Research On Evolutionary Optimization Algorithm And Its Application In Decision-making Of Operation Indices Of Beneficiation Process

Due to the influence of various external environments and internal disturbances,complex industrial production processes are often in a dynamically changing environment.Many optimization decisions of complex industrial processes with complex mechanisms are affected by large-scale variables,and often have more than one optimization objective.Therefore,many optimization decisions of complex industrial process are a large-scale dynamic multi-objective optimization problem.Compared with dynamic single objective optimization problems,Dynamic multiobjective opitmization problems(DMOPs)pose a bigger challenge to an optimization algorithm in tracking the moving Pareto set(PS)or Pareto front(PF)in a changing environment.Recently predicting the initial population in the new environment based on the historical information of the population obtained by the algorithm in the evolutionary process to guide the algorithm to solve the problem in the new environment has been increasing researched.More recently a class of DMOPs,whose PS rotate with time,is proposed.To solve that DMOPs,this paper proposes a reference vector based multidirectional prediction strategy,and designs a reference vector based offspring generation strategy to trade-off the convergence and diversity of population.Large-scale optimization problems is another hotspot in the field of evolutionary computation.Cooperative co-evolution(CC)is an effective framework for solving large-scale optimization problems via using "divide-and-conquer" mechanism.The problem decomposition has a significant impact on the performance of a CC framework,and recursive differential grouping(RDG)can decompose a large-scale optimization problem faster compared with other differential grouping method in the experiments.However,current analysis for RDG methods cannot guarantee the worst computational complexity of decomposing any large-scale optimization problem is O(nlog(n)).Based on the above problems,the dynamic multi-objective optimization and large-scale optimization algorithm are studied and applied to the optimization of operation indices of beneficiation process.The main works are as follows:1)A reference vector based multidirectional prediction dynamic multiobjective optimization algorithm is proposed.Firstly,a reference vector based multidirectional prediction strategy is designed to fastly response to environmental changes.When the environment changes has been detected,the new location of PS and PF is predicted using the reference vector based multidirection prediction strategy,and to improve the convergence of population and increase the diversity of the population in the optimization process,this paper proposes a reference vector based offspring creation strategy.In this paper,seven benchmark test problems are selected to test the performance of the algorithm.To verify the superiority of the proposed algorithm,this paper selects DNSGA-II-A algorithm and MDP algorithm as the comparison algorithm,and the mean of generational distance(MGD)is used to evaluate the convergence performance of the three algorithms and the mean of inverted generational distance(MIGD)is used to evaluate the comprehensive performance of the three algorithms.The experimental result shows proposed algorithm has better performance in the most benchmark problems and obtained excellent experimental result in the new proposed DMOPs,whose PSs rotate with time.2)The computational complexity of the recursive differential grouping method for solving large-scale continuous optimization problems is mathematically pro ved.Firstly,the large-scale optimization problem is defined and the difficulties of large-scale optimization problems are analyzed.Then,the existing methods for solving large-scale continuous optimization problems are listed.The principle of recursive differential grouping(RDG)strategy are introduced in detail,and then the shortcomings of computational complexity of RDG is analyzed.Finally,this paper mathematically proves that the worst computational complexity of RDG for decomposing any large-scale optimization problem is O(nlog(n)).3)The practical application research on the dynamic multi-objective optimization problem of operational indices of beneficiation processes is carried out.In order to study the dynamic optimization decision of operational indices,this paper selects six environmental production conditions as the working condition environment of the experimental research according to the actual production conditions,and establishes the model of dynamic multiobjective optimization problem of beneficiation processes.The problem model is solved by DNSGA-II-A,MDP and the proposed RVMDP.The experimental result shows that the solutions obtained by the proposed algorithm is better in the six working conditions of the experimental design.Therefore,the superiority of the proposed algorithm on the dynamic multi-objective optimization problem of operational indices for beneficiation processes is verified,and the feasibility and effectiveness in practical applications is further illustrated.