The set of optimal solutions obtained in the form of Pareto front includes all equally good trade-off solutions. But I was wondering, whether these solutions are global optima or local optima or mix of both. In other words, does an evolutionary algorithm like NSGA-II guaranties global optimum solutions?
Thank you in anticipation.
Dear Joy,
In general, genetic algorithms can perform a global search in the entire search space, but they are poor at exploring the search space within the convergence area generated by the genetic algorithm loop!
More details can be tarcked in the following paper:
Article A tuned NSGA-II to optimize the total cost and service level...
Good luck!
No, a Pareto front produced by an evolutionary algorithm does not necessarily include both global and local optima. The Pareto front represents the set of non-dominated solutions in multi-objective optimization problems. These solutions are not dominated by any other solution in terms of all the objective functions simultaneously.
In a multi-objective optimization problem, there can be multiple optimal solutions, known as Pareto optimal solutions, that represent trade-offs between conflicting objectives. These solutions lie on the Pareto front and are considered efficient solutions because improving one objective would require sacrificing performance in another objective.
The Pareto front typically contains a mixture of global and local optima. Global optima are solutions that provide the best performance across all objectives in the entire search space. Local optima, on the other hand, are solutions that are optimal within a specific region of the search space but may not be globally optimal.
The evolutionary algorithm aims to explore the search space and find a diverse set of Pareto optimal solutions across the entire front, which may include both global and local optima. However, the algorithm's ability to discover global optima depends on its exploration and exploitation capabilities, the problem complexity, and the specific settings and parameters of the algorithm.
It's important to note that the distribution and representation of global and local optima on the Pareto front can vary depending on the problem and algorithm used. Analyzing the Pareto front and its solutions can provide valuable insights into the trade-offs and optimal solutions available in multi-objective optimization problems.
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