guide for the bibliographic reference. The function gets the dimensionality of the objective space (num_eval minus num_constraint) and the number of partition to use.

• Or set reference directions (in the objective space) with the reference_directions parameter, number of partitions for these directions with the refdir_partitions parameter (see das_dennis above, this uses Das/Dennis points internally), and a scale factor with the parameter refdir_scale.

You can set both, these parameters are not mutually exclusive.

I have tested pgapy on Linux only and I’ll currently not provide Windows versions. You also can find my PGAPack fork on github this repository has the three upstream releases as versions in git and contains some updates concerning support of newer MPI versions and documentation updates. I’ve also included patches in the git repository of the Debian maintainer of the package, Dirk Eddelbuettel.

To get you started, I’ve included some very simple examples in examples, e.g., one-max.py implements the “Maxbit” example similar to one in the PGAPack documentation. The examples were inspired by the book “Genetic Algorithms in Python” but are written from scratch and don’t include any code from the book. The examples illustrates several points:

• Your class implementing the genetic algorithm needs to inherit from pga.PGA (pga is the PGAPy wrapper module).

• You need to define an evaluation function called evaluate that returns a sequence of numbers indicating the fitness of the gene given. It gets the parameters p and pop that can be used to fetch allele values from the gene using the get_allele method, for more details refer to the PGAPack documentation. The number of evaluations returned by your function is defined with the constructor parameter num_eval, the default for this parameter is 1. If your evaluation function does not return multiple evaluations (with the default setting of num_eval) you can either return a one-element sequence or a single return value.

• When using multiple evaluations, these can either be used for constraints (the default) or for multi-objective optimization. In the latter case, the number of constraints (which by default is one less than the number of evaluations set with the parameter num_eval) must be set to a number that leaves at least two evaluations for objectives. The number of constraints can be set with the parameter num_constraint. When using multi-objective optimization, you need one of the two replacement-types PGA_POPREPL_NSGA_II or PGA_POPREPL_NSGA_III, set this with the pop_replace_type parameter.

• You can define additional functions overriding built-in functions of the PGAPack library, illustrated by the example of print_string. Note that we could call the original print_string method of our PGA superclass. In the same way you can implement, e.g., your own crossover method.

• The constructor of the class needs to define the Gene type, in the examples we use int and bool built-in datatypes.

• The length of the gene needs to be given in the constructor.

• We often want to maximize the numbers returned by our evaluation function, set the parameter maximize to False if you want to minimize.

• For non-binary genes we can define an array of init values, each entry containing a sequence with lower and upper bound. The array has to have the length of the gene. Note that the upper bound is included in the range of possible values (unlike the python range operator but compatible with the PGAPack definition).

• In the constructor of the class we can add parameters of the genetic algorithm. Not all parameters of PGAPack are wrapped yet, currently you would need to consult the sourcecode of PGAPy to find out which parameters are wrapped. In the example we define several print options.

• Finally the genetic algorithm is started with the run method.

Naming conventions in PGAPy

When you extend PGAPy – remember not all functions of PGAPack are wrapped yet and you may need additional functions – you should stick to my naming conventions when making changes. The following naming conventions were used for the wrapper:

• Constants of PGAPack like PGA_REPORT_STRING are used as-is in uppercase. These constants can be directly imported from the wrapper module. Not all constants are wrapped so far, if you need more, add them to the constdef array in pgamodule.c and send me a patch.

• For methods of the pga.PGA class I’ve removed the PGA prefix used throughout PGAPack and converted the method to lowercase with underscores between uppercase words in the original function name, so PGARun becomes run, PGACheckStoppingConditions becomes check_stopping_conditions. An exception of the lowercase-rule is whenever a name contains “GA” (for “genetic algorithm”), So PGASetMaxGAIterValue becomes max_GA_iter.

• Where possible I’ve made a single class method where PGAPack needs a separate function for each datatype, so PGAGetBinaryAllele, PGAGetCharacterAllele, PGAGetIntegerAllele, PGAGetRealAllele all become get_allele. Same holds true for set_allele.

• Whenever a name in PGApack has a “Value” or “Flag” suffix, I’ve left this out, so PGAGetFitnessCmaxValue becomes fitness_cmax and PGAGetMutationAndCrossoverFlag becomes mutation_and_crossover, the only exception to this rule is for the two functions PGAGetMutationRealValue and PGAGetMutationIntegerValue which become mutation_value not just mutation.

• Some fields can take multiple values (they are implemented by ORing integer constants, in python they are specified as a list or tuple of constants). These are converted to plural (if not already plural in PGApack), e.g., PGASetStoppingRuleType becomes stopping_rule_types.

• Internal method names in the wrapper program have a leading PGA_ – so the class method set_allele is implemented by the C-function PGA_set_allele in pgamodule.c.

Constructor Parameters

PGApack has a lot of PGASet and PGAGet functions for setting parameters. These are reflected in constructor parameters on the one hand and in read-only properties of a PGA object on the other hand. The following table gives an overview of all the original PGApack names and the names of the python wrapper. For the PGApack name I’ve only listed the PGASet function, in many cases there is a corresponding PGAGet function. If a corresponding read-only property exists for a constructor parameter this is indicated in the “Prop” column. In some cases properties are missing because no corresponding PGAGet function is implemented in PGApack, in other cases returning a numeric value that has a symbolic constant in PGApy doesn’t make much sense. The properties have the same name as the constructor parameter. There are Properties that don’t have a corresponding constructor parameter, namely the eval_count property (returning the count of function evaluations) and the GA_iter property that returns the current GA generation. In the type column I’m listing the Python type. If the type is followed by a number, more than one item of that type is specified (a sequence in Python). Some entries contain “sym”, these are integer values with a symbolic constant, the value “msym” indicates that several values denoted by a list of symbolic constants can be given. A special case are the PGASetRealInitRange, PGASetRealInitPercent, PGASetIntegerInitRange functions. These take two values for each allele of the gene. In python this is a sequence of 2-tuples. Note that this means that you can have different ranges of allowed values for each allele.

The num_eval property is special: Due to limitations of the C programming language, for multiple evaluations in C the first evaluation is returned as the function return-value of the evaluate function and all other parameters are returned in an auxiliary array. PGApack specifies the number of auxiliary evaluations to be returned. In Python the evaluation function can always return a sequence of evaluation values and the num_eval is one more than PGAGetNumAuxEval would return. The default for num_eval is 1.

The first two (mandatory) constructor parameters are the type of the gene (this takes a Python type, e.g., bool for a binary genome or int for an integer genome) and the length. Note that the string_length is implicitly set with the length parameter. The string_length is also available as the length of the PGA object using the Python built-in len function.

PGApack name	Constructor parameter	Type	Prop
PGASetCrossoverBoundedFlag	crossover_bounded	int	yes
PGASetCrossoverBounceBackFlag	crossover_bounce_back	int	yes
PGASetCrossoverSBXEta	crossover_SBX_eta	float	yes
PGASetCrossoverSBXOncePerString	crossover_SBX_once_per_string	int	yes
PGASetCrossoverProb	crossover_prob	float	yes
PGASetCrossoverType	crossover_type	sym	no
PGAGetEvalCount	eval_count	int	yes
PGASetFitnessCmaxValue	fitness_cmax	float	yes
PGASetFitnessType	fitness_type	sym	no
PGAGetGAIterValue	GA_iter	int	yes
PGASetIntegerInitPermute	integer_init_permute	int2	no
PGASetIntegerInitRange	init		no
PGASetMaxFitnessRank	max_fitness_rank	float	yes
PGASetMaxGAIterValue	max_GA_iter	int	yes
PGASetMaxNoChangeValue	max_no_change	int	no
PGASetMaxSimilarityValue	max_similarity	int	no
PGASetMutationAndCrossoverFlag	mutation_and_crossover	int	yes
PGASetMutationBounceBackFlag	mutation_bounce_back	int	yes
PGASetMutationBoundedFlag	mutation_bounded	int	yes
PGASetMutationIntegerValue	mutation_value	int	yes
PGASetMutationOrCrossoverFlag	mutation_or_crossover	int	yes
PGASetMutationPolyEta	mutation_poly_eta	float	yes
PGASetMutationPolyValue	mutation_poly_value	float	yes
PGASetMutationProb	mutation_prob	float	yes
PGASetMutationRealValue	mutation_value	float	yes
PGASetMutationType	mutation_type	sym	no
PGASetNoDuplicatesFlag	no_duplicates	int	no
PGASetNumAuxEval	num_eval	int	yes
PGASetNumConstraint	num_constraint	int	yes
PGASetNumReplaceValue	num_replace	int	yes
PGASetPopSize	pop_size	int	yes
PGASetPopReplaceType	pop_replace_type	sym	no
PGASetPrintFrequencyValue	print_frequency	int	yes
PGASetPrintOptions	print_options	msym	no
PGASetPTournamentProb	p_tournament_prob	float	yes
PGASetRandomizeSelect	randomize_select	int	yes
PGASetRandomSeed	random_seed	int	yes
PGASetRealInitRange	init		no
PGASetRealInitPercent	init_percent		no
PGASetRestartFlag	restart	int	yes
PGASetRestartFrequencyValue	restart_frequency	int	yes
PGASetRTRWindowSize	rtr_window_size	int	yes
PGASetSelectType	select_type	sym	no
PGASetStoppingRuleType	stopping_rule_types	msym	no
PGASetStringLength	string_length	int	yes
PGASetSumConstraintsFlag	sum_constraints	int	yes
PGASetTournamentSize	tournament_size	int	yes
PGASetTournamentWithReplacement	tournament_with_replacement	int	yes
PGASetTruncationProportion	truncation_proportion	float	yes
PGASetUniformCrossoverProb	uniform_crossover_prob	float	yes

PGA Object Methods

The following are the methods that can be used during the run of the genetic search. The run method is used to start the search. This can be used, to, e.g., set an allele during hill-climbing in a custom endofgen method. Note that some methods only apply to certain gene types, e.g. the encode_int_ methods can only be used on binary alleles (they encode an integer value as a binary or gray code representation into the gene). Other methods take or return different types depending on the type of gene, e.g. get_allele or set_allele, they call different backend functions depending on the gene type. With the set_random_seed method, the random number generator can be re-seeded. It is usually best to seed the generator once at (before) the beginning by specifying random_seed in the constructor. For further details consult the user guide. The method get_evaluation will return a double for a single evaluation and a tuple of double for multiple evaluations (when num_eval is >1)

Method	Parameters	Return
check_stopping_conditions		True if stop should occur
encode_int_as_binary	p, pop, frm, to, val	None
encode_int_as_gray_code	p, pop, frm, to, val	None
encode_real_as_binary	p, pop, frm, to l, u, val	None
encode_real_as_gray_code	p, pop, frm, to l, u, val	None
euclidian_distance	p1, pop1 p2, pop2	float
fitness	pop	None
get_allele	p, pop, index	allele value
get_best_index	pop	index of best string
get_best_report_index	pop, idx	index of best eval with idx
get_evaluation	p, pop	evaluation of p
get_evaluation_up_to_date	p, pop	True if up-to-date
get_fitness	p, pop	fitness of p (float)
get_int_from_binary	p, pop, frm, to	int
get_int_from_gray_code	p, pop, frm, to	int
get_iteration		deprecated, use GA_iter
get_real_from_binary	p, pop, frm, to, l, u	float
get_real_from_gray_code	p, pop, frm, to, l, u	float
random01		float between 0 and 1
random_flip	probability	0 or 1
random_gaussian	mean, stddev	float
random_interval	l, r	int between l, r
random_uniform	l, r	float between l, r
run		None
select_next_index	pop	index selected individual
set_allele	p, pop, i, value	None
set_evaluation	p, pop, value	None
set_evaluation_up_to_date	p, pop, status	None
set_random_seed	seed	None (use constructor!)

User-Methods

PGApack has the concept of user functions. These allow customization of different areas of a genetic algorihm. In Python they are implemented as methods that can be changed in a derived class. One of the methods that must be implemented in a derived class is the evaluate function (although technically it is not a user function in PGApack). It interprets the gene and returns an evaluation value or a sequence of evaluation values if you set the num_eval constructor parameter. PGApack computes a fitness from the raw evaluation value. For some methods an up-call into the PGA class is possible, for some methods this is not possible (and in most cases not reasonable). Note that for the stop_cond method, the standard check for stopping conditions can be called with:

self.check_stopping_conditions()

The following table lists the overridable methods with their parameters (for the function signature the first parameter self is omitted). Note that in PGApack there are additional user functions that are needed for user-defined data types which are currently not exposed in Python. In the function signatures p denotes the index of the individual and pop denotes the population. If more than one individual is specified (e.g., for crossover) these can be followed by a number. For crossover c1 and c2 denote the destination individuals (children). The propability for the mutation method is a floating-point value between 0 and 1. Remember to count the number of mutations that happen, and return that value for the mutation method!

Method	Call Signature	Return Value	Up-Call
check_duplicate	p1, pop1, p2, pop2	True if dupe	no
stop_cond		True to stop	no
crossover	p1, p2, p_pop, c1, c2, c_pop	None	no
endofgen		None	no
evaluate	p, pop	sequence of float	no
gene_difference	p1, pop1, p2, pop2	float	no
initstring	p, pop	None	no
mutation	p, pop, propability	#mutations	no
pre_eval	pop	None	no
print_string	file, p, pop	None	yes

Constants

The following PGApack constants are available:

Constant	Description
PGA_CROSSOVER_ONEPT	One-point Crossover
PGA_CROSSOVER_SBX	Simulated Binary Crossover
PGA_CROSSOVER_TWOPT	Two-point Crossover
PGA_CROSSOVER_UNIFORM	Uniform Crossover
PGA_FITNESSMIN_CMAX	Map fitness by subtracting worst
PGA_FITNESSMIN_RECIPROCAL	Map fitness via reciprocal
PGA_FITNESS_NORMAL	Linear normalization of fitness
PGA_FITNESS_RANKING	Linear fitness ranking
PGA_FITNESS_RAW	Identity fitness function
PGA_MUTATION_CONSTANT	Mutation by adding/subtracting constant
PGA_MUTATION_GAUSSIAN	Mutation by selecting from Gaussian distribution
PGA_MUTATION_PERMUTE	Mutation swaps two random genes
PGA_MUTATION_POLY	Polynomial Mutation
PGA_MUTATION_RANGE	Replace gene with uniform selection from init range
PGA_MUTATION_UNIFORM	Mutation uniform from interval
PGA_NEWPOP	Symbolic constant for new population
PGA_OLDPOP	Symbolic constant for old population
PGA_POPREPL_BEST	Population replacement best strings
PGA_POPREPL_NSGA_II	Use NSGA-II replacement for multi-objective opt.
PGA_POPREPL_NSGA_III	Use NSGA-III replacement for multi-objective opt.
PGA_POPREPL_PAIRWISE_BEST	Compare same index in old and new population
PGA_POPREPL_RANDOM_NOREP	Population replacement random no replacement
PGA_POPREPL_RANDOM_REP	Population replacement random with replacement
PGA_POPREPL_RTR	Restricted Tournament Replacement
PGA_REPORT_AVERAGE	Report average evaluation
PGA_REPORT_HAMMING	Report hamming distance
PGA_REPORT_OFFLINE	Report offline
PGA_REPORT_ONLINE	Report online
PGA_REPORT_STRING	Report the string
PGA_REPORT_WORST	Report the worst evaluation
PGA_SELECT_LINEAR	Return individuals in population order
PGA_SELECT_PROPORTIONAL	Fitness-proportional selection
PGA_SELECT_PTOURNAMENT	Binary probabilistic tournament selection
PGA_SELECT_SUS	Stochastic universal selection
PGA_SELECT_TOURNAMENT	Tournament selection
PGA_SELECT_TRUNCATION	Truncation selection
PGA_STOP_MAXITER	Stop on max iterations
PGA_STOP_NOCHANGE	Stop on max number of generations no change
PGA_STOP_TOOSIMILAR	Stop when individuals too similar

Missing Features

As already mentioned, not all functions and constants of PGAPack are wrapped yet – still for many applications the given set should be enough. If you need additional functions, you may want to wrap these and send me a patch.

Another feature of PGAPack is currently not implemented in the wrapper, the usage of custom datatypes. With PGAPack you can define your own datatypes complete with their custom implementations of the genetic algorithm functionality like crossover, mutation, etc. I don’t expect problems implementing these, though.

Reporting Bugs

Please use the Sourceforge Bug Tracker or the Github Bug Tracker and

• give a short description of what you think is the correct behaviour

• give a description of the observed behaviour

• tell me exactly what you did.

• if you can publish your source code this makes it a lot easier to debug for me

Resources

Project information and download from Sourceforge main page

or checkout from Github

or directly install via pypi.

Installation

PGApy, as the name suggests, supports parallelizing the evaluation function of the genetic algorithm. This uses the Message Passing Interface (MPI) standard.

To install a serial version (without parallel programming using MPI) you can simply install from pypi using pip. Alternatively when you have unpacked or checked out from sources you can install with:

python3 setup.py install --prefix=/usr/local

If you want a parallel version using an MPI (Message-Passing Interface) library you will have to install a parallel version of PGApack first. The easiest way to do this is to use my pgapack debian package builder from github. Clone this repository, check out the branch debian/sid, install the build dependencies, they’re listed in the file debian/control and build the debian packages using:

dpkg-buildpackage -rfakeroot

This builds pgapack debian packages for all supported MPI libraries in debian, currently these are mpich, openmpi, and lam. In addition to the MPI libraries a serial version of the pgapack library is also built. Proceed by installing the package pgapack and the MPI backend library of choice. If you don’t have a preference for an MPI library, libpgapack-openmpi is the package that uses the Debians default preferences of an MPI library.

Once a parallel version of PGApack is installed, you can install PGApy as follows: You set environment variables for the PGA_PARALLEL_VARIANT (one of mpich, openmpi, or lam) and set the PGA_MODULE to module_from_parallel_install. Finally you envoke the setup, e.g.:

export PGA_PARALLEL_VARIANT=openmpi
export PGA_MODULE=module_from_parallel_install
python3 setup.py install --prefix=/usr/local

If your MPI library is installed in a different place you should study the Extension configurations in setup.py to come up with an Extension definition that fits your installation. If your installation is interesting to more people, feel free to submit a patch that adds your Extension-configuration to the standard setup.py.

Changes

Version 1.2: Many-objective optimization with NSGA-III

• Implement NSGA-III

Version 1.1.6: Polynomial mutation and simulated binary crossover (SBX)

• Simulated binary crossover (SBX)

• Polynomial mutation

Version 1.1.1-1.1.5: Small PGAPack updates, fixes for non-debian

• Fix setup.py for non-debian systems

• Update to latest PGAPack with small changes

Version 1.1: Add multi-objective optimization with NSGA-II

• Wrap latest pgapack version 1.4

• This add multi-objective optimization using the Nondominated Sorting Genetic Algorithm version 2 (NSGA-II) by Deb et. al. This makes use of the previously-introduced option to return more than one value in the objective function. To use the feature you need to set the num_constraint parameter to a value that leave some of the function values returned by your evaluation function as objective function values (and not as constraints). See example in examples/multi.py.

Version 1.0: Add constraint handling

• Wrap latest pgapack version 1.3

• This adds auxiliary evaluations. Now your evaluation function can return multiple floating-point values as a sequence if you set the num_eval paramter >1 in the constructor. Currently additional evaluation values are used for constraint handling. Constraint values are minimized. Once they reach zero or a negative value they no longer count: The sum of all positive constraints is the overall constraint violation. For details see paper by Deb, 2000, see user guide for citation. If you’re not using constraints, nothing in your code needs changes.

• This release may change the path an optimization takes. So for the same seed of the random number generator you will get a different result, at least if during the search there are individuals with the same evaluation (and different genetic material). This is due to a change of the sort function in pgapack (it switched to a stable sort from the C standard library).

Version 0.9: Allow installation of parallel version

• Pass argv (or sys.argv) to PGACreate

• Add a stanza to setup.py to allow a parallel installation with a given pgapack variant compiled for an MPI library. This currently needs a pre-installed pgapack debian package.

Version 0.8: Bugfix in real mutation

• Fix a core-dump in the latest pgapack

Version 0.7: Major changes in wrapping

• Now Differential Evolution is implemented, see the minfloat example and the user guide of pgapack.

Version 0.6: Major changes in wrapping

• Now the wrapping uses the standard Python recommendations on how to create a custom class.

• Update documentation

• Rename fitness_cmax (from fitness_cmax_value)

• Better error checking of parameters

Version 0.5: Bug-fix release

• Now the setup.py works, previous version had an encoding problem

• Wrap some minor new methods

• Bug-fix in PGAPack truncation selection

Version 0.4: Bundle PGAPack

• The PGAPack package is now included as a git submodule. By default we build against this library

• License fixes: The module long shipped a COPYING file that includes the 2-clause BSD license. But the headers of setup.py and pgamodule.c still included another license. This has been corrected.

Version 0.3: Feature enhancements, Bug fixes

Port to Python3, Python2 is still supported, license change.

• C-Code of wrapper updated to support both, Python2 and Python3

• Update documentation

• Fix some memory leaks that could result when errors occurred during some callback methods

• License change: We now have the 2-clause BSD license (similar to the MPICH license of PGAPack), this used to be LGPL.

Version 0.2: Feature enhancements, Bug fixes

64 bit support, more PGAPack functions and attributes wrapped, Readme-update: Sourceforge logo, Changes chapter.

• Bug-fixes for 64 bit architectures

• More functions and attributes of PGAPack wrapped

• Add a build-rule to setup.py to allow building for standard-install of PGAPack – this currently needs editing of setup.py – should use autodetect here but this would require that I set up a machine with standard install of PGAPack for testing.

• Add Sourceforge logo as required

• Add Changes chapter for automagic releases

• Add the __module__ string to class PGA in module pga. Now calling:: help (pga) in python works as expected, previously no help-text was given for the included module

Version 0.1: Initial freshmeat announcement

PGAPy is a wrapper for PGAPack, the parallel genetic algorithm library, a powerful genetic algorithm library. PGAPy wraps this library for use with Python. Pgapack is one of the most complete and accurate genetic algorithm implementations out there with a lot of features for experimentation.

• Initial Release