Most of the derivative-free optimization (DFO) algorithms rely on a comparison function able to compare any pair of points with respect to a blackbox objective function. Recently, new dedicated derivative-free optimization algorithms have emerged to tackle multi-objective optimization problems and provide a Pareto front approximation to the user. This work aims at reusing single objective DFO a...

In this paper, we propose and analyze two schemes to integrate an objective reduction technique into a multi-objective evolutionary algorithm (MOEA) in order to cope with many-objective problems. One scheme reduces periodically the number objectives during the search until the required objective subset size has been reached and, towards the end of the search, the original objective set is used ...

When facing a real world, optimization problems mainly become multiobjective i.e. they have several criteria of excellence. A multi-criteria problem submitted for multi-criteria evaluation is a complex problem, as usually there is no optimal solution, and no alternative is the best one according to all criteria. However, if a metaheuristic algorithm is combined with a Multi-Criteria Decision-Ma...

I shall argue that there is no such property of an event as its “probability.” This is why standard interpretations cannot give a sound definition in empirical terms of what “probability” is, and this is why empirical sciences like physics can manage without such a definition. “Probability” is a collective term, the meaning of which varies from context to context: it means different—dimensionle...

A common approach in multiobjective optimization is to perform the decision making process after the search process: first, a search heuristic approximates the set of Pareto-optimal solutions, and then the decision maker chooses an appropriate trade-off solution from the resulting approximation set. Both processes are strongly affected by the number of optimization criteria. The more objectives...

A key feature of an efficient and reliable multi-objective evolutionary algorithm is the ability to maintain genetic diversity within a population of solutions. In this paper, we present a new diversity-preserving mechanism, the Genetic Diversity Evaluation Method (GeDEM), which considers a distance-based measure of genetic diversity as a real objective in fitness assignment. This provides a du...