Multiobjective optimization and evolutionary algorithms

What is Multiobjective optimization

Multiobjective optimization (MO), also known as multicritera optimization is an optimization of a vector function $\mathbf{f}(\mathbf{x})$, where $\mathbf{x}$ is a vector of parameters to the vector function $\mathbf{f}$, usually being a minimisation of components of $\mathbf{x}$ with respect to Pareto efficiency.

Pareto efficiency, also known as Pareto optimality, is a best choice of criteria, such that no criterion must be worsened in order to better some another criterion. $\mathbf{x}$ is Pareto optimal, iff does not exist $\mathbf{y}:y_i < x_i$.

What are Evolutionary Algorithms

Evolutionary Algorithms (EAs) are problem solving principles from nature applied to the metaheuristic search. Using mutation, crossover, and selection operators, stochastic search is developed to evolve better individuals in quest for (a) globally best individual(s).

When applying EAs to MO, multiple pareto optimal solutions are in the quest. One of the possible EAs for exploring the MO search space is the Differential Evolution (e.g. jDE). The most known Genetic Algorithm (GA) for the MO is the Non-dominated Sorting Genetic Algorithm - II (NSGA-II) by Deb.

External links

• Prof. Kalyanmoy Deb's Homepage @ Kanpur Genetic Algorithms Laboratory
• Carlos A. Coello Coello's Publications
• Walking Fish Group