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...g the size of basins, and the label “fit”, the fitness of the local optima). The edges depict the transition probabilities between basins as defined in the text. next section. Following previous work =-=[7, 8]-=-, we use the well-known family of NK landscapes [4] as an example, as it allows the exploration of landscapes of tunable ruggedness and search difficulty. The article is structured as follows. Section...

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...hods (see [4] and references therein). Doye has called this graph the Inherent Structure Network; here we prefer to use the term Local Optima Network (LON). Inspired by this approach, in our own work =-=[5, 6]-=- we have applied similar ideas to the case of the configuration spaces of difficult combinatorial optimization problems. Although the problems look superficially similar, hard combinatorial spaces pos...

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... information given by the whole problem configuration space into a smaller mathematical object that is the graph having as vertices the local optima and as edges the possible transitions between them =-=[15, 16]-=-. This characterization of landscapes as complex networks enables the use of tools and metrics of the complex networks domain [4] and has brought new insights into the global structure of the landscap...

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... The number and distribution of local optima in a search space have, therefore, an important impact on the performance of heuristic search algorithms. A recently proposed model: Local Optima Networks =-=[22, 25]-=-, provides an intermediate level of description for combinatorial fitness landscapes. The model has a higher descriptive power than a single statistical metric or set of metrics; but it also compresse...

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...orial counterpart considers oriented and weighted edges. In a first version, the weights represent an approximation to the probability of transition between the respective basins in a given direction =-=[32,33,41,44,45]-=-. This definition, although informative, produced densely connected networks and required exhaustive sampling of the basins of attraction. A second version, escape edges was proposed in [43], which do...

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...vantage to using Avg(N(x)) as a surrogate fitness function over using f(x). We hypothesize that more plateaus are found in NKq-landscapes, which should favor the use of the Avg(N(x)) fitness function =-=[1,8]-=-. Second, a fundamental decision is what to do when a local optimum is encountered. One simple answer is to use a random restart. However, the proof of O(1) complexity suggests that there is a signifi...

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... are defined differently, and are oriented and weighted. In a first version, the weights represent an approximation to the probability of transition between the respective basins in a given direction =-=[6, 16, 23, 25]-=-. This definition, although2 F. Daolio, S. Verel, G. Ochoa and M. Tomassini informative, produced densely connected networks and required exhaustive sampling of the basins of attraction. A second ver...

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...e funnels at evaluations close to the global optimum. A similar recombination operator [12] is used by Helsgaun [8] in the so called LKH-solver. This article uses the Local Optima Network (LON) model =-=[15, 16, 14, 18]-=- in order to explore in more detail the structure of TSP landscapes near the global optimum. Local optima networks compress the whole search spaces into a graph having as vertices the local optima, an...