algormeter 1.1.1

Tool for developing, testing and measuring optimizers algorithms

AlgorMeter: Tool for developing, testing, measuring and exchange optimizers algorithms

AlgorMeter is a python implementation of an environment for develop, test, measure, report and compare optimization algorithms. Having a common platform that simplifies developing, testing and exchange of optimization algorithms allows for better collaboration and sharing of resources among researchers in the field. This can lead to more efficient development and testing of new algorithms, as well as faster progress in the field overall. AlgorMeter produces comparative measures among algorithms in csv format with effective test function call count.
It embeds a specific feature devoted to optimize the number of function calls, so that multiple function calls at the same point are accounted for just once, without storing intermediate results, with benefit in terms of algorithm coding.
AlgorMeter contains a standard library of 10 DC problems and 7 convex problems for testing algorithms. More problem collections can be easily added.
AlgorMeter provide integrated performance profiles graphics, as developed by E. D. Dolan and J. J. More. They are a powerful standard tool, within the optimization community, to assess the performance of optimization software.

problems + algorithms = experiments

• A problem is a function f where f: R(n) -> R with n called dimension.
• f = f1() - f2() difference of convex function where f1, f2: R(n) -> R.
• 'problems' is a list of problem
• 'algorithm' is a code that try to find problem local minima
• 'experiment' is an algorMeter run with a list of problems and a list of algorithms that produce a result report

How to use...

Implement an algorithm...

Copy and customize algorithm examples like the following (there are many included example?.py)

def gradient(p, **kwargs):
    '''Simple gradient'''
    for k in p.loop():
        p.Xkp1 = p.Xk - 1/(k+1) * p.gfXk / np.linalg.norm(p.gfXk) 

and refer to the available following system properties

algorMeter properties	Description
k, p.K	current iteration
p.Xk	current point
p.Xkp1	next point. to be set for next iteration
p.fXk	p.f(p.Xk) = p.f1(p.Xk) - p.f2(p.Xk)
p.fXkPrev	previous iteration f(x)
p.f1Xk	p.f1(p.Xk)
p.f2Xk	p.f1(p.Xk)
p.gfXk	p.gf(p.Xk) = p.gf1(p.Xk) - p.gf2(p.Xk)
p.gf1Xk	p.gf1(p.Xk)
p.gf2Xk	p.gf2(p.Xk)
p.optimumPoint	Optimum X
p.optimumValue	p.f(p.optimumPoint)
p.XStart	Start Point

to determine the p.Xkp1 for the next iteration.
...and run it:

df, pv = algorMeter(algorithms = [gradient], problems = probList_covx, iterations = 500, absTol=1E-2)
print('\n', pv,'\n', df)

pv and df are pandas dataframe with run result.

A .csv file with result is also created in csv folder.

(see example*.py)

AlgorMeter interface

def algorMeter(algorithms, problems, tuneParameters = None, iterations = 500, timeout = 180
    runs = 1, trace = False, dbprint= False, csv = True, savedata = False,
     absTol =1.E-4, relTol = 1.E-5,  **kwargs):

• algorithms: algorithms list. (algoList_simple is available )
• problems: problem list. See problems list in example4.py for syntax. (probList_base, probList_covx, probList_DCJBKM are available)
• tuneParameters = None: see tuneParameters section
• iterations = 500: max iterations number
• timeout = 180: time out in seconds
• runs = 1: see random section
• trace = False: see trace section
• dbprint= False: see dbprint section
• csv = True: write a report in csv format in csv folder
• savedata = False: save data in data folder
• absTol =1.E-4, relTol = 1.E-5: tolerance used in numpy allClose and isClose
• **kwargs: python kwargs propagated to algorithms

call to algorMeter returns two pandas dataframe p1, p2. p2 is a success and fail summary count. p1 is a detailed report with the following columns.

• Problem
• Dim
• Algorithm
• Status: Success, Fail or Error
• Iterations
• f(XStar
• f(BKXStar)
• Delta: absolute difference between f(XStar) and f(BKXStar)
• Seconds
• Start point
• XStar: minimum
• BKXStar: best known minum
• \f1 f2 gf1 gf2: effective calls count
• ... : other columns with count to counter.up utility (see below)

Stop and success condition

    def stop(self) -> bool:
        '''return True if experiment must stop. Override it if needed'''
        return bool(np.isclose(self.fXk,self.fXkPrev,rtol=self.relTol,atol=self.absTol)  
                  or np.allclose (self.gfXk,np.zeros(self.dimension),rtol=self.relTol,atol=self.absTol) )

    def isSuccess(self) -> bool:
        '''return True if experiment success. Override it if needed'''
        return  self.isMinimum(self.XStar)
 

can be overriden like in

    def stop():
        return status 
        ...

    p.stop = stop
    p.isSuccess = stop

Another maybe more simple way is to call statement break in main loop.
See example3.py

Problems function call optimization

AlgorMeter embeds a specific feature devoted to optimize the number of function calls, so that multiple function calls at the same point are accounted for just once, without storing intermediate results, with benefit in terms of algorithm coding. So in algorithm implementation is not necessary to store the previous result in variables to reduce f1, f2, gf1, gf2 function calls. AlgorMeter cache 128 previous calls to obtain such automatic optimization.

Problems ready to use

Importing 'algormeter.libs' probList_base, probList_covx, probList_DCJBKM problems list are available.
probList_DCJBKM contains ten frequently used unconstrained DC optimization problems, where objective functions are presented as DC (Difference of Convex) functions: 𝑓(𝑥)=𝑓1(𝑥)−𝑓2(𝑥). Joki, Bagirov

probList_covx contains DemMal,Mifflin1, Miffilin2,LQ,QL,MAXQ,MAXL,CB2,CB3,MaxQuad, Rosen, Shor, TR48, A48 and Goffin test convex functions/problem

probList_no_covx contains special no convex functions: Rosenbrock, Crescent

probList_base contains Parab, ParAbs, Acad simple functions for algorithms early development and test.

See 'ProblemsLib.pdf'

Counters

Instruction like

counter.up('lb<0', cls='qp')

is used to count events in code, summerized in statistics at the end of experiment as a column, available in dataframe returned by call to algorMeter and in final csv. For the code above a column with count of counter.up calls and head 'qp.lb>0' is produced.
Also are automatically available columns 'f1', 'f2', 'gf1', 'gf1' with effective calls to f1, f2, gf1, gf2
See example3.py

dbprint = True

Instruction dbx.print produce print out only if algorMeter call has option dbprint == True

dbx.print('t:',t, 'Xprev:',Xprev, 'f(Xprev):',p.f(Xprev) ).

See example3.py
NB: If dbprint = True python exceptions are not handled and raised.

Trace == True

If Default.TRACE = True a line with function values are shown as follows in the console for each iteration for algorithms analysis purpose.

Acad-2 k:0,f:-0.420,x:[ 0.7 -1.3],gf:[ 1.4 -0.6],f1:2.670,gf1:[ 3.1 -2.9],f2:3.090,gf2:[ 1.7 -2.3]
Acad-2 k:1,f:-1.816,x:[-1.0004 -0.5712],gf:[-8.3661e-04 8.5750e-01],f1:0.419,gf1:[-2.0013 -0.7137],f2:2.235,gf2:[-2.0004 -1.5712]
Acad-2 k:2,f:-1.754,x:[-0.9995 -1.4962],gf:[ 9.6832e-04 -9.9250e-01],f1:2.361,gf1:[-1.9985 -3.4887],f2:4.115,gf2:[-1.9995 -2.4962]

These lines represent the path followed by the algorithm for the specific problem.
NB: If trace = True python exceptions are not handled and raised.
See example3.py

tuneParameters

Some time is necessary tune some parameter combinations. Procede as follow (See example4.py):

• Define and use module, non locals parameters in your algo code.
• Define a list of lists with possible values of tuning parameters as follows:

tpar = [ # [name, [values list]]
    ('alpha', [1. + i for i in np.arange(.05,.9,.05)]),
    # ('beta', [1. + i for i in np.arange(.05,.9,.05)]),
]

• call algorMeter with csv = True and tuneParameters= like tuneParameters=tpar.
• open csv file produced and analyze the performance of parameters combinations by looking column '# TuneParams'. Useful is a pivot table on such columns. See example4.py

Random start point

If algorMeter parameter run is set with a number greater than 1, each algorithm is repeated on the same problem with random start point in range -1 to 1 for all dimensions. By the method setRandom(center, size) random X can be set in [center-size, center+size] interval.
See example5.py

Record data

with option data == True store in 'npy' folder one file in numpy format, for each experiment with X and Y=f(X) for all iterations. It is a numpy array with:

X = data[:,:-1]
Y = data[:,-1]

File name is like 'gradient,JB05-50.npy'.
These files are read by viewer.py data visualizer.

Performance Profile

Performance profiles graphics, as developed by E. D. Dolan and J. J. More, are a powerful tool to assess the performance of optimization software. For this reason they are standard accepted within the optimization community. See example2.py

    df, pv = algorMeter(algorithms = algorithms, ...)

    perfProf(df, costs= ['f1','Iterations'] ) 
    # df: first pandas dataframe output of algormeter call
    # costs: list of column labels in df

    plt.show(block=True)

It is possible to graph performance profiles by preparing a pandas data frame using a spreadsheet with the mandatory columns 'Problem','Dim','Algorithm','Status' and the columns costs that you want to draw

    df = pd.read_excel(r'Path of Excel file\File name.xlsx', sheet_name='your Excel sheet name')

    perfProf(df, costs= ['cost1','cost2'] ) 

    plt.show(block=True)

Minimize

In case you need to find the minimum of a problem/function by applying an algorithm developed with algormeter, the minimize method is available. (See example6.py):

    p = MyProb(K) 
    found, x, y = p.minimize(myAlgo)

Visualizer.py

Running visualizer.py produce or updates contour image in folder 'pics' for each experiment with dimension = 2 with data in folder 'npy'.

Examples index

• example1.py: Simplest possible example
• example2.py: Dolan, More performance profile
• example3.py: dbx.print, trace,counter.up, counter.log, override stop, break example
• example4.py: algorithm parameters tuning
• example5.py: multiple run of each problem with random start point
• example6.py: minimize new problem with algometer algorithm

Contributing

You can download or fork the repository freely.
https://github.com/xedla/algormeter
If you see a mistake you can send me a mail at [e-mail] If you open up a ticket, please make sure it describes the problem or feature request fully.
Any suggestion are welcome.

License

If you use AlgorMeter for the preparation of a scientific paper, the citation with a link to this repository would be appreciated.

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY.

Installation

Algormeter is available as pypi pip package.

    pip3 install algormeter

Dependencies

Python version at least

• Python 3.10.6

Package installable with pip3

• numpy
• pandas
• matplotlib

Algormeter plays well with Visual Studio Code and in jupyter