Multiobjective Optimisation For Cost Minimisation and Emission Reduction

Hi there,

I have a problem which more or less goes like this.

I have a set of vehicles listed x1,x2,x3,x4 and x5 these are configured for 2 fuel types (fossil fuel and electric).

They have emissions and fuel prices separately depending on the type of fuel used.

say for the fossil fuel configuration (running cost): x1=100,x2:120,x3:140,x4:160,x5:180 and emissions: x1=200, x2, 220, x3=240, x4=260, x5=280

and for the electrical configuration (running cost): x1=120, x=140, x3= 160, x4=180, x5=200 and emissions x1-x5=0

How can I find the cost optimal configuration of diesel vehicles and electric vehicles with the lowest possible emissions?

Many thanks!

Answer 1

[Akash]

Hi,

I understand that you are looking for the cost-optimal configuration of diesel and electric vehicles while minimizing emissions. This is a multiobjective optimization problem, as there are multiple objectives to consider.

In order to find the optimal solution that minimizes emissions while considering the running cost, you can utilize multiobjective optimization techniques.

MATLAB offers various approaches for multiobjective optimization, including goal attainment, minimax, and Pareto front methods.

• The “goal attainment” approach allows you to reduce the values of a linear or nonlinear vector function to achieve specific goal values, while considering the relative importance of each goal using a weight vector. This approach can also take linear and nonlinear constraints into account.
• The “minimax” approach aims to minimize the worst-case values of a set of multivariate functions, subject to linear and nonlinear constraints.
• The “Pareto front” approach focuses on finding noninferior solutions, where improving one objective may require a tradeoff with another. This approach can be implemented using direct search solvers or genetic algorithms, and can handle both smooth and nonsmooth problems with linear and nonlinear constraints.

You can learn more about it from the link below:

https://www.mathworks.com/discovery/multiobjective-optimization.html

The optimization problem that you mentioned is related to the “Goal attainment” approach. To solve your specific problem, you can explore MATLAB's optimization toolboxes, such as the “Optimization Toolbox” and the “Global Optimization Toolbox”. These toolboxes provide the necessary functions and algorithms to define and solve optimization problems, including multiobjective optimization.

For more information on multiobjective optimization and the available MATLAB toolboxes, I recommend visiting the links provided below:

https://www.mathworks.com/products/optimization.html#defining-optimization-problems

https://www.mathworks.com/products/global-optimization.html

These resources will provide you with a deeper understanding of the concepts and techniques involved in multiobjective optimization and guide you in using MATLAB to find the cost-optimal configuration of diesel and electric vehicles with the lowest possible emissions.