This simplified example aims to demonstrate how you can easily implement and solve complex problems using SOLVER-AI. We will be looking at a simplified design problem for an electric vehicle (EV), considering various components such as the motor, battery, and body of the EV. Each component has different parameters and prices, and we aim to find a combination that minimizes cost while maximizing range.

Following is the data and equations we will be using for this example.

Files

The csv and python for this example can be downloaded form here.

Motors Table

Let's imagine we have different motors to chose from.

The Motors Table lists different models of motors, each with its power, efficiency, price, and voltage compatibility.

Batteries Table

Now let's consider we have a number of batteries to chose from.

The Batteries Table lists different models of batteries, each with its capacity, efficiency, price, and voltage compatibility.

Bodies Table

The bodies table contains the list of bodies available.

The Bodies Table lists different models of car bodies, each with its aerodynamics, weight, and price.

Machine Learning Table

Let's now immagine we have data relative to previous builds for which we know the range per unit of energy, a parameter that allows us to estimate the range of a vehicle.

The Machine Learning Table is used to train a model that predicts the range per unit of energy (range_unit_energy) given the power of the motor, the capacity of the battery, and the weight of the body.

Total Cost Equation

The total_cost is calculated by adding up the price of the motor motor_price, the price of the battery battery_price, and the price of the body body_price:

total_cost = motor_price + battery_price * efficiency_price_factor + body_price

This equation is used to calculate the total cost of an EV given its design parameters.

Range Estimate Equation

The range estimate range is calculated by multiplying the power of the motor motor_power, the capacity of the battery battery_capacity, and the factor range_unit_energy:

range = motor_power * battery_capacity * range_unit_energy

This equation is used to estimate the range of an EV given its design parameters and the predicted range per unit of energy (range_unit_energy) from the machine learning model.

Battery Efficiency Price Factor

Let's consider that the efficiency_price_factor has a value of 1.2 for a battery with efficiency above 0.9 and 1.0 otherwise.

Download the csv files from github as specified in the introduction.

Modules Setup

Once logged in let's create the HardData for the csv files:

• Batteries.csv
• Bodies.csv
• Motors.csv

On page API page in “2 - Module Management” click on the HardDatas button and for each file do the following:

1. Specify a relevant name for the HardData module (must be unique).
2. Click on Choose File and select the csv file.
3. Leave VectorizationIndices empty.
4. Click on POST.

This is all that is required for setting up the HardData.

Let's now set up the ML data for the range_unit_energy.csv. On page API page in “2 - Module Management” click on the SoftDatas (ML) button and for each file do the following:

1. Specify a relevant name for the SoftData module (must be unique).
2. Click on Choose File and select the csv file.
3. For VariablesStringIn specify: motor_power, battery_capacity, body_weight
4. For VariablesStringOut specify: range_unit_energy
5. Leave VectorizationIndices empty.
6. Click on POST.

By doing so we have specified that range_unit_energy will be predicted by applying ML, given motor_power, battery_capacity and body_weight.

We can now set up the two equations for total_cost and range. On page API page in “2 - Module Management” click on the Equations button and for each equation do the following:

1. Specify a relevant name for the Equation module (must be unique).
2. Specify the EquationString:
   • for the total_cost: total_cost = motor_price + battery_price * efficiency_price_factor + body_price
   • for the range: range = motor_power * battery_capacity * range_unit_energy
3. For VariablesString specify:
   • for the total_cost: motor_price, battery_price, body_price, efficiency_price_factor
   • for the range: motor_power, battery_capacity, range_unit_energy
4. Leave VectorizationIndices empty.
5. Click on POST.

Finally, let's set up the computation of the efficiency_price_factor for file efficiency_price_factor.py. On page API page in “2 - Module Management” click on the Codes button and do the following:

1. Specify a relevant name for the Code module (must be unique).
2. Click on Choose File and select the Python v3.9 file.
3. For VariablesStringIn specify: battery_efficiency
4. For VariablesStringOut specify: efficiency_price_factor
5. Leave VectorizationIndices empty.
6. Click on POST.

Problem Setup

On page API page in “3 - Problem Management” click on the Problems button and:

1. Specify a relevant name for the Problem (must be unique).
2. Specify the Equations by selecting, using Ctrl/Command or Shift, the two Equation modules you have just created for computing total_cost and range.
3. Specify the Codes by selecting the Code module you have just created for computing the efficiency_price_factor.
4. Specify the Harddatas by selecting, using Ctrl/Command or Shift, the three HardData modules you have just created for the Batteries, Bodies and Motors.
5. Specify the Softdatas by selecting the SoftData module you have just created for predicting the range_unit_energy.

Selecting the Problem

On page API page in “4 - Problem Setup” select the problem you have just created from the drop-down menu. By doing so three tables are displayed: Inputs, Constraints and Objectives. Note that:

1. The Inputs table has only headers but no rows, this is because no variables were found which require any input. For this particular case all of the inputs are the table raws and are therefore implicitly defined.
2. Constraints and objectives are the outputs of the Equation, HardData and SoftData modules which contain numerical values.
3. Parameter range_unit_energy_std in Objectives and Constraints refers to the standard deviation of the predicted value for the parameter range_unit_energy. In the context of machine learning, a prediction is an estimate of a value based on the data uploaded via the csv file to the SoftData module.

Following are a number of different setups and the expected results. For each, on page API page, in “4 - Problem Setup” setup the problem Objectives and Constraints. Then, click on the Submit button in section “5 - Problem Execution” and view the results displayed in section “6 - Results”.

Execution With No Setup

Executing the problem will display a table displaying a number of different solutions, each on a different row of the table, with Input and Output values as columns.

Experiment With Objectives and Constraints

Try experimenting with changing the setup and executing the problem. For example, by setting in “4 - Problem Setup”:

• Constraint range as greater than 200000.
• Objective range as maximise.
• Objective total_cost as minimize

you will obtain a range of optimal solutions, from one which has the lowest total_cost possible to one that has maximum range, and all the best compromise solutions found in between.

The problem is automatically updated when any of the modules are updated. Let's consider that rather than one battery, we can have up to three. We can then consider the following equations.

total_cost = motor_price + battery_num * battery_price * efficiency_price_factor + body_price

range = motor_power * battery_num * battery_capacity * range_unit_energy

Modifying the Equations

On page API page in “2 - Module Management”:

1. Click on the Equations button.
2. Click on the URL of the equation.

Update the two equations by:

1. Specifying the EquationString:
   • for the total_cost: total_cost = motor_price + battery_num * battery_price * efficiency_price_factor + body_price
   • for the range: range = motor_power * battery_num * battery_capacity * range_unit_energy
2. For both the total_cost and range equations add to VariablesString: battery_num
3. Leave VectorizationIndices empty.
4. Click on PUT.

Solver Setup and Execution

After selecting the problem on page API page, in “4 - Problem Setup” you will find the battery_num is now available in the inputs.

Specify the Min and Max values as 1 and 3, respectively and check the Integer checkboxClick on the Submit button in section “5 - Problem Execution” and view the results displayed in section “6 - Results”.

Note that by having modified the Equation modules, which are already part of the Problem, the Problem is automatically updated. This is true for any of the modules, allowing for example, to easily update ML data (in SoftData modules) on the fly, without requiring the Problem to have to be redefined. This can be particularly useful when SOLVER-AI is being used by a microcontroller for which new data is collected from sensors and fed to SoftData modules.