Grouping Microscale Searching Algorithm For Large-scale Optimization And Its Application

Intelligent optimization is a kind of heuristic optimization algorithm that can solve problems by simulating the evolution law of nature or the behavior of biological groups.It has the advantages of global optimization,strong search ability,and strong adaptability,so it can be used to solve large-scale optimization problems with complex search space and difficulty in constructing optimization targets.Therefore,research on intelligent optimization algorithms has received increasing attention in recent years.However,due to the inherent complexity of large-scale optimization problems such as high dimensionality of decision space,complex search space,and randomness,intelligent optimization algorithms have low efficiency for solving large-scale optimization problems.For the two classical problems of microwave filter tuning and high-resolution image matting,this work proposes the idea and method of microscale(small-size subsets of the decomposed decision set)searching algorithms,and discusses and verifies the proposed method theoretically and experimentally.The main research contents are as follows:1)For the large-scale search space optimization problem,a mathematical model of the large-scale optimization problem is established based on the idea of solving the problem in groups.The model can describe the decomposition law of optimization problem,and provides the design basis of microscale searching algorithms for solving different large-scale optimization problems.With the model,we propose the concept of effective decision subspace and the framework of microscale searching algorithms.To analyze the performance of microscale searching algorithms,this work proposes a performance comparison model of microscale searching algorithms for the stochastic process theory of expected first hitting time.Under the assumption of microscale search,we prove that the intelligent optimization algorithm based on the microscale search outperforms the original algorithm.2)For the large-scale decision space optimization problem,this work proposes a mathematical model of grouping optimization for the high-resolution image matting.Based on this model,we design a decision space grouping optimization strategy to achieve effective dimensionality reduction of large-scale optimization problem for high-resolution images.Furthermore,we propose a group optimization strategy for collaborative objective feedback to achieve group collaborative solutions of large-scale decision space optimization problems by feeding back the optimal foreground background pixel pairs in the cooperative objective to each group.With the strategy,this work designs a high-definition matting algorithm based on decision space grouping microscale search from the perspectives of decision space clustering and grouping optimization,inter-group association optimization and multi-scale optimization.The algorithm solves the solving efficiency of large-scale optimization problem for highdefinition image matting by optimizing the small-scale optimization problem step by step.Experimental results show that the proposed high-definition matting algorithm based on decision space grouping microscale search can significantly reduce the problem size and improve the quality of high-definition image matting compared with the typical optimization algorithm with grouping strategies.3)For the large-scale objective space optimization problem,this work proposes a mathematical model of coupling matrix optimization to find the accurate coupling matrix for multi-version microwave filters,a core step of automated microwave filter tuning.To solve the problem of strong correlations between coupling matrix elements,we design a decision set grouping strategy,which solves the decomposition of large-scale objective space problem by dividing the whole frequency interval of coupling matrix transformation into multiple subintervals(coupling matrix elements grouping).With the strategy,we design a grouped microscale searching algorithm of coupling matrix optimization,which solves each suboptimization problem by searching the decision subset instead of the whole decision set.The experimental results show that the proposed grouping microscale searching algorithm of coupling matrix optimization is feasible within the industrial error for the multiple-version microwave filter tuning problem.Besides,the proposed algorithm outperforms the state-ofthe-art optimization algorithms in the large-scale objective space optimization problem(coupling matrix optimization problem).