scholarly journals Search Patterns Based on Trajectories Extracted from the Response of Second-Order Systems

2021 ◽  
Vol 11 (8) ◽  
pp. 3430
Author(s):  
Erik Cuevas ◽  
Héctor Becerra ◽  
Héctor Escobar ◽  
Alberto Luque-Chang ◽  
Marco Pérez ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Second Order ◽  
Order System ◽  
Search Patterns ◽  
Multiple Behaviors ◽  
Complex Optimization ◽  
Second Order Systems ◽  
Order Algorithm

Recently, several new metaheuristic schemes have been introduced in the literature. Although all these approaches consider very different phenomena as metaphors, the search patterns used to explore the search space are very similar. On the other hand, second-order systems are models that present different temporal behaviors depending on the value of their parameters. Such temporal behaviors can be conceived as search patterns with multiple behaviors and simple configurations. In this paper, a set of new search patterns are introduced to explore the search space efficiently. They emulate the response of a second-order system. The proposed set of search patterns have been integrated as a complete search strategy, called Second-Order Algorithm (SOA), to obtain the global solution of complex optimization problems. To analyze the performance of the proposed scheme, it has been compared in a set of representative optimization problems, including multimodal, unimodal, and hybrid benchmark formulations. Numerical results demonstrate that the proposed SOA method exhibits remarkable performance in terms of accuracy and high convergence rates.

Two-sided form, differentiation and second-order observation in Escher’s artworks and Calvino’s stories

Kybernetes ◽  
2019 ◽  
Vol 48 (5) ◽  
pp. 1060-1077
Author(s):  
Laura Appignanesi
Keyword(s):  
Twentieth Century ◽  
Systems Theory ◽  
Second Order ◽  
Order System ◽  
Literary Works ◽  
Content Type ◽  
Theoretical Concepts ◽  
Art And Literature ◽  
Second Order Systems ◽  
Late Works

Purpose The purpose of this paper is to find a leading idea of the mid-twentieth century, demonstrating the pervasive nature of some concepts belonging to second-order systems theory. To achieve this objective, the paper looks at the art and literature of this era, to identify the principles developed by Luhmann in his late works. In particular, Escher’s drawings, Calvino’s stories and Luhmann’s concepts seem to express, in different ways, the same functioning mechanism of the complex social system. Design/methodology/approach With reference to theoretical approach and methodology, this paper carries out an interdisciplinary demonstration by alternative modes of logos and mythos. Some of the pillars of general systems theory are examined through the logical articulation of concepts developed by Spencer-Brown, von Foerster, and first of all through the late works of Luhmann, as well as through the analysis of Escher’s artworks and Calvino’s literary works. This paper interprets these artistic and literary works using cybernetic principles and systemic concepts, in particular, “two-sided forms,” “system–environment differentiation” and “second-order observation.” Findings In general, the main finding is the similarity of fascination with paradoxes and forms, with post-ontological reasoning, in twentieth century. The result of the cross-reading of Escher, Calvino and Luhmann reveals the presence of what Simmel called the “hidden king”: a philosophical paradigm of an era. In mid-1900s, this leading idea seems to express itself in the discoveries of biology and cybernetics, such as in Luhmann’s theory, art and literature. Escher’s drawings, Calvino’s stories and the concepts of Luhmann are projections of second-order system theory, in its constructivist value. Originality/value The originality of this paper lies mainly in the demonstration of theoretical concepts through the alternative modes of logos and mythos. These reflections can provide a new perspective to investigate social sciences from a cultural angle. This particular approach allows a deep awareness of the theory. The concrete value is to provide a better understanding to manage complexity.

Periodic Behavior of a Nonlinear Third Order Vibrating System

2002 ◽  
Author(s):  
Gholamreza Nakhaie Jazar ◽  
Mohammad H. Alimi ◽  
Mohammad Mahinfalah ◽  
Ali Khazaei
Keyword(s):  
Differential Equation ◽  
Dynamical Systems ◽  
Ad Hoc ◽  
Order Differential Equation ◽  
Second Order ◽  
Order System ◽  
Third Order ◽  
Modeling Process ◽  
Third Order Differential Equation ◽  
Second Order Systems

In modeling of dynamical systems, differential equations, either ordinary or partial, are a common outcome of the modeling process. The basic problem becomes the existence of solution of these deferential equations. In the early days of the solution of deferential equations at the beginning of the eighteenth century the methods for determining the existence of nontrivial solution were so limited and developed very much on an ad hoc basis. Most of the efforts on dynamical system are related to the second order systems, derived by applying Newton equation of motion to dynamical systems. But, behavior of some dynamical systems is governed by equations falling down in the general nonlinear third order differential equation x″′+f(t,x,x′,x″)=0, sometimes as a result of combination of a first and a second order system. It is shown in this paper that these equations could have nontrivial solutions, if x, x′, x″, and f(t,x,x′,x″) are bounded. Furthermore, it is shown that the third order differential equation has a τ-periodic solution if f(t,x,x′,x″) is an even function with respect to x′. For this purpose, the concept of Green’s function and the Schauder’s fixed-point theorem has been used.

scholarly journals Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization

2020 ◽  
Vol 30 (6) ◽  
pp. 1645-1663
Author(s):  
Ömer Deniz Akyildiz ◽  
Dan Crisan ◽  
Joaquín Míguez
Keyword(s):  
Monte Carlo ◽  
Cost Function ◽  
Global Minimum ◽  
Sequential Monte Carlo ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Gradient Based ◽  
Multiple Minima ◽  
The Cost

Abstract We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth-order optimization algorithm which demands only the capability to evaluate small subsets of components of the cost function. It can be depicted as a bank of samplers that generate particle approximations of several sequences of probability measures. These measures are constructed in such a way that they have associated probability density functions whose global maxima coincide with the global minima of the original cost function. The algorithm selects the best performing sampler and uses it to approximate a global minimum of the cost function. We prove analytically that the resulting estimator converges to a global minimum of the cost function almost surely and provide explicit convergence rates in terms of the number of generated Monte Carlo samples and the dimension of the search space. We show, by way of numerical examples, that the algorithm can tackle cost functions with multiple minima or with broad “flat” regions which are hard to minimize using gradient-based techniques.

scholarly journals Filtering Method Based on Symmetrical Second Order Systems

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 813
Author(s):  
Cristian Toma
Keyword(s):  
Time Moment ◽  
Sampling Procedure ◽  
Second Order ◽  
Sampling Time ◽  
Half Period ◽  
Order System ◽  
Filtering Method ◽  
Oscillating Systems ◽  
Sampling Structure ◽  
Second Order Systems

This study presents a filtering and sampling structure based on symmetrical second order systems working on half-period. It is shown that undamped second order oscillating systems working on half-period could provide: (i) a large attenuation coefficient for an alternating signal (due to the filtering second order system), and (ii) a robust sampling procedure (the slope of the generated output being zero at the sampling time moment). Unlike previous studies on the same topics, these results are achieved without the use of an additional integrator.

A Reduced Second-Order Approach for Linear Viscoelastic Oscillators

2010 ◽  
Vol 77 (4) ◽  
Author(s):  
Sondipon Adhikari
Keyword(s):  
Past History ◽  
Kernel Functions ◽  
Second Order ◽  
Order System ◽  
Closed Form Expression ◽  
Internal Variables ◽  
Dynamical Response ◽  
Convolution Integrals ◽  
History Of ◽  
Second Order Systems

This paper proposes a new approach for the reduction in the model-order of linear multiple-degree-of-freedom viscoelastic systems via equivalent second-order systems. The assumed viscoelastic forces depend on the past history of motion via convolution integrals over kernel functions. Current methods to solve this type of problem normally use the state-space approach involving additional internal variables. Such approaches often increase the order of the eigenvalue problem to be solved and can become computationally expensive for large systems. Here, an approximate reduced second-order approach is proposed for this type of problems. The proposed approximation utilizes the idea of generalized proportional damping and expressions of approximate eigenvalues of the system. A closed-form expression of the equivalent second-order system has been derived. The new expression is obtained by elementary operations involving the mass, stiffness, and the kernel function matrix only. This enables one to approximately calculate the dynamical response of complex viscoelastic systems using the standard tools for conventional second-order systems. Representative numerical examples are given to verify the accuracy of the derived expressions.

scholarly journals Hybrid Simulated Annealing with Meta-Heuristic Methods to Solve UCT Problem

2018 ◽  
Vol 12 (11) ◽  
pp. 366 ◽  
Author(s):  
Issam AlHadid ◽  
Khalid Kaabneh ◽  
Hassan Tarawneh
Keyword(s):  
Simulated Annealing ◽  
Optimization Problems ◽  
Search Space ◽  
Local Optimum ◽  
Solution Quality ◽  
University Course Timetabling ◽  
Hybrid Simulated Annealing ◽  
Complex Optimization ◽  
List Memory ◽  
University Course

Simulated Annealing (SA) is a common meta-heuristic algorithm that has been widely used to solve complex optimization problems. This work proposes a hybrid SA with EMC to divert the search effectively to another promising region. Moreover, a Tabu list memory applied to avoid cycling. Experimental results showed that the solution quality has enhanced using SA-EMCQ by escaping the search space from local optimum to another promising region space. In addition, the results showed that our proposed technique has outperformed the standard SA and gave comparable results to other approaches in the literature when tested on ITC2007-Track3 university course timetabling datasets.

Performance Study of a Bat Searching Algorithm From System Dynamics Perspective

2019 ◽  
Author(s):  
Haopeng Zhang ◽  
Nathan Schutte
Keyword(s):  
System Dynamics ◽  
Optimization Problems ◽  
Second Order ◽  
Point Of View ◽  
Great Success ◽  
Performance Study ◽  
Step Size ◽  
Discrete Time Systems ◽  
Second Order Systems ◽  
Time Systems

Abstract In this paper, the performance of a bat searching algorithm is studied from system dynamics point of view. Bat searching algorithm (BA) is a recently developed swarm intelligence based optimization algorithm which has shown great success when solving complicated optimization problems. Each bat in the BA has two main states: velocity and position. The position represents the solution of the optimization problems while the velocity represents the searching direction and step size during each iteration. Due to the nature of the update equations, the dynamics of the bats are formulated as a group of second-order discrete-time systems. In this paper, the performance of the algorithm is analyzed based on the nature of the responses in the second-order systems. The over-damped response, under-damped responses are studied and the parameters requirements are derived. Moreover, unstable scenarios of the bats are also considered when examining the performance of the algorithm. Numerical evaluations are conducted to test different choices of the parameters in the BA.

A New Multi-Objective Firework Algorithm to Solve the Multimodal Planning Network Problem

2020 ◽  
Vol 11 (4) ◽  
pp. 91-113
Author(s):  
Mouna Gargouri Mnif ◽  
Sadok Bouamama
Keyword(s):  
Optimization Problems ◽  
Transportation Network ◽  
Search Space ◽  
Search Technique ◽  
Multimodal Transportation ◽  
New Approach ◽  
Multi Objective ◽  
Network Problem ◽  
Complex Optimization ◽  
Stochastic Search Technique

This article introduces a new approach called multi-objective firework algorithm (MFWA). The proposed approach allows for solving the multimodal transportation network problem (MTNP). The main goal is to develop a decision system that optimizes and determines the planning network of the multimodal transportation (PNMT) problem. The optimization involves reaching the efficient transport mode and multimodal path, in order to move from one country to another while satisfying the set of objectives. Moreover, the firework algorithm has distinct advantages in solving complex optimization problems and in obtaining a solution by a distributed and oriented research system. This approach presents a search way, which is different from the swarm intelligence-based stochastic search technique. For each firework, the process starts by exploding a firework in the sky. The search space is filled with a shower of sparks to get diversity solutions. This new approach proves their efficacy in solving the multi-objective problem, which is shown by the experimental results.

scholarly journals Extracting second-order system matrices from state space system

2006 ◽  
Vol 220 (8) ◽  
pp. 1147-1149 ◽  
Author(s):  
P R Houlston
Keyword(s):  
Technical Note ◽  
Second Order ◽  
Order System ◽  
System Modelling ◽  
Direct Control ◽  
Space System ◽  
First Order ◽  
The Reformation ◽  
State Space System ◽  
Second Order Systems

This technical note concerns the reformation of a second-order system from an arbitrary first-order system. At present, the majority of control literature is concerned with controlling systems within the first-order linearization of a system. The author is part of a growing community looking to expand the direct control of second-order systems and the benefits associated in doing so. However, there are potential stages of system modelling that may result in it being necessary to form the first-order form of the system, such as model reduction. This may have the effect of destroying the second-order notion of the system. The purpose of this note is to regain the structure of the second-order system and thus enable the benefits of direct second-order control to be realized. Although the problem itself has been previously resolved, the author proposes the virtue of a simpler method.

Catastrophe-Based Antibody Clone Algorithm

2011 ◽  
Vol 121-126 ◽  
pp. 4415-4420
Author(s):  
Yu Zhang ◽  
Li Hua Wu ◽  
Zi Qiang Luo
Keyword(s):  
Optimization Problems ◽  
Optimization Algorithms ◽  
Search Space ◽  
Natural World ◽  
Population Diversity ◽  
Selection Algorithm ◽  
Intelligent Optimization Algorithms ◽  
Complex Optimization ◽  
Search Capability ◽  
Better Than

In solving complex optimization problems, intelligent optimization algorithms such as immune algorithm show better advantages than traditional optimization algorithms. Most of these immune algorithms, however, have disadvantages in population diversity and preservation of elitist antibodies genes, which will lead to the degenerative phenomenon, the zigzag phenomenon, poor global optimization, and low convergence speed. By introducing the catastrophe factor into the ACAMHC algorithm, we propose a novel catastrophe-based antibody clone algorithm (CACA) to solve the above problems. CACA preserves elitist antibody genes through the vaccine library to improve its local search capability; it improves the antibody population diversity by gene mutation that mimics the catastrophe events to the natural world to enhance its global search capability. To expand the antibody search space, CACA will add some new random immigrant antibodies with a certain ratio. The convergence of CACA is theoretically proved. The experiments of CACA compared with the clone selection algorithm (ACAMHC) on some benchmark functions are carried out. The experimental results indicate that the performance of CACA is better than that of ACAMHC. The CACA algorithm provides new opportunities for solving previously intractable optimization problems.

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