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.

Transient Performance of the Particle Swarm Optimization Algorithm From System Dynamics Point of View

2020 ◽  
Vol 20 (4) ◽  
Author(s):  
Haopeng Zhang
Keyword(s):  
Particle Swarm Optimization ◽  
System Dynamics ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Continuous Model ◽  
Second Order ◽  
Point Of View ◽  
Swarm Optimization ◽  
Sampling Ratio ◽  
Second Order Systems

Abstract In this paper, the performance of the particle swarm optimization(PSO) algorithm is studied from the system dynamics point of view. The dynamics of the particles in PSO algorithm are considered as second-order systems. Depending on the selections of the parameters, the second-order systems have over-damped, critically damped, underdamped, or undamped responses. Different responses give the algorithm different types of performance. Therefore, in this paper, we derive the conditions for parameters in the PSO algorithm such that the particles have different responses. The exploration and exploitation of PSO are discussed numerically. Moreover, due to the fact that the discrete model of PSO is converted from a continuous model by certain sampling ratio, the sampling ratio variable is introduced to the PSO algorithm. With different sampling ratios, the stability region of the PSO algorithm is increased and the performance of the algorithm is changed. Numerical examples are provided to demonstrate the performance of the PSO algorithm with different selections of the parameters.

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.

Fixed final time and free final state optimal control problem for fractional dynamic systems – linear quadratic discrete-time case

2013 ◽  
Vol 61 (3) ◽  
pp. 681-690 ◽  
Author(s):  
A. Dzieliński ◽  
P.M. Czyronis
Keyword(s):  
Discrete Time ◽  
Optimization Problems ◽  
Linear Quadratic ◽  
Final Time ◽  
Final State ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Quadratic Performance ◽  
Discrete Time Case ◽  
Time Systems

Abstract The optimization problem for fractional discrete-time systems with a quadratic performance index has been formulated and solved. The case of fixed final time and a free final state has been considered. A method for numerical computation of optimization problems has been presented. The presented method is a generalization of the well-known method for discrete-time systems of integer order. The efficiency of the method has been demonstrated on numerical examples and illustrated by graphs. Graphs also show the differences between the fractional and classical (standard) systems theory. Results for other cases of the fractional system order (coefficient ) and not illustrated with numerical examples have been obtained through a computer algorithm written for this purpose.

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