2,625 research outputs found
A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model
We present a simple transformation of the formulation of the log-periodic
power law formula of the Johansen-Ledoit-Sornette model of financial bubbles
that reduces it to a function of only three nonlinear parameters. The
transformation significantly decreases the complexity of the fitting procedure
and improves its stability tremendously because the modified cost function is
now characterized by good smooth properties with in general a single minimum in
the case where the model is appropriate to the empirical data. We complement
the approach with an additional subordination procedure that slaves two of the
nonlinear parameters to what can be considered to be the most crucial nonlinear
parameter, the critical time defined as the end of the bubble and the
most probably time for a crash to occur. This further decreases the complexity
of the search and provides an intuitive representation of the results of the
calibration. With our proposed methodology, metaheuristic searches are not
longer necessary and one can resort solely to rigorous controlled local search
algorithms, leading to dramatic increase in efficiency. Empirical tests on the
Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our
findings
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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
Damage identification in steel plate using FRF and inverse analysis
Metaheuristic algorithms have known vast development in recent years. And their applicability in engineering projects is constantly growing; however, their deferent exploration and exploitation techniques cause the engineering problems to favor some algorithms over others. This paper studies damage identification in steel plates using Frequency Response Function (FRF) damage indicator to detect and localize the healthy and damaged structure. The study is formulated as an inverse analysis, investigating the performance of three new metaheuristic algorithms of Wild Horse Optimizer (WHO), Harris Hawks Optimization (HHO), and Arithmetic Optimization Algorithm (AOA). The objective function is based on measured and calculated FRF damage indicators. The results showed that the case of four damages with different damage severity levels presented a good challenge where the HWO algorithm was shown to have the best performance. Both in convergence speed and CPU time
Multipitch estimation using judge-based model
Multipitch estimation, also known as multiple fundamental frequency (F0) estimation, is an important part of the Music Information Retrieval (MIR) field. Although there have been many different approaches proposed, none of them has ever exceeded the abilities of a trained musician. In this work, an iterative cancellation method is analysed, being applied to three different sound representations - salience spectrum obtained using Constant-Q Transform, cepstrum and enhanced autocorrelation result. Real-life recordings of different musical instruments are used as a database and the parameters of the solution are optimized using a simple yet effective metaheuristic approach - the Luus-Jaakola algorithm. The presented approach results in 85% efficiency on the test database
A Metaheuristic for Amortized Search in High-Dimensional Parameter Spaces
Parameter inference for dynamical models of (bio)physical systems remains a
challenging problem. Intractable gradients, high-dimensional spaces, and
non-linear model functions are typically problematic without large
computational budgets. A recent body of work in that area has focused on
Bayesian inference methods, which consider parameters under their statistical
distributions and therefore, do not derive point estimates of optimal parameter
values. Here we propose a new metaheuristic that drives dimensionality
reductions from feature-informed transformations (DR-FFIT) to address these
bottlenecks. DR-FFIT implements an efficient sampling strategy that facilitates
a gradient-free parameter search in high-dimensional spaces. We use artificial
neural networks to obtain differentiable proxies for the model's features of
interest. The resulting gradients enable the estimation of a local active
subspace of the model within a defined sampling region. This approach enables
efficient dimensionality reductions of highly non-linear search spaces at a low
computational cost. Our test data show that DR-FFIT boosts the performances of
random-search and simulated-annealing against well-established metaheuristics,
and improves the goodness-of-fit of the model, all within contained run-time
costs
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