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.     

Particle swarm optimisation for feature selection in classification: Novel initialisation and updating mechanisms

In classification, feature selection is an important data pre-processing technique, but it is a difficult problem due mainly to the large search space. Particle swarm optimisation (PSO) is an efficient evolutionary computation technique. However, the traditional personal best and global best updating mechanism in PSO limits its performance for feature selection and the potential of PSO for feature selection has not been fully investigated. This paper proposes three new initialisation strategies and three new personal best and global best updating mechanisms in PSO to develop novel feature selection approaches with the goals of maximising the classification performance, minimising the number of features and reducing the computational time. The proposed initialisation strategies and updating mechanisms are compared with the traditional initialisation and the traditional updating mechanism. Meanwhile, the most promising initialisation strategy and updating mechanism are combined to form a new approach (PSO(4-2)) to address feature selection problems and it is compared with two traditional feature selection methods and two PSO based methods. Experiments on twenty benchmark datasets show that PSO with the new initialisation strategies and/or the new updating mechanisms can automatically evolve a feature subset with a smaller number of features and higher classification performance than using all features. PSO(4-2) outperforms the two traditional methods and two PSO based algorithm in terms of the computational time, the number of features and the classification performance. The superior performance of this algorithm is due mainly to both the proposed initialisation strategy, which aims to take the advantages of both the forward selection and backward selection to decrease the number of features and the computational time, and the new updating mechanism, which can overcome the limitations of traditional updating mechanisms by taking the number of features into account, which reduces the number of features and the computational time.     

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.     

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.     

A new multi-objective particle swarm optimisation algorithm based on R2 indicator selection mechanism

In recent years, Pareto-based selection mechanism has been successfully applied in dealing with complex multi-objective optimisation problems (MOPs), while indicators-based have been explored to apply in solving this problems. Therefore, a new multi-objective particle swarm optimisation algorithm based on R2 indicator selection mechanism (R2SMMOPSO) is presented in this paper. In the proposed algorithm, R2 indicator is designed as a selection mechanism for ensuring convergence and distribution of the algorithm simultaneously. In addition, an improved cosine-adjusted inertia weight balances the ability of algorithm exploitation and exploration effectively. Besides, Gaussian mutation strategy is designed to prevent particles from falling into the local optimum when the particle does not satisfy the condition of the position update formula, polynomial mutation is applied in the external archive to increase the diversity of elite solutions. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems. Experimental studies demonstrate that the proposed algorithm shows very competitive performance when dealing with complex MOPs.     

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.     

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.     

粒子群优化算法中惯性权值调整的一种新策略

惯性权值的设置对粒子群优化（PSO）算法的性能起着关键作用,现有的基于惯性权值的改进算法提高了算法的性能,但都把惯性权值作为全局参数,很难控制算法的搜索能力。本文在充分分析惯性权值的关键作用基础上给出一种新的惯性权值调整策略及其相应的粒子群优化算法,使用不同的惯性权值更新同一代种群。测试结果表明,新算法提高了算算法的性能,并具有更快的收敛速度和跳出局部最优的能力。     

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.     

Markerless human articulated tracking using hierarchical particle swarm optimisation

In this paper, we address markerless full-body articulated human motion tracking from multi-view video sequences acquired in a studio environment. The tracking is formulated as a multi-dimensional non-linear optimisation and solved using particle swarm optimisation (PSO), a swarm-intelligence algorithm which has gained popularity in recent years due to its ability to solve difficult non-linear optimisation problems. We show that a small number of particles achieves accuracy levels comparable with several recent algorithms. PSO initialises automatically, does not need a sequence-specific motion model and recovers from temporary tracking divergence through the use of a powerful hierarchical search algorithm (HPSO). We compare experimentally HPSO with particle filter (PF), annealed particle filter (APF) and partitioned sampling annealed particle filter (PSAPF) using the computational framework provided by Balan et al. HPSO accuracy and consistency are better than PF and compare favourably with those of APF and PSAPF, outperforming it in sequences with sudden and fast motion. We also report an extensive experimental study of HPSO over ranges of values of its parameters.     

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.     

Binary particle swarm optimisation with quadratic transfer function: A new binary optimisation algorithm for optimal scheduling of appliances in smart homes

Demand response (DR) is the response of electricity consumers to time-varying tariffs or incentives awarded by the utility. Home energy management systems are systems whose role is to control the consumption of appliances under DR programs, in a way that electricity bill is minimised. While, most researchers have done optimal scheduling only for non-interruptible appliances, in this paper, the interruptible appliances such as electric water heaters are considered. In optimal scheduling of non-interruptible appliances, the problem is commonly formulated as an optimisation problem with integer decision variables. However, consideration of interruptible appliances leads to a binary optimisation problem which is more difficult than integer optimisation problems. Since, the basic version of binary particle swarm optimisation (PSO) does not perform well in solving binary engineering optimisation problems, in this paper a new binary particle swarm optimisation with quadratic transfer function, named as quadratic binary PSO (QBPSO) is proposed for scheduling shiftable appliances in smart homes. The proposed methodology is applied for optimal scheduling in a smart home with 10 appliances, where the number of decision variables is as high as 264. Optimal scheduling is done for both RTP and TOU tariffs both with and without consideration of consumers’ comfort. The achieved results indicate the drastic effect of optimal scheduling on the reduction of electricity bill, while consumers’ comfort is not much affected. The results testify that the proposed QBPSO outperforms basic binary PSO variant and 9 other binary PSO variants with different transfer functions.     

基于粒距和动态区间的粒子群权值调整策略

由于标准粒子群优化(PSO)算法把惯性权值作为全局参数,因此很难适应复杂的非线性优化过程。针对这一问题,提出了一种基于粒距和动态区间的权值调整策略（PSSIW）,根据粒子的粒距大小在动态区间内选取不同的权值,并通过区间的动态变化来控制算法的收敛速度。设计了四种不同的动态区间,并采用三个常用的标准测试函数测试不同区间对算法性能的影响。通过与标准粒子群算法比较发现,该策略提高了算法摆脱局部极值的能力,是一种新型全局收敛粒子群算法。     

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).     

A particle swarm optimizer with modified velocity update and adaptive diversity regulation

This study introduces reverse direction supported particle swarm optimization (RDS‐PSO) with an adaptive regulation procedure. It benefits from identifying the global worst and global best particles to increase the diversity of the PSO. The velocity update equation of the original PSO was changed according to this idea. To control the impacts of the global best and global worst particles on the velocity update equation, the alpha parameter was added to the velocity update equation. Moreover, a procedure for diversity regulation based on cosine amplitude or max–min methods was introduced. Alpha value was changed adaptively with respect to this diversity measure. Besides, RDS‐PSO was implemented with both linearly increasing and decreasing inertia weight (with 1,000 and 2,000 iterations) in order to survey the effects of these variations on RDS‐PSO performances. Six most commonly used benchmark functions and three medical classification problems were selected as experimental data sets. All experimental results showed that when the grain searching ability is not so small in the last generations, the algorithm performance continues to increase. Experimental proof of it was showed up especially in RDS‐PSO using the cosine amplitude approach. Because the best results among all the RDS‐PSO types for decreasing inertia weight modes were obtained with 2,000 maximal iterations rather than 1,000 ones.     

A memetic particle swarm optimisation algorithm for dynamic multi-modal optimisation problems

Many real-world optimisation problems are both dynamic and multi-modal, which require an optimisation algorithm not only to find as many optima under a specific environment as possible, but also to track their moving trajectory over dynamic environments. To address this requirement, this article investigates a memetic computing approach based on particle swarm optimisation for dynamic multi-modal optimisation problems (DMMOPs). Within the framework of the proposed algorithm, a new speciation method is employed to locate and track multiple peaks and an adaptive local search method is also hybridised to accelerate the exploitation of species generated by the speciation method. In addition, a memory-based re-initialisation scheme is introduced into the proposed algorithm in order to further enhance its performance in dynamic multi-modal environments. Based on the moving peaks benchmark problems, experiments are carried out to investigate the performance of the proposed algorithm in comparison with several state-of-the-art algorithms taken from the literature. The experimental results show the efficiency of the proposed algorithm for DMMOPs.     

基于改进惯性权重的粒子群优化算法

惯性权重是粒子群算法中平衡全局搜索和局部搜索能力的重要参数,提出了一种基于改进惯性权重的粒子群优化算法。该算法在进化初期采用基于不同粒子不同维的动态自适应惯性权重策略,加快收敛速度,在进化后期采用线性递减权重策略,同时为防止陷入局优,适时引入混沌变异增加种群多样性。对5个典型测试函数的测试结果表明,NPSO在收敛速度、收敛精度、稳定性和全局搜索能力等方面比线性权重PSO(LDIWPSO)均有很大程度上的提高。     

融合隶属度函数的自适应惯性权重模式的粒子群优化算法

粒子群算法(Particle Swarm Optimization,PSO)的性能极大地依赖于其惯性权重参数的选择策略。当在一次迭代中更新粒子速度时,PSO忽略了粒子间的差异,在所有粒子上应用了相同的惯性权重。针对这一问题,提出一种自适应惯性权重的粒子群算法PSO-AIWA,有效合理地均衡PSO的全局搜索和局部搜索能力。根据当前粒子与全局最优粒子间的差异,算法可以通过基于粒子间距的隶属度函数动态调整粒子的惯性权重,使得每次迭代中,粒子可以根据当前状态在每个维度上的搜索空间内选择合适的惯性权重进行状态更新。在6种基准函数下进行了算法的性能测试,结果表明,与随机式惯性权重PSO算法与线性递减惯性权重PSO-LDIW算法相比,该算法可以获得更好的粒子分布和收敛性。     

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.