In multi-objective optimization, the Pareto front (also called Pareto frontier or Pareto curve) is the set of all Pareto efficient solutions. Colloquially, this means when there are many distinct factors to consider in an optimization problem, a Pareto front represents the set of solutions that are "equally good" overall, albeit by making different concessions and compromises. The concept is widely used in engineering. It allows the designer to restrict attention to the set of efficient choices, and to make tradeoffs within this set, rather than considering the full range of every parameter.
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👉 Pareto front in the context of Test functions for optimization
In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as convergence rate, precision, robustness and general performance.
Here some test functions are presented with the aim of giving an idea about the different situations that optimization algorithms have to face when coping with these kinds of problems. In the first part, some objective functions for single-objective optimization cases are presented. In the second part, test functions with their respective Pareto fronts for multi-objective optimization problems (MOP) are given.
In this Dossier