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Auto2Fit User Manual
7D Soft High Technology Inc.
May/1
st
/2009
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Chapter 1 Introduction
1.1 General Information about Auto2Fit
Auto2Fit is a software package for the analysis of mathematical optimization problem. It is
developed by 7D-Soft High Technology Inc independently with complete intellectual property
rights. It is in a world-leading place in the area of non-linear regression, curve fitting, non-linear
complex model parameters estimation and solving, linear / nonlinear programming compared with
other similar commercial software. Besides easy-to-use user interface, its computation core is
based on the innovative research results, Universal Global Optimization (UGO) algorithm, from
more than a decade of scientific research work done by experts in 7D-Soft. This algorithm solved
the problem of the initial value must be given for numerical optimization calculation, namely, the
initial value is given by Auto2Fit randomly instead of user, then find the optimal solution through
its Universal Global Optimization algorithm. Take nonlinear regression as an example, the most
famous software packages in this area, such as Matlab, OriginPro, SAS, SPSS, DataFit, GraphPad,
etc., all need the appropriate initial values of parameters provided or guessed by users for finding
the optimal solution. If the initial value of the parameter is set incorrectly, then result is difficult to
converge and it is impossible to get the correct answers finally. In practice, it is quite difficult to
provide (guess) the appropriate initial values of parameters for most users. Especially when the
amount of parameters is large, guess of initial start values would be a nightmare for users. With
the superiors of optimization and fault tolerance, Auto2Fit can achieve the correct result with
random initial start value in most of cases (>90%).
1.2 State-of-the-art of similar software national and
international
In the area of comprehensive data analysis, there is no doubt that foreign software dominates
markets. In the area of nonlinear curve fit, parameter optimization, there are several well-known
software products, such as OriginPro. Matlab, SAS, SPSS, DataFit, GraphPad, TableCurve2D,
TableCurve3D, etc.. No matter what the user interface is and how the history and reputation is, the
most used algorithms, i.e., Levenberg-marquardt or Simplex Method, can all categorized to local
optimization algorithm. Thus how to define appropriate initial parameters is always a bottleneck
that is difficult to overcome and some practical problems may never get correct solutions.
Nationally though there is few data analysis software in the market, they cannot compete with
foreign similar products due to poor functionality and weakness in theory and methodology, not
mention to make some noises in the world. With its innovative algorithm theory, Auto2Fit is
advanced than any known software package in the world in the area of nonlinear curve fit and
parameter estimation. The English version of Auto2Fit is on sale in many countries, like USA,
Germany, France, UK, Finland, Sweden, Netherlands, South Africa, Australia, New Zealand,
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Turkey, etc.
1.3 The optimization algorithms adopted in Auto2Fit
The optimization algorithms Auto2Fit adopt include:
1) Universal Global Optimization (UGO)
2) Simplex Method (SM) + Universal Global Optimization (UGO)
3) Differential Evolution (DE)
4) Max Inherit Optimization (MIO)
5) Genetic Algorithms (GA)
6) Simulated Annealing (SA)
7) Particle Swarm Optimization (PSO)
8) Self-Organizing Migrating Algorithms (SOMA)
9) Tabu Search (TS)
10) Simplex Linear Program
1.4 The application areas of Auto2Fit
The application areas of Auto2Fit include:
1) Auto-calibration
2) Parameter estimation
3) Linear or nonlinear curve fit and regression
4) Nonlinear simultaneous system equations solving
5) Ordinary differential equation (ODE) and simultaneous equation, initial value problems
(IVP) and boundary value problems (BVP)
6) Function optimization with any dimensions, including implicitly function
7) Function chart, chart of implicit function
8) Linear, nonlinear or integer programming
9) Combination optimization
10) Advanced calculator
1.5 Features of Auto2Fit
1) Powerful: it is the only software packages that can find the optimal solution of nonlinear
regression test dataset of National Institute of Standards and Technology (NIST) using
random initial start-values in current world market.
2) It can be widely used in hydrology, water resources and other engineering optimization
problems. As embedded with VB and Pascal, it can help describing and dealing with
complex optimization model.
3) Link the objective function of external dynamic link library (dll) or command-line
executive file (exe) which are complied from any other programming language (such as,
C++, FORTRAN, Basic, Pascal ...).
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4) Nonlinear curve fit can deal with any formation of user-defined equations, any number
of parameters and variables, batch processing of data fitting, weight fitting, fitting with
constraints, fitting with missing variables.
5) Process multiple data files simultaneously when model does auto-calibration.
6) Easily handle multiple outputs.
7) Real-time calculation results display.
8) Read and save different format of files, such as Excel, CSV, etc.
9) User-friendly interface, easy to use.
10) Come with more than one hundred examples, covering almost all optimization issues.
Users can easily understand the usage of Auto2Fit through different type of examples.
1.6 Key words of Auto2Fit
Main key words:
Name of key words Meaning and example
Parameter
Parameter definition
E.g.: Define a, b, c, d, four parameters: Parameter a, b, c, d;
E.g.: Define a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, ten parameters:
Parameter a1, a2, a3, a4, a5, a6, a7, a8, a9, a10;
Can be abbreviated: Parameter a(1:10);
or: Parameter a(10);
E.g.: Define a, ranged in [-1,1], whose initial value is 0.5
Parameter a = 0.5[-1,1];
E.g.: Define a as an integer, ranged in [-100,100]
Parameter a[-100,100,0]; or IntParameter a=[-100,100];
ParameterDomain
Define parameters’range in a batch
E.g.: Define parameter a, ranged in [-1,1],other parameters ranged in [0,10];
Parameter a = 0.5[-1,1],b,c,d,e,f,g;
ParameterDomain = [0,10];
BinParameter
Define 0-1 parameter
E.g.: Define a as a parameter whose value is either 0 or 1
BinParameter a;
IntParameter
Define positive interger parameter
E.g.: Define a as positive integer
Parameter a=[0,,0]; or IntParameter a;
StartRange
Define the range of initial value of parameter
E.g.: Define the range of initial value of parameter, a, as [-100,100]
StartRange a = [-100,100];
Va ri ab le
Define variable
E.g.: Define three variables, x, y, and z: Variable x, y, z;
QuickReg Set fast fitting function
Function
Define function
E.g.: Curve fit with two variables: Function y = a + b*exp(c – x);
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E.g.: Function optimization with two variables: Function
(x+((2-x)*(2+y))^2)*sin(x*y);
Constant
Define constant
E.g.: Constant a=1, b=2;
E.g.: Constant p(3)=[1,2,3];
ConstStr
Define constant string
E.g.: Curve fit with two variables: Function y = a*
（
c-x
）
^2 + b*exp((c – x)^4);
can be expressed as:
ConstStr B
＝
（
c-x
）
^2
Function y = a*B + b*exp(B^2);
VarConstant Define varconstant
VarParameter Define varparameter
Data Define start of data
RowData Define start of data,with row formation
DataFile Define data file
NewDivision Define new code section
SubDivision Define sub code section
StartProgram Define start of program
EndProgram Define end of program
Maximum Find the maximum
Minimum Find the minimum
PlotFunction Plot function
Algorithms Define optimization algorithm
Exclusive Define exclusive problem, such as TSP problem
MutliRun
HotRun
SharedModel Define share parameter
DataSet EndDataSet
Define dataset
Define end of dataset
RowDataSet
EndRowDataSet
MinFunction Find the solution of getting the maximum value of a function
MaxFunction Find the solution of getting the minimum value of a function
PlotParaFunction Plot graph of a function
Title Define a title of a code section
RegType Set the least absolute value method fitting
MDataSet
EndMDataSet
Define network node data format, equivalent to matrix format
ConstrainedResult Value of constrained function in programming mode
ObjectiveResult Value of objective function in programming mode
BatchFileModel
FullLoopModel Full loop calculation mode
MinMax Solution of minmax optimization problem
