Most real-world optimization problems often come with multiple global optima or local optima. Therefore, increasing niching metaheuristic algorithms, which devote to finding multiple optima in a single run, are developed to solve these multimodal optimization problems. However, there are two difficulties urgently to be solved for most existing niching metaheuristic algorithms: how to set the niching parameter values for different optimization problems and how to jump out of the local optima efficiently. These two difficulties limit their practicality largely. Based on Whale Swarm Algorithm (WSA) we proposed previously, this paper presents a new multimodal optimizer named WSA with Iterative Counter (WSA-IC) to address these two difficulties. On the one hand, WSA-IC improves the iteration rule of the original WSA for multimodal optimization, which removes the need of specifying different values of attenuation coefficient for different problems to form multiple subpopulations, without introducing any niching parameter. On the other hand, WSA-IC enables the identification of extreme points during the iterations relying on two new parameters (i.e., stability threshold (T_ s ) and fitness threshold (T_ f )), to jump out of the located extreme points. Moreover, the convergence of WSA-IC is proved. Finally, the proposed WSA-IC is compared with several niching metaheuristic algorithms on CEC2015 niching benchmark test functions and on five additional high-dimensional multimodal functions. The experimental results demonstrate that WSA-IC statistically outperforms other niching metaheuristic algorithms on most test functions.
The speciation technique was also introduced into the conventional PSO by Li @cite_22 to solve multimodal optimization problems. In each iteration of Species-based PSO (SPSO), after the population is divided into multiple species and the species seeds are determined, each species seed is assigned to its member individuals as the @math . Then, each individual updates its position according to the iterative equations of velocity and position in the @math PSO. The experimental results showed that SPSO is comparable or better than SNGA @cite_2 , SCGA and NichePSO @cite_11 over a set of multimodal functions.
@cite_11 @cite_22 @cite_2
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This paper proposes an improved particle swarm optimizer using the notion of species to determine its neighbourhood best values, for solving multimodal optimization problems. In the proposed species- based PSO (SPSO), the swarm population is divided into species sub- populations based on their similarity. Each species is grouped around a dominating particle called the species seed. At each iteration step, species seeds are identified from the entire population and then adopted as neig- hbourhood bests for these individual species groups separately. Species are formed adaptively at each step based on the feedback obtained from the multimodal fitness landscape. Over successive iterations, species are able to simultaneously optimize towards multiple optima, regardless of if they are global or local optima. Our experiments demonstrated that SPSO is very effective in dealing with multimodal optimization functions with lower dimensions. This paper presents a variant of particle swarm optimizers (PSOs) that we call the comprehensive learning particle swarm optimizer (CLPSO), which uses a novel learning strategy whereby all other particles' historical best information is used to update a particle's velocity. This strategy enables the diversity of the swarm to be preserved to discourage premature convergence. Experiments were conducted (using codes available from http: www.ntu.edu.sg home epnsugan) on multimodal test functions such as Rosenbrock, Griewank, Rastrigin, Ackley, and Schwefel and composition functions both with and without coordinate rotation. The results demonstrate good performance of the CLPSO in solving multimodal problems when compared with eight other recent variants of the PSO. The initial state of an Unmanned Aerial Vehicle (UAV) system and the relative state of the system, the continuous inputs of each flight unit are piecewise linear by a Control Parameterization and Time Discretization (CPTD) method. The approximation piecewise linearization control inputs are used to substitute for the continuous inputs. In this way, the multi-UAV formation reconfiguration problem can be formulated as an optimal control problem with dynamical and algebraic constraints. With strict constraints and mutual interference, the multi-UAV formation reconfiguration in 3-D space is a complicated problem. The recent boom of bio-inspired algorithms has attracted many researchers to the field of applying such intelligent approaches to complicated optimization problems in multi-UAVs. In this paper, a Hybrid Particle Swarm Optimization and Genetic Algorithm (HPSOGA) is proposed to solve the multi-UAV formation reconfiguration problem, which is modeled as a parameter optimization problem. This new approach combines the advantages of Particle Swarm Optimization (PSO) and Genetic Algorithm (GA), which can find the time-optimal solutions simultaneously. The proposed HPSOGA will also be compared with basic PSO algorithm and the series of experimental results will show that our HPSOGA outperforms PSO in solving multi-UAV formation reconfiguration problem under complicated environments. Feature selection (FS) is an important data preprocessing technique, which has two goals of minimising the classification error and minimising the number of features selected. Based on particle swarm optimisation (PSO), this paper proposes two multi-objective algorithms for selecting the Pareto front of non-dominated solutions (feature subsets) for classification. The first algorithm introduces the idea of non-dominated sorting based multi-objective genetic algorithm II into PSO for FS. In the second algorithm, multi-objective PSO uses the ideas of crowding, mutation and dominance to search for the Pareto front solutions. The two algorithms are compared with two single objective FS methods and a conventional FS method on nine datasets. Experimental results show that both proposed algorithms can automatically evolve a smaller number of features and achieve better classification performance than using all features and feature subsets obtained from the two single objective methods and the conventional method. Both the continuous and the binary versions of PSO are investigated in the two proposed algorithms and the results show that continuous version generally achieves better performance than the binary version. The second new algorithm outperforms the first algorithm in both continuous and binary versions.