# Quick Start Model Building¶

## Variable Types¶

GEKKO has eight types of variables, four of which have extra properties.

Constants, Parameters, Variables and Intermediates are the standard types. Constants and Parameters are fixed by the user, while Variables and Intermediates are degrees of freedom and are changed by the solver. All variable declarations return references to a new object.

Fixed Variables (FV), Manipulated Variables (MV), State Variables (SV) and Controlled Variables (CV) expand parameters and variables with extra attributes and features to facilitate dynamic optimization problem formulation and robustness for online use. These attributes are discussed in Manipulated Variable Options and Controlled Variable Options.

All of these variable types have the optional argument ‘name’. The name is used on the back-end to write the model file and is only useful if the user intends to manually use the model file later. Names are case-insensitive, must begin with a letter, and can only contain alphanumeric characters and underscores. If a name is not provided, one is automatically assigned a unique letter/number (c#/p#/v#/i#).

### Constants¶

Define a Constant. There is no functional difference between using a GEKKO Constant, a python variable or a magic number in the Equations. However, the Constant can be provided a name to make the .apm model more clear:

```
c = m.Const(value, [name]):
```

- Value must be provided and must be a scalar

### Parameters¶

Parameters are capable of becoming MVs and FVs. Since GEKKO defines MVs and FVs directly, parameters just serve as constant values. However, Parameters (unlike Constants) can be (and usually are) arrays.:

```
p = m.Param([value], [name])
```

- The value can be a python scalar, python list of numpy array. If the value is a scalar, it will be used throughout the horizon.

### Variable¶

Calculated by solver to meet constraints (Equations):

```
v = m.Var([value], [lb], [ub], [integer], [name]):
```

- lb and ub provide lower and upper variable bounds, respectively, to the solver.
- integer is a boolean that specifies an integer variable for mixed-integer solvers

### Intermediates¶

Intermediates are a unique GEKKO variable type. Intermediates, and their associated equations, are like variables except their values and gradients are evaluated explicitly, rather than being solved implicitly by the optimizer. Intermediate variables essentially blend the benefits of sequential solver approaches into simultaneous methods.

The function creates an intermediate variable i and sets it equal to argument equation:

```
i = m.Intermediate(equation,[name])
```

Equation must be an explicitly equality. Each intermediate equation is solved in order of declaration. All variable values used in the explicit equation come from either the previous iteration or an intermediate variable declared previously.

### Fixed Variable¶

Fixed Variables (FV) inherit Parameters, but potentially add a degree of freedom and are always fixed throughout the horizon (i.e. they are not discretized in dynamic modes).:

```
f = m.FV([value], [lb], [ub], [integer], [name])
```

- lb and ub provide lower and upper variable bounds, respectively, to the solver.
- integer is a boolean that specifies an integer variable for mixed-integer solvers

### Manipulated Variable¶

Manipulated Variables (MV) inherit FVs but are discretized throughout the horizon and have time-dependent attributes:

```
m = m.MV([value], [lb], [ub], [integer], [name])
```

- lb and ub provide lower and upper variable bounds, respectively, to the solver.
- integer is a boolean that specifies an integer variable for mixed-integer solvers

### State Variable¶

State Variables (SV) inherit Variables with just a couple extra attributes:

```
s = m.SV([value], [lb], [ub], [integer], [name])
```

### Controlled Variable¶

Controlled Variables (CV) inherit SVs but potentially add an objective (such as reaching a setpoint in control applications or matching model and measured values in estimation):

```
c = m.CV([value], [lb], [ub], [integer], [name])
```

## Equations¶

Equations are defined with the variables defined and python syntax:

```
m.Equation(equation)
```

For example, with variables `x`

, `y`

and `z`

:

```
m.Equation(3*x == (y**2)/z)
```

- Multiple equations can be defined at once if provided in an array or python list::
- m.Equations(eqs)

Equations are all solved implicitly together.

## Objectives¶

Objectives are defined like equations, except they must not be equality or inequality expressions. Objectives with m.Obj() are minimized (maximization is possible by multiplying the objective by -1) or by using the m.Maximize() function. It is best practice to use m.Minimize() or m.Maximize() for a more readable model:

```
m.Obj(obj)
m.Minimize(obj)
m.Maximize(obj)
```

## Connections¶

Connections are processed after the parameters and variables are parsed, but before the initialization of the values. Connections are the merging of two variables or connecting specific nodes of a discretized variable. Once the variable is connected to another, the variable is only listed as an alias. Any other references to the connected value are referred to the principal variable (var1). The alias variable (var2) can be referenced in other parts of the model, but will not appear in the solution files.

```
m.Connection(var1,var2,pos1=None,pos2=None,node1='end',node2='end')
```

var1 must be a GEKKO variable, but var2 can be a static value. If pos1 or pos2 is not None, the associated var must be a GEKKO variable and the position is the (0-indexed) time-discretized index of the variable.

## Example¶

Here’s an example script for solving problem HS71

```
from gekko import GEKKO
#Initialize Model
m = GEKKO()
#define parameter
eq = m.Param(value=40)
#initialize variables
x1,x2,x3,x4 = [m.Var(lb=1, ub=5) for i in range(4)]
#initial values
x1.value = 1
x2.value = 5
x3.value = 5
x4.value = 1
#Equations
m.Equation(x1*x2*x3*x4>=25)
m.Equation(x1**2+x2**2+x3**2+x4**2==eq)
#Objective
m.Minimize(x1*x4*(x1+x2+x3)+x3)
#Set global options
m.options.IMODE = 3 #steady state optimization
#Solve simulation
m.solve()
#Results
print('')
print('Results')
print('x1: ' + str(x1.value))
print('x2: ' + str(x2.value))
print('x3: ' + str(x3.value))
print('x4: ' + str(x4.value))
```

A more compact version of the same problem:

```
from gekko import GEKKO
import numpy as np
m = GEKKO()
x = m.Array(m.Var,4,value=1,lb=1,ub=5)
x1,x2,x3,x4 = x # rename variables
x2.value = 5; x3.value = 5 # change guess
m.Equation(np.prod(x)>=25) # prod>=25
m.Equation(m.sum([xi**2 for xi in x])==40) # sum=40
m.Minimize(x1*x4*(x1+x2+x3)+x3) # objective
m.solve()
print(x)
```

## Diagnostics¶

The run directory m.path contains the model file gk0_model.apm and other files required to run the optimization problem either remotely (default) or locally (m=GEKKO(remote=False)). Use m.open_folder() to open the run directory. The run directory also contains diagnostic files such as infeasibilities.txt that is produced if the solver fails to find a solution. The default run directory can be changed:

```
from gekko import GEKKO
import numpy as np
import os
# create and change run directory
rd=r'.\RunDir'
if not os.path.isdir(os.path.abspath(rd)):
os.mkdir(os.path.abspath(rd))
m = GEKKO(remote=False) # solve locally
m.path = os.path.abspath(rd) # change run directory
x = m.Array(m.Var,4,value=1,lb=1,ub=5)
x1,x2,x3,x4 = x # rename variables
x2.value = 5; x3.value = 5 # change guess
m.Equation(np.prod(x)>=25) # prod>=25
m.Equation(m.sum([xi**2 for xi in x])==40) # sum=40
m.Minimize(x1*x4*(x1+x2+x3)+x3) # objective
m.solve(disp=False)
print(x)
```

The diagnostic level can be adjusted with m.options.DIAGLEVEL between 0 and 10. At level 0, there is minimal information reported that typically includes a summary of the problem and the solver output. At level 1, there are more information messages and timing information for the different parts of the program execution. At level 2, there are diagnostic files created at every major step of the program execution. A diagnostic level of >=2 slows down the application because of increased file input and output, validation steps, and reports on problem structure. Additional diagnostic files are created at level 4. The analytic 1st derivatives are verified with finite differences at level 5 and analytic 2nd derivatives are verified with finite differences at level 6. The DIAGLEVEL is also sent to the solver to indicate a desire for more verbose output as the level is increased. Some solvers do not support increased output as the diagnostic level is increased. A diagnostic level up to 10 is allowed.

## Clean Up¶

Delete the temporary folder (m.path) and any files associated with the application with the command

```
m.cleanup()
```

Do not call the m.cleanup() function if the application requires another calls to m.solve() with updated inputs or objectives.