Particle Swarm Optimisation (PSO)

A discrete particle swarm optimisation algorithm is designed in order to solve this optimisation problem and compute an alignment of two ontologies. A num- ber of characteristics of traditional PSO algorithms are partially relaxed in this article, such as fixed dimensionality of particles. A complex fitness function based on similarity measures of ontological entities, as well as a tailored par- ticle update procedure are presented. This approach brings several benefits for solving the ontology alignment problem, such as inherent parallelisation, anytime behaviour, and flexibility according to the characteristics of particu- lar ontologies. The presented algorithm has been implemented under the name MapPSO (Ontology Mapping using Particle Swarm Optimisation). Experi- ments demonstrate that applying PSO in the context of ontology alignment is a feasible approach.

Abstract Classification problems often have a large number of features, but not all of them are useful for classification. Irrelevant and redundant features may even reduce the classification accuracy. Feature selection is a process of selecting a subset of relevant features, which can decrease the dimen- sionality, shorten the running time, and/or improve the classification ac- curacy. There are two types of feature selection approaches, i.e. wrapper and filter approaches. Their main difference is that wrappers use a clas- sification algorithm to evaluate the goodness of the features during the feature selection process while filters are independent of any classification algorithm. Feature selection is a difficult task because of feature interac- tions and the large search space. Existing feature selection methods suf- fer from different problems, such as stagnation in local optima and high computational cost. Evolutionary computation (EC) techniques are well- known global search algorithms. Particle swarm optimisation (PSO) is an EC technique that is computationally less expensive and can converge faster than other methods. PSO has been successfully applied to many areas, but its potential for feature selection has not been fully investigated.

Keywords: Particle swarm optimisation, improved learning strategy, global optimisation, metaheuristic search, swarm intelligence 1. INTRODUCTION Inspired by the collective and collaborative behaviours of bird flocking and fish schooling in searching for food sources, 1,2 Kennedy and Eberhart 1 proposed a new population-based metaheuristic search (MS) algorithm called particle swarm optimisation (PSO) in 1995. From the optimisation perspective, each individual member (i.e., particle) of the PSO swarm represents a potential solution to a given problem, whereas the location of the food source denotes the global optimum solution. Each particle moves stochastically to locate the food source during the search process. In addition, all the population members of the PSO swarm collaborate with each other through information sharing. This interaction enables all the particles to gradually move towards the food sources and eventually leads to the swarm convergence. 2 Since the inception of PSO, this algorithm has been applied to address various real-world problems due to its simplicity. 3,4

2 School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China * Correspondence: fengbaiwei@126.com (B.-W.F.); wtulzy@whut.edu.cn (Z.-Y.L.) Abstract: The particle swarm optimisation (PSO) algorithm has been widely used in hull form optimisation owing to its feasibility and fast convergence. However, similar to other intelligent algorithms, PSO also has the disadvantages of local premature convergence and low convergence performance. Moreover, optimization data are not used to analyse and reduce the range of values for relevant design variables. Our study aimed to solve these existing problems in the PSO algorithm and improve PSO from four aspects, namely data processing of particle swarm population initialisation, data processing of iterative optimisation, particle velocity adjustment, and particle cross-boundary configuration, in combination with space reduction technology. The improved PSO algorithm was used to optimise the hull form of an engineering vessel at Fn = 0.24 to reduce the wave-making resistance coefficient under static constraints. The results showed that the improved PSO algorithm could effectively improve the optimisation efficiency and reliability of PSO and effectively overcome the drawbacks of the PSO algorithm.

Solving real life optimisation problems is a challenging engineering ven- ture. Since the early days of research on optimisation it was realised that many problems do not simply have one optimisation objective. This led to the development of multi-objective optimizers that try to look at the optimisation problem from different points of view and reach a set of com- promised solutions among the different objectives. The presented research brings together recent advances in the field of multi-objective optimisation and particle swarm optimisation raising several challenges. This is tackled from different aspects including the proposal of new archiving techniques to developing new methods and quality measures. Smart Multi-objective Particle Swarm Optimisation based on Decomposition (SDMOPSO) is first proposed to incorporate multi-objective problem decomposition techniques with PSO. A novel archiving technique is developed using a clustering based mapping approach between the objective and solution spaces and is applied to general multi-objective optimizers. D 2 M OP SO is introduced as a new MOPSO that uses problem decomposition and a new archive utilising dom- inance based mapping between objective and solution spaces. Finally the thesis presents a novel multi-objective quality measure that uses mutual information to compare among solutions generated by different algorithms.

5.6 Summary In this chapter, a novel local thresholding technique was proposed for a particle swarm optimisation (PSO)-based algorithm to detect edges with greater continuity. The new technique was based on the Sauvola-Pietkinen method which is often used for binarising the illuminated document im- ages but normally cannot be applied to edge magnitude images. This method was equipped by an integral imaging technique for more effi- ciency and adopted into the PSO-based algorithm to detect edges in grey level illuminated noisy images. We compared the performance of the new algorithm with our previous PSO-based edge detector utilising Otsu’s method which is commonly used as a thresholding technique in edge de- tection. Experimental results showed that the PSO-based algorithm utilis- ing the new local thresholding technique performs better than the one that uses Otsu’s method.

* E-mail: athivimal@gmail.com AbStrACt Particle swarm optimisation (PSO) based cryptanalysis has gained much attention due to its fast convergence rate. This paper proposes a PSO-based cryptanalysis scheme for breaking the key employed in simplified-advance encryption standard (S-AES). The cost function is derived using letter frequency analysis. The novelty in our approach is to apply ciphertext-only attack for an S-AES encryption system, where we obtained the key in a minimum search space compared to the Brute-Force attack. Experimental results prove that PSO can be used as an effective tool to attack the key used in S-AES.

SASTRA University, Thanjavur Tamilnadu-613402 ABSTRACT This article presents a novelimplementation of Particle Swarm Optimisation(PSO)forfinding the most optimal solution to path planning problem for a swarm of robots. The swarm canvasses through the configuration space having static obstaclesby applying PSO on potential fields generated by the target. The best possible path by the momentary leaders of the group is retraced toget the solution. The designed algorithm was simulated on a specially developed simulator adhering to real time constraints and conditions faced by the mobile robots. The solutions for various configuration spaces are presented to verify the effectiveness of the algorithm.

This issue involves many relevant features, such as material condition, process operation, part and process design, working environment, and so on. While existing studies reveal that AM energy consumption modelling largely depends on the design-relevant features in practice, it has not been given sufficient attention. Therefore, in this study, design-relevant features are firstly examined with respect to energy modelling. These features are typically determined by part designers and process operators before production. The AM energy consumption knowledge, hidden in the design-relevant features, is exploited for prediction modelling through a design-relevant data analytics approach. Based on the new modelling approach, a novel deep learning-driven particle swarm optimisation (DLD-PSO) method is proposed to optimise the energy utility. Deep learning is introduced to address several issues, in terms of increasing the search speed and enhancing the global best of PSO. Finally, using the design-relevant data collected from a real-world AM system in production, a case study is presented to validate the proposed modelling approach, and the results reveal its merits. Meanwhile, optimisation has also been carried out to guide part designers and process operators to revise their designs and decisions in order to reduce the energy consumption of the designated AM system under study.

The particle swarm optimisation (PSO) is a population-based stochastic optimisation technique (Kennedy and Eberhart, 1995, 2001) inspired by social behaviour of bird flocking or fish schooling. The algorithm starts with a random initialisation of a swarm of individuals, referred to as particles, within the problem search space. It then endeavours to find a global optimal solution by simply adjusting the trajectory of each individual toward its own best location visited so far and toward the best position of the entire swarm at each evolutionary optimisation step. The attractions of the PSO method include its simplicity in implementation, ability to quickly converge to a reasonably good solution and its robustness against local minima. The PSO technique has been applied to wide-ranging practical optimisation problems successfully (Kennedy and Eberhart, 2001; Ratnaweera et al., 2004; Guru et al., 2005; Sun et al., 2006, 2008; Feng, 2006; El-Metwally et al., 2006; Soo et al., 2007; Awadallah and Soliman, 2008; Guerra and Coelho, 2008; Leong and Yen, 2008; Soliman et al., 2008;

So it is replaced by a new method known as Particle Swarm Optimisation (PSO) which is a biological method based on particle swarming. It consists of a group of particles moving towards optimal solution. Feasible solutions are obtained as particles move in feasible solution space rather than infeasible ones. Thus the method reduces computational time. In this paper PSO is applied to IEEE 30 bus test system with six generators so that fuel cost of each generator is reduced using PSO

3.2 PARTICLE SWARM OPTIMISATION: PSO simulates the behaviors of bird flocking. Suppose the following scenario: a group of birds are randomly searching food in an area. There is only one piece of food in the area being searched. All the birds do not know where the food is. But they know how far the food is in each iteration. So what's the best strategy to find the food? The effective one is to follow the bird, which is nearest to the food. PSO learned from the scenario and used it to solve the optimization problems. In PSO, each single solution is a "bird" in the search space. We call it "particle". All of particles have fitness values, which are evaluated by the fitness function to be optimized, and have velocities, which direct the flying of the particles. The particles fly through the problem space by following the current optimum particles.

Divya Ananthan 1 , Prof.S.Nishanthinivalli 2 1 (P.G Student, Jayaram college of Engineering & Technology, Tiruchirapalli) 2 (Assistant Professor, Department of EEE, Jayaram College of Engineering and Technology, Tiruchirapalli) Abstract: - Existing unit commitment methods have the problem of stopping at local optimum and slow convergence. So it is replaced by a new method known as Particle Swarm Optimisation (PSO) which is a biological method based on particle swarming. It consists of a group of particles moving towards optimal solution. Feasible solutions are obtained as particles move in feasible solution space rather than infeasible ones.

2.2 Particle Swarm Optimisation PSO is a population-based search method proposed by Kennedy and Eberhart (1995). The main motivation came from the behaviour of group organisms such as bee swarm, fish school, and bird flock. PSO imitates the physical movements of the individuals in the swarm as well as its cognitive and social behaviour as a searching method. In PSO, a problem solution is represented by the position value of a multi-dimensional particle. Particle’s velocity represents particle searching ability. The basic version of PSO algorithm starts by initialising the population of particles, which is usually called a swarm, with random position and velocity. In each iteration step, every particle moves to a new position following its velocity; and its velocity is updated based on its personal and global best position. Personal best position of a particle, which expresses the cognitive behaviour of a particle, is defined as the best position found by the particle. It will be updated whenever the particle reaches a position with better fitness value than the fitness value of the previous local best. Global best position, which expresses the social behaviour, is defined as the best position found by the whole swarm. It will be updated whenever a particle reaches a position with better fitness value than the fitness value of the previous global best. Comprehensive details of the PSO mechanism, technique, and applications are provided by Kennedy and Eberhart (2001) and also Clerc (2006).

This paper develops a particle swarm optimisation (PSO) based framework for multi-objective optimisation (MOO). As a part of development, a new PSO method, named self-adaptive PSO (SAPSO), is first proposed. Since the convergence of SAPSO determines the quality of the obtained Pareto front, this paper analytically investigates the convergence of SAPSO and provides a parameter selection principle that guarantees the convergence. Leveraging the proposed SAPSO, this paper then designs a SAPSO-based MOO framework, named SAMOPSO. To gain a well- distributed Pareto front, we also design an external repository that keeps the non-dominated solutions. Next, a circular sorting method, which is integrated with the elitist-preserving approach, is designed to update the external repository in the developed MOO framework. The performance of the SAMOPSO framework is validated through 12 benchmark test functions and a real-word MOO problem. For rigorous validation, the performance of the proposed framework is compared with those of four well-known MOO algorithms. The simulation results confirm that the proposed SAMOPSO outperforms its contenders with respect to the quality of the Pareto front over the majority of the studied cases. The non-parametric comparison results reveal that the proposed method is significantly better than the four algorithms compared at the confidence level of 90% over the 12 test functions.

Exeter, UK J.E.Fieldsend@exeter.ac.uk ABSTRACT The particle swarm optimisation (PSO) heuristic has been used for a number of years now to perform multi-objective optimisation, however its performance on many-objective op- timisation (problems with four or more competing objec- tives) has been less well examined. Many-objective opti- misation is well-known to cause problems for Pareto-based evolutionary optimisers, so it is of interest to see how well PSO copes in this domain, and how non-Pareto quality mea- sures perform when integrated into PSO. Here we compare and contrast the performance of canonical PSO, using a wide range of many-objective quality measures, on a number of different parametrised test functions for up to 20 compet- ing objectives. We examine the use of eight quality mea- sures as selection operators for guides when truncated non- dominated archives of guides are maintained, and as main- tenance operators, for choosing which solutions should be maintained as guides from one generation to the next. We find that the Controlling Dominance Area of Solutions ap- proach performs exceptionally well as a quality measure to determine archive membership for global and local guides.

Chapter 3 MODERN HEURISTIC TECHNIQUE: PARTICLE SWARM OPTIMISATION ALGORITHM The modern heuristic techniques mainly include the application of the Artificial Intelligence (AI) approaches such as Genetic Algorithm (GA), Particle Swarm Optimisation (PSO) al- gorithm, Ant Colony Optimisation (ACO), Stochastic Diffusion Search (SDS), Differential Evolution (DE), etc. [71]. The main aspect of these techniques is their flexibility for solv- ing the optimisation problems that have different mathematical constraints. In a power system area, the competition between the electric utilities is gradually increased due to the deregulation of the electrical markets. For this reason, the generation expansion problem presents itself as an important issue that needs to be considered in order to achieve rea- sonable economic decisions. The applicable plan to address this problem is how to install new generation units that should meet the requirements of the power system such as load demand, power quality, reliability, operating conditions, and security [72]. In that case, while the generation expansion problem can be mathematically formulated such as high dimensional, mix-integer, nonlinear, and optimisation problem with an objective function, so the heuristic techniques have been developed to handle numerous qualitative problems which are common in the electric power field.

Abstract: This article presents an evaluation of Particle Swarm Optimisation (PSO) with variable inertia weight and Free Search (FS) with variable neighbour space applied to non- constrained numerical test. The objectives are to assess how high convergence speed reflects on adaptation to various test problems and to identify possible balance between convergence speed and adaptation, which allows the algorithms to complete successfully the process of search on heterogeneous tasks with limited computational resources within a reasonable finite time and with acceptable for engineering purposes precision. Modification strategies of both algorithms are compared in terms of their ability for search space exploration. Five numerical tests are explored. Achieved experimental results are presented and analysed.

Railway timetabling is an important process in train service provision as it matches the transportation demand with the infrastructure capacity while customer satisfaction is also considered. It is a multi-objective optimisation problem, in which a feasible solution, rather than the optimal one, is usually taken in practice because of the time constraint. The quality of services may suffer as a result. In a railway open market, timetabling usually involves rounds of negotiations among a number of self-interested and independent stakeholders and hence additional objectives and constraints are imposed on the timetabling problem. While the requirements of all stakeholders are taken into consideration simultaneously, the computation demand is inevitably immense. Intelligent solution-searching techniques provide a possible solution. This paper attempts to employ a particle swarm optimisation (PSO) approach to devise a railway timetable in an open market. The suitability and performance of PSO are studied on a multi-agent-based railway open-market negotiation simulation platform.

Railway timetabling is an important process in train service provision as it matches the transportation demand with the infrastructure capacity while customer satisfaction is also considered. It is a multi-objective optimisation problem, in which a feasible solution, rather than the optimal one, is usually taken in practice because of the time constraint. The quality of services may suffer as a result. In a railway open market, timetabling usually involves rounds of negotiations among a number of self-interested and independent stakeholders and hence additional objectives and constraints are imposed on the timetabling problem. While the requirements of all stakeholders are taken into consideration simultaneously, the computation demand is inevitably immense. Intelligent solution-searching techniques provide a possible solution. This paper attempts to employ a particle swarm optimisation (PSO) approach to devise a railway timetable in an open market. The suitability and performance of PSO are studied on a multi-agent-based railway open-market negotiation simulation platform.