The optimizer minimizes the absolute value of the difference from the target outputs and the evaluated outputs. Future versions may include options for function minimization absent target values.

The current internal optimization function takes 3 inputs, and has 2 outputs. It was created as a simple 3-variable optimization objective function that would be quick to converge.

There are three functions included in the repository:

1) Himmelblau's function, which takes 2 inputs and has 1 output

2) A multi-objective function with 3 inputs and 2 outputs (see lundquist_3_var)

3) A single-objective function with 1 input and 1 output (see one_dim_x_test)

Each function has four files in a directory:

1) configs_F.py - contains imports for the objective function and constraints, CONSTANT assignments for functions and labeling, boundary ranges, the number of input variables, the number of output values, and the target values for the output

2) constr_F.py - contains a function with the problem constraints, both for the function and for error handling in the case of under/overflow.

3) func_F.py - contains a function with the objective function.

4) graph.py - contains a script to graph the function for visualization.

Other multi-objective functions can be applied to this project by following the same format (and several have been collected into a compatible library, and will be released in a separate repo)

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</p>

<palign="center">Function Feasible Decision Space and Objective Space with Pareto Front</p>

<palign="center">Plotted Himmelblau Function with 3D Plot on the Left, and a 2D Contour on the Right</p>

| Global Minima| Boundary| Constraints|

|----------|----------|----------|

| f(3, 2) = 0| $-5 \leq x,y \leq 5$||

| f(-2.805118, 3.121212) = 0| $-5 \leq x,y \leq 5$||

| f(-3.779310, -3.283186) = 0| $-5 \leq x,y \leq 5$||

| f(3.584428, -1.848126) = 0| $-5 \leq x,y \leq 5$||

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</p>

<palign="center">Plotted Multi-Objective Function Feasible Decision Space and Objective Space with Pareto Front</p>

|----------|----------|----------|

| 3| $0.21\leq x_1\leq 1$ <br> $0\leq x_2\leq 1$ <br> $0.1 \leq x_3\leq 0.5$| $x_3\gt \frac{x_1}{2}$ or $x_3\lt 0.1$|

This function has three files:

1) configs_F.py - contains imports for the objective function and constraints, CONSTANT assignments for functions and labeling, boundary ranges, the number of input variables, the number of output values, and the target values for the output

2) constr_F.py - contains a function with the problem constraints, both for the function and for error handling in the case of under/overflow.

3) func_F.py - contains a function with the objective function.

Other multi-objective functions can be applied to this project by following the same format (and several have been collected into a compatible library, and will be released in a separate repo)

<palign="center">

</p>

<palign="center">Plotted Single Input, Single-objective Function Feasible Decision Space and Objective Space with Pareto Front</p>