Improved Multi-objective Optimization Algorithm And Its Application In The Desulfurization Process

Multi-objective optimization problems,which require the simultaneous optimization of numerous conflicting objective functions,are common in scientific research and practical engineering.An intelligent optimization algorithm does not require extensive prior information and can generate a set of compromise solutions in a single operation,making it one of the most successful methods for solving multiobjective optimization problems.However,multi-objective optimization algorithms face significant difficulties when handling optimization problems with a variety of characteristics,which are primarily reflected in: 1)When tackling challenging multiobjective optimization problems,it is challenging to balance convergence and variety while searching the effective space.2)In practical engineering,the dimension of the objective that must be optimized keeps increasing,the characteristics of the problem become more complex,and the challenges of solving in high-dimensional objective space are numerous,including the recombination operator’s lack of expressiveness,the degradation of selection pressure,the sharp increase in convergence and diversity contradictions,and the challenge of adapting to the frontier of different shapes,which further complicates the problem.3)Since many real-world optimization problems involve costly experiments or time-consuming simulations,using optimization algorithms to solve them typically necessitates a significant amount of real evaluation,which lowers optimization efficiency.As a result,this paper addresses the challenges of resolving complex multi-objective,many-objective,and expensive multi-objective optimization problems with poor search mechanism effectiveness and the challenge of balancing convergence and diversity,and conducts research from algorithm design to experimental simulation to practical application,with the following main work:(1)A multi-objective particle swarm optimization algorithm based on enhanced selectionIn order to tackle the challenge of striking a balance between convergence and diversity in multi-objective optimization problems with complicated characteristics,a multi-objective particle swarm optimization algorithm based on an enhanced selection strategy.The algorithm uses the adjustable weight vector strategy to direct the update of individual optimal particles to improve the population’s local exploitation ability.The weighting method of the objective function is proposed to guide the update of global optimal particles,and the weighting strategy enhances the global exploration ability.The R2 indicator fast ranking mechanism guides the update of archive set to promote the balance of population convergence and diversity.The simulation results demonstrate the effectiveness of the proposed algorithm in solving challenging multiobjective optimization problems,improving the search for useful space,and achieving convergence while maintaining diversity.(2)An achievement scalarizing function sorting for strength Pareto evolutionary algorithm in many-objective optimizationAn achievement scalarizing function sorting for strength Pareto evolutionary algorithm in many-objective optimization is proposed to address the issues of degradation of selection pressure,difficulty in convergence,and difficulty in maintaining diversity in regular many-objective optimization problems.A new fitness value method that merges reference vectors is applied to the classical strengthdominated evolutionary algorithm to reinforce the relationships between individuals.The searchability of the population in the reference vector’s direction is improved by measuring diversity as the distance between individuals and a reference vector with uniform distribution.Second,the environment selection is performed using an achievement scalarizing function sorting technique.The population is separated into several clusters based on the distance between each individual and the reference vector,and the individual scalar function value is calculated in the smaller population to speed up convergence.The next generation population is chosen from the lower frontier individuals to improve the selection pressure and improve the population diversity.The simulation results show that the proposed algorithm can effectively enhance the selection pressure in the regular many-objective space and improve the ability of balanced convergence and diversity.(3)A strength Pareto evolutionary algorithm based on adaptive reference pointsA strength Pareto evolutionary algorithm based on adaptive reference points is proposed to address the issues of difficult to search the entire frontier,insufficient selection pressure,and difficult to balance convergence and diversity in highdimensional irregular multi-objective optimization problems.In this algorithm,the angle distance scaling function is used in the matching strategy to improve the population search ability and guide the population to explore and exploit the objective space.Second,the active solution and active reference point information are obtained by making full use of the current population information to adjust the distribution of reference points.The population is then made more able to adapt to the irregular Pareto frontier by converting the individuals in the elite solution concentration to a sparse reference point regional plane.Finally,the two-criterion strategy is used to increase the selection pressure in environment selection.The first criterion to enhance population convergence is the angle distance scaling function,and the second criterion to preserve population variety is angle-based selection.The results of the simulations demonstrate that the suggested algorithm can efficiently explore the irregular frontier space in the irregular many-objective space,enhance the selection pressure,and balance the population’s overall performance.(4)A weighted uncertainty measure-based surrogate-assisted evolutionary algorithmA weighted uncertainty measure-based surrogate-assisted evolutionary algorithm is proposed for expensive many-objective optimization problems with difficult to converge and unevenly distributed solution sets within a limited number of evaluations.In this algorithm,the uncertainty information calculated by different Kriging models is weighted to make the model output approximate to the objective function values,which reduces the expensive evaluation of the algorithm and improves the accuracy of the prediction.The fill sampling criteria based on adaptive reference points identify people who match the convergence and diversity requirements.This method identifies active reference sites and individuals,predicts the general frontier model using current population information and then selects fill sampling solutions based on the angle between active and candidate solutions.In order to increase the model’s training accuracy,expensive objective functions are then used to evaluate the infill sampling solutions before they are added to the training set.The simulation results demonstrate that the proposed algorithm achieves uniform distribution and convergence in an expensive many-objective space with limited evaluations.(5)Multi-objective optimization of wet flue gas desulfurization processThe optimization of the limestone wet flue gas desulfurization process is a typical multi-objective optimization problem.In order to provide a dependable energysaving and consumption-reduction schedule for the industrial wet flue gas desulfurization process,this paper aims to improve the environmental performance of desulfurization and decrease energy and material consumption.Two Many-objective optimization algorithms are applied to the optimization of the limestone wet flue gas desulfurization process.The simulation results show that the optimized candidate solutions of the wet FGD process optimization problem can reduce energy consumption and material consumption while ensuring the satisfaction of environmental performance,which has a certain guiding significance in the actual industrial process.