Research On Improvements Of Swarm Intelligence Algorithms

Many real-world problems can be converted into optimization problems.Therefore,the optimization is an important area in engineering applications and scientific researches.However,some difficult optimization problems have complex characteristics such as multimodality,highly non-linearity,non-differentiability,and so on.The converntional mathematical and analytical methods are inefficient and ineffective for solving these difficult optimization problems.Hence,there is a growing need for more effective algorithms.In recent decades,some new evolutionary algorithms(EAs)have been proposed.The swarm intelligence algorithm is a branch of the evolutionary algorithm.Particle swarm optimization(PSO)is one of the most popular and efficient swarm intelligence algorithms,which is a population-based meta-heuristic algorithm.The main idea of PSO is to simulate the collective and collaborative behaviors of birds flocking.PSO uses a simple mechanism the imitateds swarm behaviors of birds flocking to guide the particles to search for globally optimal solutions.Similar to other evolutionary algorithms,it is a population-based iterative algorithm.Owing to its simplicity of implementation,the PSO has been successfully applied in solving many real-world problems.PSO has two main disadvantages:the weak exploitation capabilities and the premature convergence on complex multimodal problems.Therefore,the improvement of particle swarm optimization is very challenging and meaningful.The Fireworks Algorithm(FWA)is a relatively new swarm intelligence algorithm and developed by simulating the explosion process of fireworks in the night sky.The main idea of the FWA is to use the explosion of the fireworks to search the feasible space of the optimization problem.Fireworks as well as the newly generated sparks represent potential solutions in the search space.In order to ensure diversity and balance the global and local search,the explosion amplitude and the population of the newly generated explosion sparks differ among the fireworks.As a brand new search manner,FWA has received extensive concerns from lots of researchers in the swarm intelligence community.So far,FWA has been successfully applied in solving some practical engineering problems.Therefore,FWA is one promising algorithm and is worthy of further research.Yet,conventional FWA has its own disadvantages.It is necessary to improve the performance of the FWA.This article first briefly introduces several evolutionary algorithms.Then,the improvement of particle swarm optimization algorithm and fireworks algorithm is studied.The main research results and innovations of this paper are described as follows:(1)A particle swarm optimization algorithm with crossover operation(PSOCO)is proposed.In the proposed PSOCO,two different crossover operations are employed.By performing crossover on the personal historical best position of each particle,the effective guiding vectors are constructed and they maintain a good diversity.In turn,these high quality guiding vectors are used to guide the evolution of particles.PSOCO adopts the velocity update scheme with learning model.This velocity update scheme can enhance the exploration capability of PSOCO and avoid the local optimal solution.PSOCO is two-layer particle swarm optimization with positive feedback mechanism.In addition,the influences of some parameters are investigated,and a better parameter configuration is found.The experimental results demonstrate that the proposed PSOCO is a competitive optimizer in terms of both solution quality and efficiency.(2)A particle swarm optimization algorithm with two differential mutation(PSOTD)is proposed.In PSOTD,a novel structure with two swarms and two layers(bottom layer and top layer)isdesigned.The top layer consists of all the personal best particles.We divide the particles in the top layer into two sub-swarms.Two different differential mutation operations are employed in order to breed the particles in thetop layer.Thus,one sub-swarm has a good exploration capability,and the other sub-swarm has a goodexploitation capability.Obviously,since the top layer leads the bottom layer,the bottom particles achievea good trade-off between exploration and exploitation.In order to enhance the exploitation ability of PSOTD,a dynamic adjustment scheme for the number of particles in two sub-swarms is proposed.This scheme is simple and effective.The numercial experimental results show that this scheme can enhance the performance of PSOTD.The experimental results demonstrate that the proposed PSOTD outperforms most of the other tested variants of the PSO in terms of both solution quality and efficiency.(3)A dynamic multiswarm differential learning particle swarm optimizer(DMSDL-PSO)is proposed.We propose a novel method to merge the differential evolution operator into each sub-swarm of the DMSDL-PSO.Combining the exploration capability of the differential mutation and employing Quasi-Newton method as a local searcher to enhance the exploitation capability,DMSDL-PSO has a good exploration and exploitation capability.According to the characteristics of the DMSDL-PSO,three modified differential mutation operators are discussed.Because the velocity updating equation of the particles in PSO has some shortcomings,a modified velocity updating equation is adopted in DMSDL-PSO.The particles in DMSDL-PSO are divided into several small and dynamic sub-swarms.The dynamic change of sub-swarms can promote the information exchange of the whole swarm.The numerical results demonstrate that DMSDL-PSO performs better on some benchmark functions.(4)We propose a particle swarm optimizer with cooperative search strategys(PSOCS).Some ideas of PSOCS are inspired by the divisions of roles and cooperations among biological populations.In PSOCS,all particles are divided into two swarms.Different search strategies are used in these two swarms such that one swarm has better exploitation ability,and the other swarm has better exploration ability.In order to ensure the cooperative search between these two swarms,a strategy of information exchange is adopted in PSOCS.This strategy is embodied in the update equation of the particles.(5)A simplified hybrid fireworks algorithm(SHFWA)is proposed in this paper.In SHFWA,in order to enhance the exploitation ability,a modified search formula is designed for core firework swarm.To enhance the exploration ability,for each firework swarm,another way of generating sparks-harmony spark is designed.In the conventional fireworks algorithm,the calculation of the number of sparks generated by each firework and the calculation of amplitude of explosion for each firework are very complex.In SHFWA,a simplified method is employed to compute these two variables.By introducing these methods,SHFWA is easy to implement and is good at exploration and exploitation.The experimental results demonstrate that SHFWA performs effectively and competitively when compared with several reported fireworks algorithms.