On the Fractal Nature of Local Optima Networks

A Local Optima Network represents fitness landscape connectivity within the space of local optima as a mathematical graph. In certain other complex networks or graphs there have been recent observations made about inherent self-similarity. An object is said to be self-similar if it shows the same patterns when measured at different scales; another word used to convey self-similarity is fractal. The fractal dimension of an object captures how the detail observed changes with the scale at which it is measured, with a high fractal dimension being associated with complexity. We conduct a detailed study on the fractal nature of the local optima networks of a benchmark combinatorial optimisation problem (NK Landscapes). The results draw connections between fractal characteristics and performance by three prominent metaheuristics: Iterated Local Search, Simulated Annealing, and Tabu Search

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

Multifractality and Dimensional Determinism in Local Optima Networks

We conduct a study of networks of local optimas in a search space using fractal dimensions. The fractal dimension (FD) of these networks is a complexity index which assigns a non-integer dimension to an object. We propose a fine-grained approach to obtaining the FD of LONs, using the probabilistic search transitions encoded in LON edge weights. We then apply multi-fractal calculations to LONs for the first time, comparing with mono-fractal analysis. For complex systems such as LONs, the dimensionality may be different between two sub-systems and multi-fractal analysis is needed. Here we focus on the Quadratic Assignment Problem (QAP), conducting fractal analyses on sampled LONs of reasonable size for the first time. We also include fully enumerated LONs of smaller size. Our results show that local optima spaces can be multi-fractal and that valuable information regarding stochastic self-similarity is encoded in the edge weights of local optima networks. Links are drawn between these phenomena and the performance of two competitive metaheuristic algorithms

The fractal urban coherence in biourbanism: the factual elements of urban fabric

This article is available online and will be inserted in also printed format in the Journal in October 2013.During the last few decades, modern urban fabric lost some very important elements, only because urban design and planning turned out to be stylistic aerial views or new landscapes of iconic technological landmarks. Biourbanism attempts to re-establish lost values and balance, not only in urban fabric, but also in reinforcing human-oriented design principles in either micro or macro scale. Biourbanism operates as a catalyst of theories and practices in both architecture and urban design to guarantee high standards in services, which are currently fundamental to the survival of communities worldwide. Human life in cities emerges during connectivity via geometrical continuity of grids and fractals, via path connectivity among highly active nodes, via exchange/movement of people and, finally via exchange of information (networks). In most human activities taking place in central areas of cities, people often feel excluded from design processes in the built environment. This paper aims at exploring the reasons for which, fractal cities, which have being conceived as symmetries and patterns, can have scientifically proven and beneficial impact on human fitness of body and mind; research has found that, brain traumas caused by visual agnosia become evident when patterns disappear from either 2D or 3D emergences in architectural and urban design.ADT Fund

Phase transitions in Pareto optimal complex networks

The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their topological structure can be diverse, resulting from different mechanisms including multiplicative processes and optimization. In spatial networks or in graphs where cost constraints are at work, as it occurs in a plethora of situations from power grids to the wiring of neurons in the brain, optimization plays an important part in shaping their organization. In this paper we study network designs resulting from a Pareto optimization process, where different simultaneous constraints are the targets of selection. We analyze three variations on a problem finding phase transitions of different kinds. Distinct phases are associated to different arrangements of the connections; but the need of drastic topological changes does not determine the presence, nor the nature of the phase transitions encountered. Instead, the functions under optimization do play a determinant role. This reinforces the view that phase transitions do not arise from intrinsic properties of a system alone, but from the interplay of that system with its external constraints.Comment: 14 pages, 7 figure

Efficiency Analysis of Swarm Intelligence and Randomization Techniques

Swarm intelligence has becoming a powerful technique in solving design and scheduling tasks. Metaheuristic algorithms are an integrated part of this paradigm, and particle swarm optimization is often viewed as an important landmark. The outstanding performance and efficiency of swarm-based algorithms inspired many new developments, though mathematical understanding of metaheuristics remains partly a mystery. In contrast to the classic deterministic algorithms, metaheuristics such as PSO always use some form of randomness, and such randomization now employs various techniques. This paper intends to review and analyze some of the convergence and efficiency associated with metaheuristics such as firefly algorithm, random walks, and L\'evy flights. We will discuss how these techniques are used and their implications for further research.Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1212.0220, arXiv:1208.0527, arXiv:1003.146

Emergent quality of service - a bacterial approach

A possible model for future network quality of service control is proposed. This is based on a community of bacterial strains, each organism handling network requests in the same way as bacteria metabolise energy sources. This model makes use of the unique methods that bacteria use to transfer and share genetic material, to create a more robust solution to the service provision problems associated with future data networks

Artificial Immune Systems - Models, algorithms and applications

Copyright © 2010 Academic Research Publishing Agency.This article has been made available through the Brunel Open Access Publishing Fund.Artificial Immune Systems (AIS) are computational paradigms that belong to the computational intelligence family and are inspired by the biological immune system. During the past decade, they have attracted a lot of interest from researchers aiming to develop immune-based models and techniques to solve complex computational or engineering problems. This work presents a survey of existing AIS models and algorithms with a focus on the last five years.This article is available through the Brunel Open Access Publishing Fun