In real life,core issues in many fields such as natural sciences,engineering applications,and economic management ultimately boil down to optimization problems.With the development of technology,the emergence of "dimensional disaster" and the universality of data make some optimization problems have hundreds of variables.Some classic optimization algorithms can't achieve better results when dealing with such problems.So many researchers have listed this type of optimization problem separately,called high-dimensional optimization problem.Evolutionary algorithms,or "evolutionary algorithms",are considered to be a general solution to solve optimization problems.They have the characteristics of fast convergence and strong global search ability,and have good performance on general low-dimensional optimization problems.However,when dealing with high-dimensional optimization problems,the optimization performance of these traditional evolutionary algorithms drops sharply as the search space grows exponentially with the number of decision variables growing.Cooperative Coevolution is an algorithmic framework for solving high-dimensional optimization problems by grouping decision variables.The core idea is to group decision variables,and to decompose the original problem into several sub-problems based on the idea of “divide and conquer” and solve them with good evolution algorithm.Compared with the strategy of cooperative coevolution,another idea is to integrate other mechanisms such as local search in the classical evolutionary algorithm,and treat the high-dimensional optimization problem as a whole and also has achieved a series of research results.This paper is based on these two ideas and has carried out in-depth research on the high-dimensional optimization problem.(1)A Solis&Wets-Opposition-based Learning Competitive Swarm Optimization(SWOBLCSO)algorithm is studied.SW-OBLCSO introduces a reverse learning mechanism and a local search strategy in the competitive learning mechanism.The algorithm has good global exploration and local development capabilities.The experimental results on 10 benchmark functions in 100,500,1000 dimensions show that the proposed algorithm not only has better optimization performance in small and medium-sized optimization problems,but also has good high-dimensional scalability;Test on fuzzy cognitive maps(Fuzzy Cognitive Maps,FCM)learning problems shows that the SW-OBLCSO algorithm also maintains good performance when solving real high-dimensional optimization problems.(2)A Random Project-Social Learning Particle Swarm Optimization(RP-SLPSO)algorithm is designed,which randomly selects several decision variable spaces by random projection strategy to generate a new search subspace and dynamically adjusts the size of the subspace,then the SLPSO algorithm is used as a suboptimizer to search the subspace to get the optimal position on the subspace,and an interrupt mechanism is introduced in the search process to improve the utilization of the evaluation times.The solution of the sub-problem obtained by SLPSO algorithm is projected back to the original problem.As the number of projections increases,the whole problem is optimized.This random projection method can effectively reduce the complexity of the problem and enable the SLPSO algorithm have the ability of solving high-dimensional optimization problems.Experiments were carried out on 15 high-dimensional global optimization test functions of CEC'2013LSGO,and the experimental results were compared with several mainstream algorithms.The experimental results show that the RP-SLPSO algorithm has faster convergence speed and higher precision.The experimental results on high-dimensional FCM learning problems show that the RP-SLPSO algorithm is also effective for practical complex optimization problems.This paper makes an in-depth study on the non-cooperative collaborative evolution framework and the cooperative coevolution framework,and proposes two algorithms,local search-based reverse learning competitive particle swarm optimization algorithm and random projection-based social learning particle swarm optimization algorithm.The former has a remarkable optimization effect on low-dimensional and medium-dimensional optimization problems,and maintains excellent performance on high-dimensional optimization problems;the latter shows good performance on 1000-dimensional large-scale global optimization problems.Applying two algorithms to the actual complex optimization problems respectively and both have achieved good results. |