Research And Improvement On Bacterial Foraging Optimization Algorithm

With the advance of modern society,optimization has penetrated into all our production and life with increasing size and complication of the problem.Traditional mathematics usually cannot meet our requirements in terms of efficiency and accuracy in solution while solving some optimization problem.Therefore,various bionic algorithm stimulating natural phenomena and evolution of species appear successively and quickly replace traditional mathematics,as these algorithms have revealed particular advantage in solution of optimization problem.BFO(Bacterial Foraging Optimization Algorithm)is an algorithm of swarm intelligence evolution which stimulating the foraging behavior of human coli bacillus.This algorithm is easy to carry out parallel processing and global search as for its strong robustness and the insensitivity to the option of initial values and parameters.Once brought forward,this algorithm has attracted extensive attention of scholars.This dissertation conducts a thorough study on BFO algorithm in terms of difficult problems,such as,high-dimensional optimization and multiple-target optimization.A series of research have been carried out resolving around how to establish an improved BFO algorithm of high-robustness and highefficiency.The main tasks carried out including:(1)The optimization procedure of BFO algorithm is demonstrated via describing the foraging behavior of coli bacillus.This dissertation has expounded and analyzed the specific role of BFO algorithm in all steps of optimization.According to the analysis results,the basic BFO algorithm is improved.With the help of chaos theory,the flora is initialized,so that the flora is evenly distributed in the optimization space,creating conditions for finding the global optimal solution later.In the elimination and dispersal operation,according to the optimal range of the problem and the adaptive stepping mechanism of the current evolutionary algebra,the crossover operation in the genetic algorithm is introduced,and some excellent genes of the current optimal individual are cross-transferred to the optimized individual,and the individual is locally Swimming,speeding up its convergence.Random migrating operator might lead to the individual bacterium approaching or already finding the optimal position to escape from the optimal position.This phenomenon is called Escape Phenomenon and might compromise the convergence rate of the algorithm.Thus,in order to avoid Escape Phenomenon,the range of migrating operator will be altered according to the generations of the generation of Bacterial's evolution.The result of testing classic functions demonstrates that the improved Bacterial foraging optimization algorithm has enhanced greatly in terms of convergence and accuracy comparing to original algorithm and other comparison algorithms.(2)Solve high dimensional optimization problems using improved BFO algorithm.The problem is analyzed.According to the relationship between multiple dimensions in the problem,the problem is divided into three categories: decomposable groupable,indecomposable groupable and non-decomposable.For different types of problems,different grouping methods are adopted,and dimensionality reduction and refinement are used to solve the problem.The improved adaptive step size formula is applied to the solution method of high dimensional optimization problems.In order to conveniently decompose and extract the single dimension information in the high dimensional problem,the reference vector in the linear algebra is introduced,and the step size and its variation are decomposed,which is expressed as the step information in each dimension.Through the combination of the reference vector and the fractal dimension step,the fractal dimension optimization is conveniently realized.The improved PDBFO(Part Dimensions Optimization BFO,PDBFO)is applied to the solution of high-dimensional optimization problems.By testing multiple standard test functions in high dimensional space and comparing the results with other algorithms,the experiment proves that the improved algorithm has significantly improved the accuracy and efficiency of finding the optimal solution compared with other improved schemes.(3)Use the improved BFO to solve multi-objective optimization problems.Traditional bacterial foraging optimization algorithm only optimizes for single-objective optimization problems.In order to further explore the advantages of bacterial group intelligence in multiobjective optimization problems,an improved multi-objective bacterial foraging optimization algorithm is raised.A normalized preference strategy is given when individuals do not dominate each other.A differential idea is introduced to complete the copy operation.The population diversity is increased.Migration by grid division improves the dispersion of the solution set.At the same time,an external set is used to store the currently found nondominated solution.External sets are also continuously optimized.By testing multiple standard functions and comparing them with several other algorithms,the proposed multitarget bacterial foraging optimization algorithm has a certain improvement in the convergence and dispersion index of the solution.It can effectively solve multi-objective optimization problems.(4)Use the improved BFO to solve TSP problems.Improve the BFO which solved the consistent optimization so that it can solve the disperse problem.According to the peculiarity of TSP,3-opt is introduced to local search operator in directional operation.It can complete the path search efficiently.In the reproduction operation,the idea of genetic algorithm is introduced,and the gene fragments in the excellent individuals are copied to the current poor individuals,and the convergence speed of the group is accelerated without reducing the diversity of the population.In the elimination and dispersal operation,according to bacterial similarity value,the migration would choose the Bacterial with high similarity and eliminate individuals with the same current path.According to experience,improved BFO algorithm designed in this dissertation solves the TSP problem with the city size not more than 100,and the solution efficiency and precision are better than the similar intelligent algorithms.In this dissertation,the BFO algorithm is deeply studied.After analyzing and improving the basic algorithm,the corresponding BFO algorithm solution is proposed for highdimensional optimization and multi-objective optimization problems,and the BFO algorithm is applied to the typical path optimization TSP problem.In the solution,a satisfactory result has been achieved.These studies have promoted the further development of the BFO algorithm and have certain theoretical significance and application value.