Search

Particle swarm optimization (PSO) is a population-based random-search optimization technique that has become an increasingly important branch of swarm intelligence studies. Population diversity is an effective measurement that shows the distribution of particles in a search space. In this paper, we propose a diversity-based PSO algorithm that is combined with multiple techniques, and population diversity is used as a search-strategy selection criterion for particles. When diversity is high, we suggest implementing a search strategy that has a strong exploration ability. When diversity is low, we suggest implementing a search strategy that has a strong exploitation ability. In addition to our diversity-based method, we introduce a gradient-based local-search technique, multi-crossover operation, and disturbance strategy to help improve the performance of the proposed algorithm. In the experiments, we compare the proposed algorithm with 10 advanced PSO variants based on 40 widely used benchmark functions, including the CEC2017 benchmark. The results indicate that the proposed algorithm yields a better solution accuracy and convergence speed than those of other PSO variants. [ABSTRACT FROM AUTHOR]

• The concept and verification method of affine invariance are presented. • Six algorithms are employed to analyze their affine invariances. • PSO, OFA and DE are affine invariant, GWO, SCA and BOA are not affine invariant. • Multiple experimental comparisons are executed to verify algorithms' affine invariance. An algorithm whose performance depends on the objective function being aligned with a privileged coordinate system is a poor choice in general because it is unlikely that the optimal orientation will be known in advance. In this paper, a property of meta -heuristic algorithms, named affine invariance, is introduced to verify whether the algorithm is depended on the privileged coordinate system or not. The concept of affine invariance is described in detail, and some classical algorithms, efficient in most test and actual problems, are proved to be affine invariant. While some recent algorithms in the literature are proved to be not affine invariant. As a conclusion, particle swarm optimization (PSO), differential evolution (DE) and optimal foraging algorithm (OFA) are affine invariant, while grey wolf optimizer (GWO), sine cosine algorithm (SCA) and butterfly optimization algorithm (BOA) are not affine invariant. Furthermore, comparison tests are designed to support the theoretical analysis results. In these tests, same random numbers and initial population are used to avoid the influence of randomness, thus, the conclusion is reliable. [ABSTRACT FROM AUTHOR]

Abstract: Some real-world optimization problems are plagued by a limited hardware availability. This situation can occur, for example, when the optimization must be performed on a device whose hardware is limited due to cost and space limitations. This paper addresses this class of optimization problems and proposes a novel algorithm, namely compact Particle Swarm Optimization (cPSO). The proposed algorithm employs the search logic typical of Particle Swarm Optimization (PSO) algorithms, but unlike classical PSO algorithms, does not use a swarm of particles and does not store neither the positions nor the velocities. On the contrary, cPSO employs a probabilistic representation of the swarm’s behaviour. This representation allows a modest memory usage for the entire algorithmic functioning, the amount of memory used is the same as what is needed for storing five solutions. A novel interpretation of compact optimization is also given in this paper. Numerical results show that cPSO appears to outperform other modern algorithms of the same category (i.e. which attempt to solve the optimization despite a modest memory usage). In addition, cPSO displays a very good performance with respect to its population-based version and a respectable performance also with respect to some more complex population-based algorithms. A real world application in the field of power engineering and energy generation is given. The presented case study shows how, on a model of an actual power plant, an advanced control system can be online and real-time optimized. In this application example the calculations are embedded directly on the real-time control system. [Copyright &y& Elsevier]

Abstract As a new evolutionary computation method, the structure of backtracking search optimization algorithm (BSA) is simple and the exploration capability of it is strong. However, the global performance of the BSA is significantly affected by mutation strategies and control parameters. Designing appropriate mutation strategies and control parameters is important to improve the global performance of the BSA. In this paper, an adaptive BSA with knowledge learning (KLBSA) is developed to improve the global performance of the BSA. In the method, an adaptive control parameter based on the global and local information of the swarms in the current iteration is designed to adjust the search step length of individuals, which helps to balance the exploration and exploitation abilities of the algorithm. Moreover, a new mutation strategy based on the guidance of different information is designed to improve the optimization ability of the algorithm. In addition, a multi-population strategy is implemented to thoroughly improve the searching ability of the algorithm for different searching areas. To this end, experiments on three groups of benchmark functions and three real-world problems are implemented to verify the performance of the proposed KLBSA algorithm. The results indicate that the proposed algorithm performs competitively and effectively when compared to some other evolutionary algorithms. [ABSTRACT FROM AUTHOR]

The diversity of solutions is of great importance for multi-objective evolutionary algorithms. In this paper, a new multi-objective particle swarm optimization algorithm based on decomposition (MPSO/D) is proposed. Firstly, the objective space of a multi-objective problem is decomposed into a set of sub-regions based on a set of direction vectors. Then MPSO/D makes each sub-region have a solution to maintain the diversity. Secondly, considering the convergence of solutions, MPSO/D uses the crowding distance to calculate the fitness values of the reserved solutions for selection operator, and uses the neighboring particles of a particle to determine the global best historical position ( gbest ) of the particle. The proposed algorithm has been compared with NSGAII, MOEA/D and NNIA on sixteen test sets. The experimental results illustrate that the proposed algorithm outperforms NSGAII, MOEA/D and NNIA in terms of convergence and diversity. [ABSTRACT FROM AUTHOR]

Abstract: Motivated by concepts in quantum mechanics and particle swarm optimization (PSO), quantum-behaved particle swarm optimization (QPSO) was proposed as a variant of PSO with better global search ability. Although it has been shown to perform well in finding optimal solutions for many optimization problems, there has so far been little theoretical analysis on its convergence and performance. This paper presents a convergence analysis and performance evaluation of the QPSO algorithm and it also proposes two variants of the QPSO algorithm. First, we investigate in detail the convergence of the QPSO algorithm on a probabilistic metric space and prove that the QPSO algorithm is a form of contraction mapping and can converge to the global optimum. This is the first time that the theory of probabilistic metric spaces has been employed to analyze a stochastic optimization algorithm. We provided a new definition for the convergence rate of a stochastic algorithm as well as definitions for three types of convergence according to the correlations between the convergence rate and the objective function values. With these definitions, the effectiveness of the QPSO is evaluated by computing and analyzing the time complexity and the convergence rate of the algorithm. Then, the QPSO with random mean best position (QPSO-RM) and the QPSO with ranking operator (QPSO-RO) are proposed as two improvements of the QPSO algorithm. Finally, some empirical studies on popular benchmark functions are performed in order to make a full performance evaluation and comparison between QPSO, QPSO-RM, QPSO-RO and other variants of PSO. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new bare-bones multi-objective particle swarm optimization algorithm to solve the environmental/economic dispatch problems. The algorithm has three distinctive features: a particle updating strategy which does not require tuning up control parameters; a mutation operator with action range varying over time to expand the search capability; and an approach based on particle diversity to update the global particle leaders. Several trials have been carried out on the IEEE 30-bus test system. By comparing with seven existing multi-objective optimization algorithms and three well-known multi-objective particle swarm optimization techniques, it is found that our algorithm is capable of generating excellent approximation of the true Pareto front and can be used to solve other types of multi-objective optimization problems. [Copyright &y& Elsevier]

Abstract: This paper presents a novel framework of the estimation of particle swarm distribution algorithms (EPSDAs). The aim is to effectively combine particle swarm optimization (PSO) with the estimation of distribution algorithms (EDAs) without losing their unique features. This aim is achieved by incorporating the following mechanisms: (1) selection is applied to the local best solutions in order to obtain more promising individuals for model building, (2) a probabilistic model of the problem is built from the selected solutions, and (3) new individuals are generated by a stochastic combination of the EDA’s model sampling method and the PSO’s particle moving mechanism. To exhibit the utility of the EPSDA framework, an extended compact particle swarm optimization (EcPSO) is developed by combining the strengths of the extended compact genetic algorithm (EcGA) with binary PSO (BPSO), along the lines of the suggested framework. Due to its effective nature of harmonizing the global search of EcGA with the local search of BPSO, EcPSO is able to discover the optimal solution in a fast and reliable manner. Experimental results on artificial to real-world problems have adduced grounds for the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: Global optimization of high-dimensional problems in practical applications remains a major challenge to the research community of evolutionary computation. The weakness of randomization-based evolutionary algorithms in searching high-dimensional spaces is demonstrated in this paper. A new strategy, SP-UCI is developed to treat complexity caused by high dimensionalities. This strategy features a slope-based searching kernel and a scheme of maintaining the particle population’s capability of searching over the full search space. Examinations of this strategy on a suite of sophisticated composition benchmark functions demonstrate that SP-UCI surpasses two popular algorithms, particle swarm optimizer (PSO) and differential evolution (DE), on high-dimensional problems. Experimental results also corroborate the argument that, in high-dimensional optimization, only problems with well-formative fitness landscapes are solvable, and slope-based schemes are preferable to randomization-based ones. [Copyright &y& Elsevier]

Abstract: Increasing attention is being paid to solve constrained optimization problems (COP) frequently encountered in real-world applications. In this paper, an improved vector particle swarm optimization (IVPSO) algorithm is proposed to solve COPs. The constraint-handling technique is based on the simple constraint-preserving method. Velocity and position of each particle, as well as the corresponding changes, are all expressed as vectors in order to present the optimization procedure in a more intuitively comprehensible manner. The NVPSO algorithm , which uses one-dimensional search approaches to find a new feasible position on the flying trajectory of the particle when it escapes from the feasible region, has been proposed to solve COP. Experimental results showed that searching only on the flying trajectory for a feasible position influenced the diversity of the swarm and thus reduced the global search capability of the NVPSO algorithm. In order to avoid neglecting any worthy position in the feasible region and improve the optimization efficiency, a multi-dimensional search algorithm is proposed to search within a local region for a new feasible position. The local region is composed of all dimensions of the escaped particle’s parent and the current positions. Obviously, the flying trajectory of the particle is also included in this local region. The new position is not only present in the feasible region but also has a better fitness value in this local region. The performance of IVPSO is tested on 13 well-known benchmark functions. Experimental results prove that the proposed IVPSO algorithm is simple, competitive and stable. [ABSTRACT FROM AUTHOR]