A small number of combinatorial optimization problems have search spaces that correspond to elementary landscapes, where the objective function f is an eigenfunction of the Laplacian that describes the neighborhood structure ...

Efficient hill climbers have been recently proposed for single- and multi-objective pseudo-Boolean optimization problems. For $k$-bounded pseudo-Boolean functions where each variable appears in at most a constant number ...

Hill climbing algorithms are at the core of many approaches to solve optimization problems. Such algorithms usually require the complete enumeration of a neighborhood of the current solution. In the case of problems defined ...

There exist local search landscapes where the evaluation function is an eigenfunction of the graph Laplacian that corresponds to the neighborhood structure of the search space. Problems that dis- play this structure are ...

Uniform crossover is a popular operator used in genetic algorithms to combine two tentative solutions of a problem represented as binary strings. We use the Walsh decomposition of pseudo-Boolean functions and properties ...

The frequency distribution of a fitness function over regions of its domain is an important quantity for understanding the behavior of algorithms that employ randomized sampling to search the function. In general, exactly ...

In gray-box optimization, the search algorithms have access to the variable interaction graph (VIG) of the optimization problem. For Mk Landscapes (and NK Landscapes) we can use the VIG to identify an improving solution ...

The output of an optimal recombination operator for two parent solutions is a solution with the best possible value for the objective function among all the solutions fulfilling the gene transmission property: the value ...