On the efficiency of worst improvement for climbing NK-landscapes

Abstract

Climbers are often used in metaheuristics in order to intensify the search and identify local optima with respect to a neighborhood structure. Even if they constitute a central component of modern heuristics, their design principally consists in choosing the pivoting rule, which is often reduced to two alternative strategies: first improvement or best improvement. The conception effort of most metaheuristics belongs in proposing techniques to escape from local optima, and not necessarily on how to climb toward better local optima. In this paper, we are interested in attaining good local optima with basic hill-climbing techniques. The NK model will be used to evaluate a set of climbers proposed in this paper. By focusing on the pivoting rule definition, we show that choosing the worst improving neighbor often leads to attain better local optima. Moreover, by slightly modifying the worst improvement strategy, one can design efficient climbers which outperform first and best improvement in terms of tradeoff between quality and computational effort.

Climbing combinatorial fitness landscapes

“…The main objective is to determine advanced pivoting rules, which allow hill-climbing algorithms to reach high local optima in a single run. For instance, in [39], we propose a new pivoting rule which clearly outperforms first and best improvement on rugged landscapes. Other original moving rules could benefit from landscape analysis to explore the search space more efficiently.…”

On the Attainability of NK Landscapes Global Optima

“…It would be interesting to find a way to estimate the proposed metrics for large of highly rugged landscapes where we are not able to enumerate all paths exhaustively. Nevertheless, this study lead us to believe that there is possibilities to improve hill-climbing search efficiency by defining alternative pivoting rules (Basseur and Goëffon 2014), which aim to increase the probability to reach the best local optima and then the average expected final fitness achieved.…”

From fitness landscapes evolution to automatic local search algorithm generation

“…$$N$$ is the landscape dimension, and $$K < N$$ specifies the average number of dependencies per variable and consequently the ruggedness of the fitness landscape. NK functions are commonly used to define fitness landscapes having specific properties in terms of size and ruggedness (Merz and Freisleben, 1998; Aguirre and Tanaka, 2003; Ochoa et al., 2008; Basseur and Goëffon, 2014).…”

“…The random neighbor NK landscape model (Kauffman and Weinberger, 1989) can be used to express binary fitness landscapes, whose properties are determined by means of two parameters N and K. N is the landscape dimension, and K < N specifies the average number of dependencies per variable and consequently the ruggedness of the fitness landscape. NK functions are commonly used to define fitness landscapes having specific properties in terms of size and ruggedness (Merz and Freisleben, 1998;Aguirre and Tanaka, 2003;Ochoa et al, 2008;Basseur and Goëffon, 2014).…”