algormeter 0.9.1

Tool for developing, testing and measuring optimizers algorithms

AlgoMeter: Tool for developing, testing and measuring optimizers algorithms

Python benchmark suite environment for optimizer algorithms.
Here is a repository where you can find a python implementation of a benchmark environment for optimizer algorithms. Produce comparative measures between algorithms in csv format with effective test function call count. It has a problem function call optimization, so more calls at the same point X count only for one call. Contains a standard library implementation of convex functions and difference of convex functions.
The hope is to have a useful, common tool for the scientific optimization community to experiment and share results.

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's minimum
• '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_coax, 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 example1.py)

AlgoMeter interface

def algorMeter(algorithms, problems, tuneParameters = None, iterations = 500, 
    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_coax, probList_DCJBKM are available)
• tuneParameters = None: see tuneParameters section
• iterations = 500: max iterations number
• 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 isSuccess(self):
        '''return True if experiment success. Reassign it if needed'''
        return self.Success and bool(np.isclose(self.f(self.XStar), self.optimumValue,atol=self.absTol, rtol= self.relTol)) 

    def isHalt(self):
        '''return True if experiment must stop. Reassign it if needed'''
        return 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) 

can be overriden like in

    def stop():
        return bool(np.isclose(p.f(p.Xk), p.optimumValue,atol=p.absTol, rtol= p.relTol)) or \
                bool(np.allclose (p.Xk, p.optimumPoint,rtol=p.relTol,atol=p.absTol))
    
    p.isHalt = stop
    p.isSuccess = stop

Problems function call optimization

Algometer uses a problems function call optimization system so more calls at the same point X count only for one call. So in algorithm implementation is not necessary to store the previous result in variables to reduce f1, f2, gf1, gf2 function calls. Algometer cache 128 previous calls to obtain such automatic optimization.

Problems ready to use

Importing 'algormeter.libs' probList_base, probList_coax, 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_coax contain DemMol,Mifflin,LQ,MAXQ,QL,CB2,CB3 convex functions

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

See 'ProblemsLib.pdf'

Counters

Instruction like

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

is used in order 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

dbprint = True

Instruction dbx.print produce print out only if algorMeter call ha option dbptint == True

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

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.

tuneParameters

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

• Use numeric parameters with TunePar as domain name, like TunePar.alpha in your algo code.
• Define a list of lists with possible values of tuning parameters as follows:

tpar = [ # [name, [values list]]
    ('TunePar.alpha', [1. + i for i in np.arange(.05,.9,.05)]),
    # ('TunePar.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 '# tunePar'. Useful is a pivot table on such column.

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.

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) 
    status, 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'.

Acknowledgment

Algometer was inspired and suggested by prof. Manlio Gaudioso of the University of Calabria and made with him.

Contributing

You can download or fork the repository freely. 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.

WARNING

AlgoMeter is still in the early stages of development.

License

If you use AlgoMeter 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.

Dependencies

Python version at least

• Python 3.10.6

Package installable with pip3

• numpy
• pandas
• matplotlib

Algometer plays well with Visual Studio Code and in jupyter