Multi-objective Optimization Based On Improved Particle Swarm Optimization And Its Application

There are numerous optimization problems in the real world.The promotion of optimized technology has the potential to generate enormous economic benefits,embody outstanding social values,and promote the rapid development of the environment.While the optimization problem exhibits a trend of diversification and scalization,it is also characterized by nonlinearity and high dimension.These practical problems may involve one or more conflicting optimization objectives,which are frequently constrained by harsh constraints.The selection of optimization schemes and the performance of optimization algorithms have become constant challenges as the complexity of the problem has increased.Particle swarm optimization is a swarm intelligence algorithm with a simple structure,few adjustable parameters,enough information interaction between individuals,simple implementation,and good robustness.Researchers from all over the world have expanded it into multi-objective optimization fields due to its outstanding performance in dealing with single-objective optimization problems.Multi-objective particle swarm optimization is used not only to solve complex multi-objective problems,but also as a search mechanism for dealing with singleobjective and multi-objective constraint problems in conjunction with various advanced constraint processing technologies.Its efficient search mechanism and excellent advantage of information interaction have drawn increasing attention from researchers both at home and abroad,and it has become a research hotspot.Despite the fact that the multi-objective particle swarm optimization algorithm is widely used,there are still some critical issues that need to be addressed.We should not only solve general problems like the unbalanced relationship between diversity and convergence and easily falling into local optimum,but also consider exclusive problems like optimal particle selection strategy,archive sets maintenance method,and diversity retention mechanism.For constrained optimization problems,it is necessary to consider not only the balance of objectives and constraints,optimality and feasibility,but also to avoid over-searching of feasible areas and strengthen exploration of constrained boundary areas.This paper focuses on constrained single-objective,unconstrained multiobjective and constrained multi-objective problems.The multi-objective particle swarm optimization algorithm is improved from different perspectives,and these modified algorithms are applied to mine production.The main contributions are summarized as follows:Firstly,a TBC-PSO(Two-stage Constrained Particle Swarm Optimization Based on Bi-objective Method)is put forward for the constrained single-objective optimization problem.The entire optimization process is split into two stages of adaptive switching,each with its own strategies of optimization algorithms.Afterwords,the target-constraint space is divided based on angle.The entire space is divided in the first stage,and the feasible area is fully developed.The partial space is partitioned in the second stage,and the partial region is thoroughly searched.Different optimal particle selection strategies are adopted in each stage.Besides,primary and secondary external archive sets are created to extract infeasible solution information and promote the maintenance of population diversity.In addition,the algorithm is applied to CEC2006 and CEC2017 test sets for simulation experiments,in order to verify the advantages of the proposed algorithm by nonparametric statistical test.Secondly,an AAD-MOPSO(Multi-objective Particle Swarm Optimization Based on Adaptive Angle Devision)is proposed for solving the unconstrained multi-objective optimization problem.In the early stage,particles are guided by boundary particles to improve the uniformity of population distribution.Then,the angle is adaptively adjusted based on the number of particles,and the region is divided in the target space.Furthermore,select the optimal particles and maintain the external storage set according to the distribution of particles in the region,so as to maintain good population diversity and improve the coverage of the optimal solution set.In addition,for areas without particle distribution,the search is enhanced by using particles in adjacent areas.Moreover,numerical simulation is carried out in ZDT test function set to verify the good distribution of the optimal solution set obtained by the algorithm and its effectiveness in maintaining population diversity.Compared with the comparison algorithm,the superiority of the proposed algorithm is shown.Thirdly,an ICDC-MOPSO(Multi-objective Particle Swarm Optimization Algorithm Based on Improved Constraint Dominance Criterion)is proposed to solve the constrained multi-objective optimization problem.To sustain population variety,the adaptive angle zoning approach is integrated into the constraint evaluation criteria,and the infeasible solution information is extracted.Following that,the double external archive sets mechanism is developed,and the search for constrained border regions is strengthened by retaining infeasible solutions.Thereafter,the optimal particle is chosen,and the relationship between global development and local search is coordinated on the basis of particle distribution.Additionally,the proposed algorithm's effectiveness is also confirmed by evaluating the standard function set.It demonstrates that the algorithm has certain advantages in contrast to the comparison algorithm.Finally,in view of the practical optimization problems in mine production,TBC-PSO algorithm and ICDC-MOPSO algorithm are applied to solve the constrained single-objective problem and constrained multi-objective problem.On the question of the scheduling optimization of mining and beneficiation,the production schedule model between mining fields and concentrators is established on the basis of fully considering the constraints of production plan and technical ability.In order to reduce the variable cost per unit of iron concentrate,TBC-PSO algorithm is applied to optimize the production schedule and a reasonable mining and ore dressing scheme is formulated.Aiming at the optimization of sintering burden,combining with the actual raw material information of a domestic iron and steel plant,considering the constraints of production requirements and composition content,the mechanism model of sintering burden system is constructed.Taking into account the two objectives of minimizing the cost of mixed materials and maximizing the total iron content,the proposed ICDC-MOPSO algorithm is utilized to the ore blending process,and the sintering burden optimization scheme is obtained.It can effectively reduce the cost of sintering burden while increasing the total iron content,which is of momentous significance to the comprehensive utilization and quality assurance of sintered iron ore resources.The application of the two improved algorithms in mine production shows practicability of the modified multi-objective particle swarm optimization algorithms.