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.

Runtime analysis of discrete particle swarm optimization algorithms: A survey

2019 ◽  
Vol 61 (4) ◽  
pp. 177-185
Author(s):  
Moritz Mühlenthaler ◽  
Alexander Raß
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Upper And Lower Bounds ◽  
Swarm Optimization ◽  
Randomized Search Heuristics ◽  
Recent Developments ◽  
Randomized Search

Abstract A discrete particle swarm optimization (PSO) algorithm is a randomized search heuristic for discrete optimization problems. A fundamental question about randomized search heuristics is how long it takes, in expectation, until an optimal solution is found. We give an overview of recent developments related to this question for discrete PSO algorithms. In particular, we give a comparison of known upper and lower bounds of expected runtimes and briefly discuss the techniques used to obtain these bounds.

scholarly journals An Adaptive Hybrid Algorithm Based on Particle Swarm Optimization and Differential Evolution for Global Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaobing Yu ◽  
Jie Cao ◽  
Haiyan Shan ◽  
Li Zhu ◽  
Jun Guo
Keyword(s):  
Particle Swarm Optimization ◽  
Differential Evolution ◽  
Hybrid Algorithm ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Population Based ◽  
Stochastic Search ◽  
Adaptive Mutation ◽  
Swarm Optimization ◽  
Local Optima

Particle swarm optimization (PSO) and differential evolution (DE) are both efficient and powerful population-based stochastic search techniques for solving optimization problems, which have been widely applied in many scientific and engineering fields. Unfortunately, both of them can easily fly into local optima and lack the ability of jumping out of local optima. A novel adaptive hybrid algorithm based on PSO and DE (HPSO-DE) is formulated by developing a balanced parameter between PSO and DE. Adaptive mutation is carried out on current population when the population clusters around local optima. The HPSO-DE enjoys the advantages of PSO and DE and maintains diversity of the population. Compared with PSO, DE, and their variants, the performance of HPSO-DE is competitive. The balanced parameter sensitivity is discussed in detail.

Application of Quantum-Behaved Particle Swarm Optimization in Engineering Constrained Optimization Problems

2011 ◽  
Vol 383-390 ◽  
pp. 7208-7213
Author(s):  
De Kun Tan
Keyword(s):  
Particle Swarm Optimization ◽  
Constrained Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Swarm Optimization ◽  
Local Optima ◽  
Standard Particle Swarm Optimization ◽  
Fixed Path

To overcome the shortage of standard Particle Swarm Optimization(SPSO) on premature convergence, Quantum-behaved Particle Swarm Optimization (QPSO) is presented to solve engineering constrained optimization problem. QPSO algorithm is a novel PSO algorithm model in terms of quantum mechanics. The model is based on Delta potential, and we think the particle has the behavior of quanta. Because the particle doesn’t have a certain trajectory, it has more randomicity than the particle which has fixed path in PSO, thus the QPSO more easily escapes from local optima, and has more capability to seek the global optimal solution. In the period of iterative optimization, outside point method is used to deal with those particles that violate the constraints. Furthermore, compared with other intelligent algorithms, the QPSO is verified by two instances of engineering constrained optimization, experimental results indicate that the algorithm performs better in terms of accuracy and robustness.

Particle Swarm Optimization by Improved Chaos Immune Genetic Algorithm

2014 ◽  
Vol 989-994 ◽  
pp. 2621-2624
Author(s):  
Shao Song Wan ◽  
Jian Cao ◽  
Qun Song Zhu
Keyword(s):  
Genetic Algorithm ◽  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Single Chip ◽  
Immune Genetic Algorithm ◽  
Swarm Optimization ◽  
Local Optima ◽  
Chaos Sequence ◽  
Multimodal Problems

In order to resolve these problems, we put forward a new design of the intelligent lock which is mainly based on the technology of wireless sensor network. Particle swarm optimization (PSO) is a recently proposed intelligent algorithm which is motivated by swarm intelligence. PSO has been shown to perform well on many benchmark and real-world optimization problems; it easily falls into local optima when solving complex multimodal problems. To avoid the local optimization, the algorithm renews population and enhances the diversity of population by using density calculation of immune theory and adjusting new chaos sequence. The paper gives the circuit diagram of the hardware components based on single chip and describe how to design the software. The experimental results show that the immune genetic algorithm based on chaos theory can search the result of the optimization and evidently improve the convergent speed and astringency.

scholarly journals Multi-objective particle swarm optimization with R2 indicator and adaptive method

2021 ◽  
Author(s):  
Qinghua Gu ◽  
Mengke Jiang ◽  
Song Jiang ◽  
Lu Chen
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Empirical Studies ◽  
Experimental Studies ◽  
Particle Swarm ◽  
Adaptive Method ◽  
Swarm Optimization ◽  
Local Optima ◽  
Multi Objective ◽  
Problem Instances

AbstractMulti-objective particle swarm optimization algorithms encounter significant challenges when tackling many-objective optimization problems. This is mainly because of the imbalance between convergence and diversity that occurs when increasing the selection pressure. In this paper, a novel adaptive MOPSO (ANMPSO) algorithm based on R2 contribution and adaptive method is developed to improve the performance of MOPSO. First, a new global best solutions selection mechanism with R2 contribution is introduced to select leaders with better diversity and convergence. Second, to obtain a uniform distribution of particles, an adaptive method is used to guide the flight of particles. Third, a re-initialization strategy is proposed to prevent particles from trapping into local optima. Empirical studies on a large number (64 in total) of problem instances have demonstrated that ANMPSO performs well in terms of inverted generational distance and hyper-volume metrics. Experimental studies on the practical application have also revealed that ANMPSO could effectively solve problems in the real world.

A Hybrid Particle Swarm Optimization Algorithm for Dynamic Environments

2014 ◽  
Vol 926-930 ◽  
pp. 3338-3341
Author(s):  
Hong Mei Ni ◽  
Zhian Yi ◽  
Jin Yue Liu
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Optimization Technique ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Swarm Optimization ◽  
Local Optima ◽  
Hybrid Particle Swarm Optimization ◽  
Moving Peaks Benchmark ◽  
Chaos Algorithm

Chaos is a non-linear phenomenon that widely exists in the nature. Due to the ease of implementation and its special ability to avoid being trapped in local optima, chaos has been a novel optimization technique and chaos-based searching algorithms have aroused intense interests. Many real world optimization problems are dynamic in which global optimum and local optima change over time. Particle swarm optimization has performed well to find and track optima in static environments. When the particle swarm optimization (PSO) algorithm is used in dynamic multi-objective problems, there exist some problems, such as easily falling into prematurely, having slow convergence rate and so on. To solve above problems, a hybrid PSO algorithm based on chaos algorithm is brought forward. The hybrid PSO algorithm not only has the efficient parallelism but also increases the diversity of population because of the chaos algorithm. The simulation result shows that the new algorithm is prior to traditional PSO algorithm, having stronger adaptability and convergence, solving better the question on moving peaks benchmark.

A Modified Particle Swarm Optimization Algorithm Based on Proportional Distribution of Particles

2011 ◽  
Vol 181-182 ◽  
pp. 937-942
Author(s):  
Bo Liu ◽  
Hong Xia Pan
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Global Optimum ◽  
The Self ◽  
Swarm Optimization ◽  
Local Optima ◽  
Modified Particle Swarm Optimization ◽  
Complex Optimization ◽  
Proportional Distribution

Particle swarm optimization (PSO) is widely used to solve complex optimization problems. However, classical PSO may be trapped in local optima and fails to converge to global optimum. In this paper, the concept of the self particles and the random particles is introduced into classical PSO to keep the particle diversity. All particles are divided into the standard particles, the self particles and the random particles according to special proportion. The feature of the proposed algorithm is analyzed and several testing functions are performed in simulation study. Experimental results show that, the proposed PDPSO algorithm can escape from local minima and significantly enhance the convergence precision.

scholarly journals Design of Two-Dimensional Recursive Digital Filter Using Multi Particle Swarm Optimization Algorithm

2020 ◽  
Vol 53 (4) ◽  
pp. 559-566
Author(s):  
Lakhdar Kaddouri ◽  
Amel B.H. Adamou-Mitiche ◽  
Lahcene Mitiche
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Search Space ◽  
Fast Convergence ◽  
Infinite Impulse Response ◽  
Two Dimensional ◽  
Swarm Optimization ◽  
Local Optima

Particle Swarm Optimization (PSO) is an evolutionary algorithm widely used in optimization problems. It is characterized by a fast convergence, which can lead the algorithm to stagnate in local optima. In the present paper, a new Multi-PSO algorithm for the design of two-dimensional infinite impulse response (IIR) filters is built. It is based on the standard PSO and uses a new initialization strategy. This strategy is relayed to two types of swarms: a principal and auxiliaries. To improve the performance of the algorithm, the search space is divided into several areas, which allows a best covering and leading to a better exploration in each zone separately. This solved the problem of fast convergence in standard PSO. The results obtained demonstrate the effectiveness of the Multi-PSO algorithm in the filter coefficients optimization.

scholarly journals Optimal value of Economic Load Dispatch using Swarm Algorithm

2021 ◽  
Vol 2070 (1) ◽  
pp. 012136
Author(s):  
B Sravan Kumar ◽  
ShaikHussain Vali ◽  
Vempalle Rafi ◽  
G Nageswara Reddy
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Population Based ◽  
Swarm Optimization ◽  
Local Optima ◽  
Space Reduction ◽  
Optimal Value ◽  
The Cost ◽  
Performance Results

Abstract In this paper space reduction particle swarm optimization(SRPSO) is proposed for solving single-objective optimization problems. Minimization of cost is considered as an objective in the economic dispatch problem. The valve point loading effect is incorporated with the cost function which transfigures to the nonlinear problem. To improve the convergence speed, space reduction is essential and parameter variation keeps away the struck of local optima. Particle swarm optimization (PSO) emphasizes global search and is encountered as a stochastic population-based method. The proposed method is validated on a 26 bus system with 6 generators and the performance results are compared with the other existing techniques.

scholarly journals Fusion Global-Local-Topology Particle Swarm Optimization for Global Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Zahra Beheshti ◽  
Siti Mariyam Shamsuddin ◽  
Sarina Sulaiman
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Convergence Speed ◽  
Swarm Optimization ◽  
Local Optima ◽  
Solution Accuracy ◽  
Global And Local ◽  
Local Topology

In recent years, particle swarm optimization (PSO) has been extensively applied in various optimization problems because of its structural and implementation simplicity. However, the PSO can sometimes find local optima or exhibit slow convergence speed when solving complex multimodal problems. To address these issues, an improved PSO scheme called fusion global-local-topology particle swarm optimization (FGLT-PSO) is proposed in this study. The algorithm employs both global and local topologies in PSO to jump out of the local optima. FGLT-PSO is evaluated using twenty (20) unimodal and multimodal nonlinear benchmark functions and its performance is compared with several well-known PSO algorithms. The experimental results showed that the proposed method improves the performance of PSO algorithm in terms of solution accuracy and convergence speed.

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