316 research outputs found
Set-based Multiobjective Fitness Landscapes: A Preliminary Study
Fitness landscape analysis aims to understand the geometry of a given
optimization problem in order to design more efficient search algorithms.
However, there is a very little knowledge on the landscape of multiobjective
problems. In this work, following a recent proposal by Zitzler et al. (2010),
we consider multiobjective optimization as a set problem. Then, we give a
general definition of set-based multiobjective fitness landscapes. An
experimental set-based fitness landscape analysis is conducted on the
multiobjective NK-landscapes with objective correlation. The aim is to adapt
and to enhance the comprehensive design of set-based multiobjective search
approaches, motivated by an a priori analysis of the corresponding set problem
properties
Problem Understanding through Landscape Theory
In order to understand the structure of a problem we need to measure some features of the problem. Some examples of measures suggested in the past are autocorrelation and fitness-distance correlation. Landscape theory, developed in the last years in the field of combinatorial optimization, provides mathematical expressions to efficiently compute statistics on optimization problems. In this paper we discuss how can we use optimización combinatoria in the context of problem understanding and present two software tools that can be used to efficiently compute the mentioned measures.Ministerio de EconomÃa y Competitividad (TIN2011-28194
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
Fitness Landscape-Based Characterisation of Nature-Inspired Algorithms
A significant challenge in nature-inspired algorithmics is the identification
of specific characteristics of problems that make them harder (or easier) to
solve using specific methods. The hope is that, by identifying these
characteristics, we may more easily predict which algorithms are best-suited to
problems sharing certain features. Here, we approach this problem using fitness
landscape analysis. Techniques already exist for measuring the "difficulty" of
specific landscapes, but these are often designed solely with evolutionary
algorithms in mind, and are generally specific to discrete optimisation. In
this paper we develop an approach for comparing a wide range of continuous
optimisation algorithms. Using a fitness landscape generation technique, we
compare six different nature-inspired algorithms and identify which methods
perform best on landscapes exhibiting specific features.Comment: 10 pages, 1 figure, submitted to the 11th International Conference on
Adaptive and Natural Computing Algorithm
Elementary landscape decomposition of the 0-1 unconstrained quadratic optimization
Journal of Heuristics, 19(4), pp.711-728Landscapes’ theory provides a formal framework in which combinatorial optimization problems can be theoretically characterized as a sum of an especial kind of landscape called elementary landscape. The elementary landscape decomposition of a combinatorial optimization problem is a useful tool for understanding the problem. Such decomposition provides an additional knowledge on the problem that can be exploited to explain the behavior of some existing algorithms when they are applied to the problem or to create new search methods for the problem. In this paper we analyze the 0-1 Unconstrained Quadratic Optimization from the point of view of landscapes’ theory. We prove that the problem can be written as the sum of two elementary components and we give the exact expressions for these components. We use the landscape decomposition to compute autocorrelation measures of the problem, and show some practical applications of the decomposition.Spanish Ministry of Sci- ence and Innovation and FEDER under contract TIN2008-06491-C04-01 (the M∗ project). Andalusian Government under contract P07-TIC-03044 (DIRICOM project)
Statics, metastable states and barriers in protein folding: A replica variational approach
Protein folding is analyzed using a replica variational formalism to
investigate some free energy landscape characteristics relevant for dynamics. A
random contact interaction model that satisfies the minimum frustration
principle is used to describe the coil-globule transition (characterized by
T_CG), glass transitions (by T_A and T_K) and folding transition (by T_F).
Trapping on the free energy landscape is characterized by two characteristic
temperatures, one dynamic, T_A the other static, T_K (T_A> T_K), which are
similar to those found in mean field theories of the Potts glass. 1)Above T_A,
the free energy landscape is monotonous and polymer is melted both dynamically
and statically. 2)Between T_A and T_K, the melted phase is still dominant
thermodynamically, but frozen metastable states, exponentially large in number,
appear. 3)A few lowest minima become thermodynamically dominant below T_K,
where the polymer is totally frozen. In the temperature range between T_A and
T_K, barriers between metastable states are shown to grow with decreasing
temperature suggesting super-Arrhenius behavior in a sufficiently large system.
Due to evolutionary constraints on fast folding, the folding temperature T_F is
expected to be higher than T_K, but may or may not be higher than T_A. Diverse
scenarios of the folding kinetics are discussed based on phase diagrams that
take into account the dynamical transition, as well as the static ones.Comment: 41 pages, LaTeX, 9 EPS figure
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