Coevolution Based Particle Swarm Optimization Algorithm For Mixed-Variable Optimization Problems

Optimization problems such as industrial production,financial investment and resource scheduling in the real world usually involve mixed types of decision variables,i.e.,continuous variables and discrete variables.This kind of optimization problems with mixed variables are called Mixed-Variable Optimization Problems(MVOPs).Evolutionary Algorithms(EAs)are widely used to solve various optimization problems because of their simplicity and effectiveness.However,the current evolutionary algorithm cannot efficiently solve the MVOPs.On the one hand,the mixed variables of the MVOPs increase the complexity of the problem space and increase the difficulty of the algorithm search;on the other hand,the reproduction operators with poor performance or the performance inconsistency among multiple reproduction operators may result in premature convergence and reduce the efficiency of the algorithm.Particle Swarm Optimization(PSO)is an evolutionary algorithm that has been widely studied and applied.However,few algorithms based on PSO for MVOPs have been proposed.Co-evolution strategy(CES)is a strategy widely used in the design of evolutionary algorithms.Competitive or cooperative operators designed based on co-evolution strategies can improve the search efficiency of the algorithm and improve the overall performance of the algorithm.Therefore,in order to solve the MVOPs more efficiently,this paper introduces the co-evolution strategy to study the particle swarm optimization algorithm to solve the MVOPs.The specific research work includes the following three points.1)In order to solve the problem of PSO premature convergence,this paper proposes a competitive coevolution based particle swarm optimization,CCPSO.CCPSO handles mixed variables based on relaxation methods and uses continuous variable reproduction operators to generate particles.In order to improve the diversity of the population,CCPSO uses a competitive coevolution based learning object generation mechanism(CELOG)to generate special learning objects for particles.At the same time,this paper proposes a competitive learning based prediction strategy(CLP)to select suitable learning objects for particles,which fully makes use of the evolutionary potential of the learning objects to improve the convergence rate of the algorithm.In order to balance diversity and convergence,CCPSO proposes a tolerance based search direction adjustment mechanism(TSDM),which makes full use of the evolutionary potential of the learning object while avoiding the particle swarm falling into local optimum.2)Since the algorithm based on the relaxation method is not suitable for solving all MVOPs,when the discrete variables are out of order,the performance of this type of algorithm will significantly decrease.In order to solve the MVOPs more efficiently,this paper further proposes a cooperative coevolution based mixed variable particle swarm optimization algorithm,PSOmv.PSOmv uses a mixed variable encoding scheme and groups variables based on a cooperative coevolution framework.PSOmv uses continuous variable reproduction operator PSO-c and discrete variable reproduction operator PSO-d to handle mixed variables.PSO-c uses a population sorting mechanism to randomly select learning objects for each particle.This mechanism improves the diversity of the particle swarm while ensuring the particle convergence speed.PSO-d generates particles based on statistical methods.The update process of the distribution probability of each discrete variable will fully consider the historical search information and current information of the particle swarm.The particles of different subpopulations generated by PSO-c and PSO-d can obtain the solution to the original problem through cooperation.PSOmv uses a random sampling based individual estimation method(RSIE)to select cooperative particles.This method can greatly improve the cooperation efficiency between particles and achieve an effective balance between evaluation accuracy and evaluation efficiency.3)In order to further expand the application scenarios of the coevolution based mixed variable particle swarm optimization algorithm,this paper combines the practical problem of cooperative multi-task scheduling of unmanned aerial vehicles,and proposes a multiple constraints and objectives cooperative multi-task assignment problem model of unmanned aerial vehicles(M-CMTAP)and the co-evolution based mixed variable particle swarm optimization algorithm.The M-CMTAP model considers a variety of constraints and optimization objectives.The decision variables include continuous variables and discrete variables.In order to solve the model,this paper proposes Coevolution based Multi-Objective Optimization Particle Swarm Optimization(C-MOPSO).C-MOPSO adopts task assignment and path planning based encoding method(TAPPE)to represent the task assignment results and path planning results of the UAV;and the constraints handling based feasible solution initialization method(CHFSI)to generates feasible particles;and structure learning based reproduction method(SLR)to update the particles.In order to further accelerate the search efficiency of the algorithm,C-MOPSO introduces the idea of coevolution to conduct cooperative evolution between the two subpopulations.In order to verify the performance of the algorithms proposed in this paper,this paper did sufficient experiments based on test functions and examples.Experimental results show that the algorithms proposed in this paper are superior in performance,and verify the effectiveness of the coevolution strategy proposed in this paper when solving MVOPs.