scholarly journals Adaptive-Uniform-Experimental-Design-Based Fractional-Order Particle Swarm Optimizer with Non-Linear Time-Varying Evolution

2019 ◽  
Vol 9 (24) ◽  
pp. 5537 ◽  
Author(s):  
Po-Yuan Yang ◽  
Fu-I Chou ◽  
Jinn-Tsong Tsai ◽  
Jyh-Horng Chou
Keyword(s):  
Experimental Design ◽  
Fractional Order ◽  
Optimization Problems ◽  
Linear Time ◽  
Particle Swarm ◽  
Time Varying ◽  
Particle Swarm Optimizer ◽  
Local Optima ◽  
Non Linear ◽  
Velocity Derivative

An adaptive-uniform-experimental-design-based fractional particle swarm optimizer (AUFPSO) with non-linear time-varying evolution (NTE) is proposed. A particle swarm optimizer (PSO) is an excellent evolutionary algorithm due to its simple structure and rapid convergence. Nevertheless, PSO has notable drawbacks. Although many proposed methods and strategies have enhanced its effectiveness and performance, PSO is limited by its tendency to fall into local optima and its tendency to obtain different solutions in each search (i.e., its weak robustness). Introducing fractional-order calculus in PSO (FPSO) can correct the order of the velocity derivative for each particle, which enhances the diversity and algorithmic effectiveness. This study used NTE of the order of the velocity derivative, inertia weight, cognitive parameter, and social parameter in an FPSO used to search for a global optimal solution. To obtain the best combination of FPSO and NTE, an adaptive uniform experimental design (AUED) method was used to deal with this essential issue. The AUED method integrates a uniform layout with the best combination phase and a stepwise ratio to assist in selecting the best combination for FPSO-NTE. Experimental applications in 15 global numerical optimization problems confirmed that the AUFPSO-NTE had a better performance and robustness than existing PSO-related algorithms.

Tracking Multiple Optima in Dynamic Environments by Quantum-Behavior Particle Swarm Using Speciation

2012 ◽  
Vol 3 (1) ◽  
pp. 55-76 ◽  
Author(s):  
Ji Zhao ◽  
Jun Sun ◽  
Vasile Palade
Keyword(s):  
Optimization Problems ◽  
Particle Swarm ◽  
Dynamic Environments ◽  
Multimodal Optimization ◽  
Complex Dynamic ◽  
Particle Swarm Optimizer ◽  
Swarm Optimization ◽  
Local Optima ◽  
Dynamic Function ◽  
Quantum Behavior

This paper presents an improved Quantum-behaved Particle Swarm Optimization, namely the Species-Based QPSO (SQPSO), using the notion of species for solving optimization problems with multiple peaks from the complex dynamic environments. In the proposed SQPSO algorithm, the swarm population is divided into species (subpopulations) based on their similarities. Each species is grouped around a dominating particle called species seed. Over successive iterations, species are able to simultaneously optimize towards multiple optima by using the QPSO procedure, so that each of the peaks can be definitely searched in parallel, regardless of whether they are global or local optima. A number of experiments are performed to test the performance of the SQPSO algorithm. The environment used in the experiments is generated by Dynamic Function # 1(DF1). The experimental results show that the SQPSO is more adaptive than the Species-Based Particle Swarm Optimizer (SPSO) in dealing with multimodal optimization in dynamic environments.

scholarly journals Exact Markov chain-based runtime analysis of a discrete particle swarm optimization algorithm on sorting and OneMax

2021 ◽  
Author(s):  
Moritz Mühlenthaler ◽  
Alexander Raß ◽  
Manuel Schmitt ◽  
Rolf Wanka
Keyword(s):  
Particle Swarm Optimization ◽  
Markov Chain ◽  
Markov Model ◽  
Optimization Problems ◽  
Formal Analysis ◽  
Particle Swarm ◽  
Upper And Lower Bounds ◽  
Swarm Optimization ◽  
Local Optima ◽  
Sorting Problem

AbstractMeta-heuristics are powerful tools for solving optimization problems whose structural properties are unknown or cannot be exploited algorithmically. We propose such a meta-heuristic for a large class of optimization problems over discrete domains based on the particle swarm optimization (PSO) paradigm. We provide a comprehensive formal analysis of the performance of this algorithm on certain “easy” reference problems in a black-box setting, namely the sorting problem and the problem OneMax. In our analysis we use a Markov model of the proposed algorithm to obtain upper and lower bounds on its expected optimization time. Our bounds are essentially tight with respect to the Markov model. We show that for a suitable choice of algorithm parameters the expected optimization time is comparable to that of known algorithms and, furthermore, for other parameter regimes, the algorithm behaves less greedy and more explorative, which can be desirable in practice in order to escape local optima. Our analysis provides a precise insight on the tradeoff between optimization time and exploration. To obtain our results we introduce the notion of indistinguishability of states of a Markov chain and provide bounds on the solution of a recurrence equation with non-constant coefficients by integration.

Improved Particle Swarm Optimizer with Dynamically Adjusted Search Space and Velocity Limits for Global Optimization

2015 ◽  
Vol 24 (05) ◽  
pp. 1550017 ◽  
Author(s):  
Aderemi Oluyinka Adewumi ◽  
Akugbe Martins Arasomwan
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Search Space ◽  
Particle Swarm Optimizer ◽  
Search Range ◽  
Original Algorithm ◽  
Inertia Weight ◽  
And Performance

This paper presents an improved particle swarm optimization (PSO) technique for global optimization. Many variants of the technique have been proposed in literature. However, two major things characterize many of these variants namely, static search space and velocity limits, which bound their flexibilities in obtaining optimal solutions for many optimization problems. Furthermore, the problem of premature convergence persists in many variants despite the introduction of additional parameters such as inertia weight and extra computation ability. This paper proposes an improved PSO algorithm without inertia weight. The proposed algorithm dynamically adjusts the search space and velocity limits for the swarm in each iteration by picking the highest and lowest values among all the dimensions of the particles, calculates their absolute values and then uses the higher of the two values to define a new search range and velocity limits for next iteration. The efficiency and performance of the proposed algorithm was shown using popular benchmark global optimization problems with low and high dimensions. Results obtained demonstrate better convergence speed and precision, stability, robustness with better global search ability when compared with six recent variants of the original algorithm.

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