Multi-layer local optima networks for the analysis of advanced local search-based algorithms

A Local Optima Network (LON) is a graph model that compresses the fitness landscape of a particular combinatorial optimization problem based on a specific neighborhood operator and a local search algorithm. Determining which and how landscape features affect the effectiveness of search algorithms is relevant for both predicting their performance and improving the design process. This paper proposes the concept of multi-layer LONs as well as a methodology to explore these models aiming at extracting metrics for fitness landscape analysis. Constructing such models, extracting and analyzing their metrics are the preliminary steps into the direction of extending the study on single neighborhood operator heuristics to more sophisticated ones that use multiple operators. Therefore, in the present paper we investigate a twolayer LON obtained from instances of a combinatorial problem using bitflip and swap operators. First, we enumerate instances of NK-landscape model and use the hill climbing heuristic to build the corresponding LONs. Then, using LON metrics, we analyze how efficiently the search might be when combining both strategies. The experiments show promising results and demonstrate the ability of multi-layer LONs to provide useful information that could be used for in metaheuristics based on multiple operators such as Variable Neighborhood Search.Comment: Accepted in GECCO202

A characterisation of S-box fitness landscapes in cryptography

Substitution Boxes (S-boxes) are nonlinear objects often used in the design of cryptographic algorithms. The design of high quality S-boxes is an interesting problem that attracts a lot of attention. Many attempts have been made in recent years to use heuristics to design S-boxes, but the results were often far from the previously known best obtained ones. Unfortunately, most of the effort went into exploring different algorithms and fitness functions while little attention has been given to the understanding why this problem is so difficult for heuristics. In this paper, we conduct a fitness landscape analysis to better understand why this problem can be difficult. Among other, we find that almost each initial starting point has its own local optimum, even though the networks are highly interconnected

Complexity Studies of Firm Dynamics

abstract: This thesis consists of three projects employing complexity economics methods to explore firm dynamics. The first is the Firm Ecosystem Model, which addresses the institutional conditions of capital access and entrenched competitive advantage. Larger firms will be more competitive than smaller firms due to efficiencies of scale, but the persistence of larger firms is also supported institutionally through mechanisms such as tax policy, capital access mechanisms and industry-favorable legislation. At the same time, evidence suggests that small firms innovate more than larger firms, and an aggressive firm-as-value perspective incentivizes early investment in new firms in an attempt to capture that value. The Ecological Firm Model explores the effects of the differences in innovation and investment patterns and persistence rates between large and small firms. The second project is the Structural Inertia Model, which is intended to build theory around why larger firms may be less successful in capturing new marketshare than smaller firms, as well as to advance fitness landscape methods. The model explores the possibility that firms with larger scopes may be less effective in mitigating the costs of cooperation because conditions may arise that cause intrafirm conflicts. The model is implemented on structured fitness landscapes derived using the maximal order of interaction (NM) formulation and described using local optima networks (LONs), thus integrating these novel techniques. Finally, firm dynamics can serve as a proxy for the ease at which people can voluntarily enter into the legal cooperative agreements that constitute firms. The third project, the Emergent Firm model, is an exploration of how this dynamic of voluntary association may be affected by differing capital institutions, and explores the macroeconomic implications of the economies that emerge out of the various resulting firm populations.Dissertation/ThesisDoctoral Dissertation Applied Mathematics for the Life and Social Sciences 201

Local optima networks and the performance of iterated local search

Local Optima Networks (LONs) have been recently proposed as an alternative model of combinatorial fitness landscapes. The model compresses the information given by the whole search space into a smaller mathematical object that is the graph having as vertices the local optima and as edges the possible weighted transitions between them. A new set of metrics can be derived from this model that capture the distribution and connectivity of the local optima in the underlying configuration space.This paper departs from the descriptive analysis of local optima networks, and actively studies the correlation between network features and the performance of a local search heuristic. The NK family of landscapes and the Iterated Local Search metaheuristic are considered. With a statisticallysound approach based on multiple linear regression, it is shown that some LONs’ features strongly influence and can even partly predict the performance of a heuristic search algorithm. This study validates the expressive power of LONs as a model of combinatorial fitness landscapes