Using network mesures to test evolved NK-landscapes

In this paper we empirically investigate which are the structural characteristics that can help to predict the complexity of NK-landscape instances for estimation of distribution algorithms. To this end, we evolve instances that maximize the estimation of distribution algorithm complexity in terms of its success rate. Similarly, instances that minimize the algorithm complexity are evolved. We then identify network measures, computed from the structures of the NK-landscape instances, that have a statistically significant difference between the set of easy and hard instances. The features identified are consistently significant for different values of N and K

Local Optima Networks of NK Landscapes with Neutrality

In previous work we have introduced a network-based model that abstracts many details of the underlying landscape and compresses the landscape information into a weighted, oriented graph which we call the local optima network. The vertices of this graph are the local optima of the given fitness landscape, while the arcs are transition probabilities between local optima basins. Here we extend this formalism to neutral fitness landscapes, which are common in difficult combinatorial search spaces. By using two known neutral variants of the NK family (i.e. NKp and NKq) in which the amount of neutrality can be tuned by a parameter, we show that our new definitions of the optima networks and the associated basins are consistent with the previous definitions for the non-neutral case. Moreover, our empirical study and statistical analysis show that the features of neutral landscapes interpolate smoothly between landscapes with maximum neutrality and non-neutral ones. We found some unknown structural differences between the two studied families of neutral landscapes. But overall, the network features studied confirmed that neutrality, in landscapes with percolating neutral networks, may enhance heuristic search. Our current methodology requires the exhaustive enumeration of the underlying search space. Therefore, sampling techniques should be developed before this analysis can have practical implications. We argue, however, that the proposed model offers a new perspective into the problem difficulty of combinatorial optimization problems and may inspire the design of more effective search heuristics.Comment: IEEE Transactions on Evolutionary Computation volume 14, 6 (2010) to appea

Benchmarking for Metaheuristic Black-Box Optimization: Perspectives and Open Challenges

Research on new optimization algorithms is often funded based on the motivation that such algorithms might improve the capabilities to deal with real-world and industrially relevant optimization challenges. Besides a huge variety of different evolutionary and metaheuristic optimization algorithms, also a large number of test problems and benchmark suites have been developed and used for comparative assessments of algorithms, in the context of global, continuous, and black-box optimization. For many of the commonly used synthetic benchmark problems or artificial fitness landscapes, there are however, no methods available, to relate the resulting algorithm performance assessments to technologically relevant real-world optimization problems, or vice versa. Also, from a theoretical perspective, many of the commonly used benchmark problems and approaches have little to no generalization value. Based on a mini-review of publications with critical comments, advice, and new approaches, this communication aims to give a constructive perspective on several open challenges and prospective research directions related to systematic and generalizable benchmarking for black-box optimization