scholarly journals An improved predator-prey particle swarm optimization algorithm for Nash equilibrium solution

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0260231
Author(s):  
Yufeng Meng ◽  
Jianhua He ◽  
Shichu Luo ◽  
Siqi Tao ◽  
Jiancheng Xu
Keyword(s):  
Particle Swarm Optimization ◽  
Nash Equilibrium ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Global Optimal Solution ◽  
Swarm Optimization ◽  
Predator Prey ◽  
Global Optimal ◽  
Zero Sum

Focusing on the problem incurred during particle swarm optimization (PSO) that tends to fall into local optimization when solving Nash equilibrium solutions of games, as well as the problem of slow convergence when solving higher order game pay off matrices, this paper proposes an improved Predator-Prey particle swarm optimization (IPP-PSO) algorithm based on a Predator-Prey particle swarm optimization (PP-PSO) algorithm. First, the convergence of the algorithm is advanced by improving the distribution of the initial predator and prey. By improving the inertia weight of both predator and prey, the problem of “precocity” of the algorithm is improved. By improving the formula used to represent particle velocity, the problems of local optimizations and slowed convergence rates are solved. By increasing pathfinder weight, the diversity of the population is increased, and the global search ability of the algorithm is improved. Then, by solving the Nash equilibrium solution of both a zero-sum game and a non-zero-sum game, the convergence speed and global optimal performance of the original PSO, the PP-PSO and the IPP-PSO are compared. Simulation results demonstrated that the improved Predator-Prey algorithm is convergent and effective. The convergence speed of the IPP-PSO is significantly higher than that of the other two algorithms. In the simulation, the PSO does not converge to the global optimal solution, and PP-PSO approximately converges to the global optimal solution after about 40 iterations, while IPP-PSO approximately converges to the global optimal solution after about 20 iterations. Furthermore, the IPP-PSO is superior to the other two algorithms in terms of global optimization and accuracy.

scholarly journals A general framework of particle swarm optimization

2021 ◽  
Author(s):  
Loc Nguyen
Keyword(s):  
Particle Swarm Optimization ◽  
General Framework ◽  
Optimization Problem ◽  
Particle Swarm ◽  
Target Function ◽  
Optimal Solution ◽  
Exploration And Exploitation ◽  
Global Optimal Solution ◽  
Swarm Optimization ◽  
Global Optimal

Particle swarm optimization (PSO) is an effective algorithm to solve the optimization problem in case that derivative of target function is inexistent or difficult to be determined. Because PSO has many parameters and variants, I propose a general framework of PSO called GPSO which aggregates important parameters and generalizes important variants so that researchers can customize PSO easily. Moreover, two main properties of PSO are exploration and exploitation. The exploration property aims to avoid premature converging so as to reach global optimal solution whereas the exploitation property aims to motivate PSO to converge as fast as possible. These two aspects are equally important. Therefore, GPSO also aims to balance the exploration and the exploitation. It is expected that GPSO supports users to tune parameters for not only solving premature problem but also fast convergence.

scholarly journals Service Composition in IoT using Genetic algorithm and Particle swarm optimization

2020 ◽  
Vol 10 (1) ◽  
pp. 56-64 ◽  
Author(s):  
Neeti Kashyap ◽  
A. Charan Kumari ◽  
Rita Chhikara
Keyword(s):  
Genetic Algorithm ◽  
Quality Of Service ◽  
Particle Swarm Optimization ◽  
Service Composition ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Critical Issue ◽  
Swarm Optimization

AbstractWeb service compositions are commendable in structuring innovative applications for different Internet-based business solutions. The existing services can be reused by the other applications via the web. Due to the availability of services that can serve similar functionality, suitable Service Composition (SC) is required. There is a set of candidates for each service in SC from which a suitable candidate service is picked based on certain criteria. Quality of service (QoS) is one of the criteria to select the appropriate service. A standout amongst the most important functionality presented by services in the Internet of Things (IoT) based system is the dynamic composability. In this paper, two of the metaheuristic algorithms namely Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) are utilized to tackle QoS based service composition issues. QoS has turned into a critical issue in the management of web services because of the immense number of services that furnish similar functionality yet with various characteristics. Quality of service in service composition comprises of different non-functional factors, for example, service cost, execution time, availability, throughput, and reliability. Choosing appropriate SC for IoT based applications in order to optimize the QoS parameters with the fulfillment of user’s necessities has turned into a critical issue that is addressed in this paper. To obtain results via simulation, the PSO algorithm is used to solve the SC problem in IoT. This is further assessed and contrasted with GA. Experimental results demonstrate that GA can enhance the proficiency of solutions for SC problem in IoT. It can also help in identifying the optimal solution and also shows preferable outcomes over PSO.

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 Enhanced Partial Search to Particle Swarm Optimization for Unconstrained Optimization

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 357 ◽  
Author(s):  
Shu-Kai S. Fan ◽  
Chih-Hung Jen
Keyword(s):  
Particle Swarm Optimization ◽  
Unconstrained Optimization ◽  
Optimization Technique ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Particle Swarm Optimizer ◽  
Swarm Optimization ◽  
Searching Strategy ◽  
Wide Range

Particle swarm optimization (PSO) is a population-based optimization technique that has been applied extensively to a wide range of engineering problems. This paper proposes a variation of the original PSO algorithm for unconstrained optimization, dubbed the enhanced partial search particle swarm optimizer (EPS-PSO), using the idea of cooperative multiple swarms in an attempt to improve the convergence and efficiency of the original PSO algorithm. The cooperative searching strategy is particularly devised to prevent the particles from being trapped into the local optimal solutions and tries to locate the global optimal solution efficiently. The effectiveness of the proposed algorithm is verified through the simulation study where the EPS-PSO algorithm is compared to a variety of exiting “cooperative” PSO algorithms in terms of noted benchmark functions.

scholarly journals Improved Adaptive Holonic Particle Swarm Optimization

2019 ◽  
Vol 2019 ◽  
pp. 1-22 ◽  
Author(s):  
Hao Li ◽  
Hongbin Jin ◽  
Hanzhong Wang ◽  
Yanyan Ma
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Standard Test ◽  
Local Optimum ◽  
Swarm Optimization ◽  
State Switching ◽  
Grouping Strategy ◽  
Number Of Iterations

For the first time , the Holonic Particle Swarm Optimization (HPSO ) algorithm applies multiagent theory about the improvement in the PSO algorithm and achieved good results. In order to further improve the performance of the algorithm, this paper proposes an improved Adaptive Holonic Particle Swarm Optimization (AHPSO) algorithm. Firstly, a brief review of the HPSO algorithm is carried out, and the HPSO algorithm can be further studied in three aspects: grouping strategy, iteration number setting, and state switching discrimination. The HPSO algorithm uses an approximately uniform grouping strategy that is the simplest but does not consider the connections between particles. And if the particles with larger or smaller differences are grouped together in different search stages, the search efficiency will be improved. Therefore, this paper proposes a grouping strategy based on information entropy and system clustering and combines two grouping strategies with corresponding search methods. The performance of the HPSO algorithm depends on the setting of the number of iterations. If it is too small, it is difficult to search for the optimal and it wastes so many computing resources. Therefore, this paper constructs an adaptive termination condition that causes the particles to terminate spontaneously after convergence. The HPSO algorithm only performs a conversion from extensive search to exact search and still has the potential to fall into local optimum. This paper proposes a state switching condition to improve the probability that the algorithm jumps out of the local optimum. Finally, AHPSO and HPSO are compared by using 22 groups of standard test functions. AHPSO is faster in convergence than HPSO, and the number of iterations of AHPSO convergence is employed in HPSO. At this point, there exists a large gap between HPSO and the optimal solution, i.e., AHPSO can have better algorithm efficiency without setting the number of iterations.

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.

scholarly journals Particle Swarm Optimization

2017 ◽  
pp. 614-635 ◽  
Author(s):  
Alaa Tharwat ◽  
Tarek Gaber ◽  
Aboul Ella Hassanien ◽  
Basem E. Elnaghi
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Algorithms ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Parameter Tuning ◽  
Pso Algorithm ◽  
Search Space ◽  
Learning Problems ◽  
Swarm Optimization ◽  
Numerical Example

Optimization algorithms are necessary to solve many problems such as parameter tuning. Particle Swarm Optimization (PSO) is one of these optimization algorithms. The aim of PSO is to search for the optimal solution in the search space. This paper highlights the basic background needed to understand and implement the PSO algorithm. This paper starts with basic definitions of the PSO algorithm and how the particles are moved in the search space to find the optimal or near optimal solution. Moreover, a numerical example is illustrated to show how the particles are moved in a convex optimization problem. Another numerical example is illustrated to show how the PSO trapped in a local minima problem. Two experiments are conducted to show how the PSO searches for the optimal parameters in one-dimensional and two-dimensional spaces to solve machine learning problems.

scholarly journals Algoritme Particle Swarm Optimization (PSO) untuk Optimasi Perencanaan Produksi Agregat Multi-Site pada Industri Tekstil Rumahan

2021 ◽  
Vol 1 (2) ◽  
Author(s):  
Agung Mustika Rizki ◽  
Afina Lina Nurlaili
Keyword(s):  
Particle Swarm Optimization ◽  
Production Planning ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Efficient Solutions ◽  
Production Costs ◽  
Aggregate Production Planning ◽  
Swarm Optimization ◽  
Aggregate Production

In the industrial world, companies need to manage their production areas well. One way is to implement aggregate production planning. The goal is that the production costs incurred by the company can be controlled properly. However, production planning cannot be formulated quickly. The problem is more complicated if the company has several production locations. The difference in location also affects the production references and standards applied in each location. Based on these problems, the authors propose to apply the Particle Swarm Optimization (PSO) algorithm to solve the problem of aggregate production planning in order to obtain the optimal solution for each production location. As a result, the algorithm proposed by the author can produce optimal and efficient solutions for 6 production sites. This is evidenced by the relatively short time required compared to the previous planning by the company.

scholarly journals An Intelligent Algorithm for Solving the Efficient Nash Equilibrium of a Single-Leader Multi-Follower Game

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 454
Author(s):  
Lu-Ping Liu ◽  
Wen-Sheng Jia
Keyword(s):  
Particle Swarm Optimization ◽  
Nash Equilibrium ◽  
Particle Swarm ◽  
Pso Algorithm ◽  
Immune Memory ◽  
Intelligent Algorithm ◽  
Mathematical Economics ◽  
Swarm Optimization ◽  
Memory Mechanism ◽  
Ipso Algorithm

This aim of this paper is to provide the immune particle swarm optimization (IPSO) algorithm for solving the single-leader–multi-follower game (SLMFG). Through cooperating with the particle swarm optimization (PSO) algorithm and an immune memory mechanism, the IPSO algorithm is designed. Furthermore, we define the efficient Nash equilibrium from the perspective of mathematical economics, which maximizes social welfare and further refines the number of Nash equilibria. In the end, numerical experiments show that the IPSO algorithm has fast convergence speed and high effectiveness.

scholarly journals Improving the Quality of Routing Service using Metaheuristic PSO algorithm in VANET Networks

2021 ◽  
Author(s):  
Amir Javadpour ◽  
Samira Rezaei ◽  
Arun Kumar Sangaiah ◽  
Adam Slowik ◽  
Shadi Mahmoodi Khaniabadi
Keyword(s):  
Particle Swarm Optimization ◽  
Information Quality ◽  
Vehicular Ad Hoc Networks ◽  
Ad Hoc ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Pso Algorithm ◽  
Swarm Optimization ◽  
Comparison Results

Abstract VANETs are organized to progress road protection with no specific need for any fixed infrastructure. Subsequently, the movement of all vehicles can be planned in the upcoming future, based on perceived information, Quality of Services Routing (QoSR) algorithms can be pressured on its available options, paths, and links and according to criteria and reliability of the QoSR. Awareness of QoSR to the environmental conditions of the network of vehicles, such as the location of vehicles, direction and speed that can be obtained. This study is to reduce the effects of unpredictable problems on the best pathway to replace the broken path / link. In this article, A QoSR with Particle Swarm Optimization (QoSR-PSO) for improving QoSs in vehicular ad-hoc networks has been used. The particle swarm optimization algorithm by modeling the behavior of a set of particles looks for the optimal solution of the problem. In order to perform simulation experiments, NS2 simulator and VanetMobisim have been used. The comparison results with benchmark studies show the improvement in packet delivery rate (PDR), delay, Packet Drop and overload.

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