# What is Multi objective optimization?

Multi objective optimization is a mathematical optimization method used to find solutions to problems that involve multiple, often conflicting, objectives.

Unlike single-objective optimization problems, where the goal is to minimize or maximize a single objective function, multiobjective optimization problems have multiple objective functions that must be optimized simultaneously.

## Multi objective optimization problems can arise in various fields, including engineering, finance, and environmental science.

For example, in engineering design, a multi-objective optimization problem might involve finding the design of a component that minimizes both weight and cost, while also satisfying constraints on performance and safety.

The solutions to multi objective optimization problems are typically represented using a set of Pareto-optimal solutions, which are solutions that are not dominated by any other solutions in the set.

### A solution is considered non-dominated if there is no other solution that is better in all objectives.

The Pareto-optimal solutions represent the trade-off between the conflicting objectives, and they can be used to support decision-making by providing multiple possible solutions for a given problem.

There are several techniques that can be used to solve multi objective optimization problems, including genetic algorithms, particle swarm optimization, and non-dominated sorting genetic algorithms (NSGA).

These techniques work by generating a set of candidate solutions and refining them over time based on the values of the objective functions.

Multi objective optimization is a challenging and complex problem, but it is also an important and valuable tool for making decisions in fields where multiple conflicting objectives must be considered.