Enhanced leader PSO (ELPSO): A new PSO variant for solving global optimisation problems

Particle swarm optimisation (PSO) is a well-established optimisation algorithm inspired from flocking behaviour of birds. The big problem in PSO is that it suffers from premature convergence, that is, in complex optimisation problems, it may easily get trapped in local optima. In this paper, a new PSO variant, named as enhanced leader PSO (ELPSO), is proposed for mitigating premature convergence problem. ELPSO is mainly based on a five-staged successive mutation strategy which is applied to swarm leader at each iteration. The experimental results confirm that in all terms of accuracy, scalability and convergence rate, ELPSO performs well.     

Profit optimisation of the multiple-vacation machine repair problem using particle swarm optimisation

This paper investigates a multiple-vacation M/M/1 warm-standby machine repair problem with an unreliable repairman. We first apply a matrix-analytic method to obtain the steady-state probabilities. Next, we construct the total expected profit per unit time and formulate an optimisation problem to find the maximum profit. The particle swarm optimisation (PSO) algorithm is implemented to determine the optimal number of warm standbys S* and the service rate μ* as well as vacation rate ν* simultaneously at the optimal maximum profit. We compare the searching results of the PSO algorithm with those of exhaustive search method to ensure the searching quality of the PSO algorithm. Sensitivity analysis with numerical illustrations is also provided.     

Cultural-based particle swarm for dynamic optimisation problems

Many practical optimisation problems are with the existence of uncertainties, among which a significant number belong to the dynamic optimisation problem (DOP) category in which the fitness function changes through time. In this study, we propose the cultural-based particle swarm optimisation (PSO) to solve DOP problems. A cultural framework is adopted incorporating the required information from the PSO into five sections of the belief space, namely situational, temporal, domain, normative and spatial knowledge. The stored information will be adopted to detect the changes in the environment and assists response to the change through a diversity-based repulsion among particles and migration among swarms in the population space, and also helps in selecting the leading particles in three different levels, personal, swarm and global levels. Comparison of the proposed heuristics over several difficult dynamic benchmark problems demonstrates the better or equal performance with respect to most of other selected state-of-the-art dynamic PSO heuristics.     

A meta optimisation analysis of particle swarm optimisation velocity update equations for watershed management learning

Particle swarm optimisation (PSO) is a general purpose optimisation algorithm used to address hard optimisation problems. The algorithm operates as a result of a number of particles converging on what is hoped to be the best solution. How the particles move through the problem space is therefore critical to the success of the algorithm. This study utilises meta optimisation to compare a number of velocity update equations to determine which features of each are of benefit to the algorithm. A number of hybrid velocity update equations are proposed based on other high performing velocity update equations. This research also presents a novel application of PSO to train a neural network function approximator to address the watershed management problem. It is found that the standard PSO with a linearly changing inertia, the proposed hybrid Attractive Repulsive PSO with avoidance of worst locations (AR PSOAWL) and Adaptive Velocity PSO (AV PSO) provide the best performance overall. The results presented in this paper also reveal that commonly used PSO parameters do not provide the best performance. Increasing and negative inertia values were found to perform better.     

Smart pricing scheme: A multi-layered scoring rule application

Defining appropriate pricing strategy for smart environment is important and complex task at the same time. It holds the primal fraction in Demand Response (DR) program. In our work, we devise an incentive based smart dynamic pricing scheme for consumers facilitating a multi-layered scoring rule. The proposed strategy characterizes both incentive based DR and price based DR programs facilities. This mechanism is applied between consumer agents (CA) to electricity provider agent (EP) and EP to Generation Company (GENCO). Based on the Continuous Ranked Probability Score (CRPS), a hierarchical scoring system is formed among these entities, CA–EP–GENCO. As CA receives the dynamic day-ahead pricing signal from EP, it will schedule the household appliances to lower price period and report the prediction in a form of a probability distribution function to EP. EP, in similar way reports the aggregated demand prediction to GENCO. Finally, GENCO computes the base discount after running a cost-optimization problem. GENCO will reward EP with a fraction of discount based on their prediction accuracy. EP will do the same to CA based on how truthful they were reporting their intentions on device scheduling. The method is tested on real data provided by Ontario Power Company and we show that this scheme is capable to reduce energy consumption and consumers’ payment.     

Applications of particle swarm optimisation in integrated process planning and scheduling

Integration of process planning and scheduling (IPPS) is an important research issue to achieve manufacturing planning optimisation. In both process planning and scheduling, vast search spaces and complex technical constraints are significant barriers to the effectiveness of the processes. In this paper, the IPPS problem has been developed as a combinatorial optimisation model, and a modern evolutionary algorithm, i.e., the particle swarm optimisation (PSO) algorithm, has been modified and applied to solve it effectively. Initial solutions are formed and encoded into particles of the PSO algorithm. The particles “fly” intelligently in the search space to achieve the best sequence according to the optimisation strategies of the PSO algorithm. Meanwhile, to explore the search space comprehensively and to avoid being trapped into local optima, several new operators have been developed to improve the particles’ movements to form a modified PSO algorithm. Case studies have been conducted to verify the performance and efficiency of the modified PSO algorithm. A comparison has been made between the result of the modified PSO algorithm and the previous results generated by the genetic algorithm (GA) and the simulated annealing (SA) algorithm, respectively, and the different characteristics of the three algorithms are indicated. Case studies show that the developed PSO can generate satisfactory results in both applications.     

Novel algorithms of particle swarm optimisation with decision criteria

The particle swarm optimisation (PSO) is a stochastic, optimisation technique based on the movement and intelligence of swarms. In this paper, three new effective optimisation algorithms BPSO, HPSO and WPSO, by incorporating some decision criteria into PSO, have been proposed and analysed both in terms of their efficiency, resistance to the problem of premature convergence and the ability to avoid local optima. In the new algorithms, for each particle except position, two sets of velocities are generated and the profit matrix is constructed. Using the decision criteria the best strategy is selected. Simulations for benchmark test nonlinear function show that the algorithms in which the decision criteria have been applied, are beneficial over classical PSO in terms of their performance and efficiency.     

An improved particle swarm optimiser based on swarm success rate for global optimisation problems

Inertia weight is one of the control parameters that influences the performance of particle swarm optimisation (PSO) in the course of solving global optimisation problems, by striking a balance between exploration and exploitation. Among many inertia weight strategies that have been proposed in literature are chaotic descending inertia weight (CDIW) and chaotic random inertia weight (CRIW). These two strategies have been claimed to perform better than linear descending inertia weight (LDIW) and random inertia weight (RIW). Despite these successes, a closer look at their results reveals that the common problem of premature convergence associated with PSO algorithm still lingers. Motivated by the better performances of CDIW and CRIW, this paper proposed two new inertia weight strategies namely: swarm success rate descending inertia weight (SSRDIW) and swarm success rate random inertia weight (SSRRIW). These two strategies use swarm success rates as a feedback parameter. Efforts were made using the proposed inertia weight strategies with PSO to further improve the effectiveness of the algorithm in terms of convergence speed, global search ability and improved solution accuracy. The proposed PSO variants, SSRDIW_PSO and SSRRIW_PSO were validated using several benchmark unconstrained global optimisation test problems and their performances compared with LDIW-PSO, CDIW-PSO, RIW-PSO, CRIW-PSO and some other existing PSO variants. Empirical results showed that the proposed variants are more efficient.     

Design of water distribution networks using accelerated momentum particle swarm optimisation technique

Optimisation of looped water distribution networks (WDNs) has been recognised as an NP-hard combinatorial problem which cannot be easily solved using traditional mathematical optimisation techniques. This article proposes the use of a new version of heuristic particle swarm optimisation (PSO) for solving this problem. In order to increase the convergence speed of the original PSO algorithm, some accelerated parameters are introduced to the velocity update equation. Furthermore, momentum parts are added to the PSO position updating formula to get away from trapping in local optimums. The new version of the PSO algorithm is called accelerated momentum particle swarm optimisation (AMPSO). The proposed AMPSO is then applied to solve WDN design problems. Some illustrative and comparative illustrative examples are presented to show the efficiency of the introduced AMPSO compared with some other heuristic algorithms.     

Train service timetabling in railway open markets by particle swarm optimisation

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 amongst 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.     

Multi-objective two-stage multiprocessor flow shop scheduling – a subgroup particle swarm optimisation approach

Flow shop production system – compared to other economically important production systems – is popular in real manufacturing environments. This study focuses on the flow shop with multiprocessor scheduling problem (FSMP), and develops an improved particle swarm optimisation heuristic to solve it. Additionally, this study designs an integer programming model to perform effectiveness and robustness testing on the proposed heuristic. Experimental results demonstrate a 10% to 50% improvement in the effectiveness of the proposed heuristic in small-scale problem tests, and a 10% to 40% improvement in the robustness of the heuristic in large-scale problem tests, indicating extremely satisfactory performance.     

Parameter optimisation of support vector machine using mutant particle swarm optimisation for diagnosis of metal-oxide surge arrester conditions

This paper proposes an enhanced support vector machine (SVM), whose parameters are optimised by a novel mutant particle swarm optimisation (mutant PSO) algorithm to identify metal-oxide surge arrester conditions. The total leakage current and its resistive component under different arrester conditions are obtained and then are inputted into a multilayer SVM for the purpose of fault identification. Then, a mutant PSO-based technique is investigated to increase the classification accuracy as well as the training speed of the SVM classifier. The proposed technique has been tested on an actual data set obtained from Taipower Company to monitor five arrester operating conditions, including normal (N), pre-fault (A), tracking (T), abnormal (U) and degradation (D). Furthermore, to demonstrate the effectiveness of the proposed mutant PSO, the obtained results are compared to those obtained by using cross-validation method, genetic algorithm and particle swarm optimisation.     

Seeker optimisation (human group optimisation) algorithm with chaos

Seeker optimisation algorithm (SOA), also referred to as human group metaheuristic optimisation algorithms form a very hot area of research, is an emerging population-based and gradient-free optimisation tool. It is inspired by searching behaviour of human beings in finding an optimal solution. The principal shortcoming of SOA is that it is easily trapped in local optima and consequently fails to achieve near-global solutions in complex optimisation problems. In an attempt to relieve this problem, in this article, chaos-based strategies are embedded into SOA. Five various chaotic-based SOA strategies with four different chaotic map functions are examined and the best strategy is chosen as the suitable chaotic scheme for SOA. The results of applying the proposed chaotic SOA to miscellaneous benchmark functions confirm that it provides accurate solutions. It surpasses basic SOA, genetic algorithm, gravitational search algorithm variant, cuckoo search optimisation algorithm, firefly swarm optimisation and harmony search the proposed chaos-based SOA is expected successfully solve complex engineering optimisation problems.     

Finding common quadratic Lyapunov functions for switched linear systems using particle swarm optimisation

It is undoubtedly important to be able to ensure the existence of a common quadratic Lyapunov function (CQLF) for a given switched system because this is proof of its asymptotic stability, but equally important is the ability to calculate it in order to obtain more specific information about the behaviour of the switched system under analysis. This article describes the development of a new methodology for calculating a CQLF based on particle swarm optimisation (PSO) once the existence of a CQLF has been assured. Several comparative analyses are presented to show the strengths and advantages of the proposed methodology.     

基于寿命的粒子群算法研究

针对粒子群算法易陷入局部最优的缺陷,提出了一种具有寿命的PSO(LS-PSO),算法赋予gbest有限的寿命,并且根据其引导能力对寿命进行自适应调整。当gbest耗尽其寿命时,它将失去领导能力,并被一个新产生并经测试具有足够引导能力的粒子所代替,继续引导群体搜索解空间的不同区域,并在两个单峰标准测试函数和六个多峰标准测试函数上对算法进行了测试。结果表明,LS-PSO比传统PSO及改进算法CLPSO有更好的求解精度和收敛速度。     

Parameter selection in particle swarm optimisation: a survey

Nowadays, particle swarm optimisation (PSO) is one of the most commonly used optimisation techniques. However, PSO parameters significantly affect its computational behaviour. That is, while it exposes desirable computational behaviour with some settings, it does not behave so by some other settings, so the way for setting them is of high importance. This paper explains and discusses thoroughly about various existent strategies for setting PSO parameters, provides some hints for its parameter setting and presents some proposals for future research on this area. There exists no other paper in literature that discusses the setting process for all PSO parameters. Using the guidelines of this paper can be strongly useful for researchers in optimisation-related fields.     

Handling many-objective optimisation problems with R2 indicator and decomposition-based particle swarm optimiser

An R2 indicator-based multi-objective particle swarm optimiser (R2-MOPSO) can obtain well-convergence and well-distributed solutions while solving two and three objectives optimisation problems. However, R2-MOPSO faces difficulty to tackle many-objective optimisation problems because balancing convergence and diversity is a key issue in high-dimensional objective space. In order to address this issue, this paper proposes a novel algorithm, named R2-MaPSO, which combines the R2 indicator and decomposition-based archiving pruning strategy into particle swarm optimiser for many-objective optimisation problems. The innovations of the proposed algorithm mainly contains three crucial factors: (1) A bi-level archiving maintenance approach based on the R2 indicator and objective space decomposition strategy is designed to balance convergence and diversity. (2) The global-best leader selection is based on the R2 indicator and the personal-best leader selection is based on the Pareto dominance. Meanwhile, the objective space decomposition leader selection adopts the feedback information from the bi-level archive. (3) A new velocity updated method is modified to enhance the exploration and exploitation ability. In addition, an elitist learning strategy and a smart Gaussian learning strategy are embedded into R2-MaPSO to help the algorithm jump out of the local optimal front. The performance of the proposed algorithm is validated and compared with some algorithms on a number of unconstraint benchmark problems, i.e. DTLZ1-DTLZ4, WFG test suites from 3 to 15 objectives. Experimental results have demonstrated a better performance of the proposed algorithm compared with several multi-objective particle swarm optimisers and multi-objective evolutionary algorithms for many-objective optimisation problems.     

The piecewise optimisation method for approximating uncertain optimal control problems under optimistic value criterion

In this paper, we introduce an approximate model and propose a piecewise optimisation method to simplify the expression of optimal control for an uncertain linear quadratic optimal control problem. First, we consider an optimal control problem of uncertain linear quadratic model under optimistic value criterion. Based on the equation of optimality, we deduce an analytic expression of optimal control. Then, we study an approximate model with control parameter and propose a piecewise optimisation method for solving the optimal parameter of such an approximate model. As an application, a four-wheel steering vehicle optimal control problem is given to show the utility of the proposed approximate model and the efficiency of the proposed piecewise optimisation method.     

A new optimal approach for multiple optimisation objectives grid resource allocation and scheduling

The article considers the resource allocation and scheduling problem in a grid computing environment. The article proposes system optimisation scheduling (SOS) that provides a potential solution of joint optimisation of objectives for both the resource and application layer, which combine both application-oriented and resource-oriented scheduling benefits. Grid systems will strive to find an optimal relation between user satisfaction and resource utilisation. Utility functions are used to express grid user's Quality of Service requirement, resource provider's benefit function and system's objectives. In order to verify the efficiency of the proposed scheduling algorithm, we compare the performance of application optimisation scheduling, resource optimisation scheduling, SOS with a traditional Round-Robin algorithm. The simulations study the effect of the request rate and task-to-resource ratio on the different scheduling algorithm.     

Chaotic bat swarm optimisation (CBSO)

Bat swarm optimisation (BSO) is a novel heuristic optimisation algorithm that is being used for solving different global optimisation problems. The paramount problem in BSO is that it severely suffers from premature convergence problem, that is, BSO is easily trapped in local optima. In this paper, chaotic-based strategies are incorporated into BSO to mitigate this problem. Ergodicity and non-repetitious nature of chaotic functions can diversify the bats and mitigate premature convergence problem. Eleven different chaotic map functions along with various chaotic BSO strategies are investigated experimentally and the best one is chosen as the suitable chaotic strategy for BSO. The results of applying the proposed chaotic BSO to different benchmark functions vividly show that premature convergence problem has been mitigated efficiently. Actually, chaotic-based BSO significantly outperforms conventional BSO, cuckoo search optimisation (CSO), big bang-big crunch algorithm (BBBC), gravitational search algorithm (GSA) and genetic algorithm (GA).