Aiming at the difficulty in selecting stock valuation features and the lack of time series relational dimension features during the prediction of stock market volatility by intelligent algorithms such as Support Vector Machine （SVM） and Long Short-Term Memory （LSTM） network， in order to accurately predict stock volatility and effectively prevent financial market risks， a new stock market volatility prediction method based on Improved Genetic Algorithm （IGA） and Graph Neural Network （GNN） named IGA-GNN was proposed. Firstly， the data of stock market trading index graph was constructed based on the time series relation between adjacent trading days. Secondly， the characteristics of evaluation indexes were used to improve Genetic Algorithm （GA） by optimizing crossover and mutation probabilities， thereby realizing the node feature selection. Then， the weight matrix of edge and node features of graph data was established. Finally， the GNN was used for the aggregation and classification of graph data nodes， and the stock market volatility prediction was realized. In the experiment stage， the studied number of total evaluation indexes of stock was 130， and 87 effective evaluation indexes were extracted from the above by IGA under GNN method， making the number of stock evaluation indexes reduced by 33.08%. The proposed IGA was applied to the intelligent algorithms for feature extraction. The obtained algorithms has the overall prediction accuracy improved by 7.38 percentage points compared with the intelligent algorithms without feature extraction. Compared with applying the traditional GA for feature extraction of the intelligent algorithms， applying the proposed IGA for feature extraction of the intelligent algorithms has the total training time shortened by 17.97%. Among them， the prediction accuracy of IGA-GNN method is the highest， which is 19.62 percentage points higher than that of GNN method without feature extraction. Compared with the GNN method applying the traditional GA for feature extraction， the IGA-GNN method has the training time shortened by 15.97% on average. Experimental results show that， the proposed method can effectively extract stock features and has good prediction effect.

Evolutionary Algorithm based on State-space model (SEA) is a novel real-coded evolutionary algorithm, it has good optimization effects in engineering optimization problems. Global convergence of crossover SEA (SCEA) was studied to promote the theory and application research of SEA. The conclusion that SCEA is not global convergent was drawn. Modified Crossover Evolutionary Algorithm based on State-space Model (SMCEA) was presented by changing the comstruction way of state evolution matrix and introducing elastic search operation. SMCEA is global convergent was proved by homogeneous finite Markov chain. By using two test functions to experimental analysis, the results show that the SMCEA are improved substantially in such aspects as convergence rate, ability of reaching the optimal value and operation time. Then, the effectiveness of SMCEA is proved and that SMCEA is better than Genetic Algorithm (GA) and SCEA was concluded.

Evolutionary Algorithm based on State-space model (SEA) is a new evolutionary algorithm using real strings, and it has broad application prospects in engineering optimization problems. Global convergence of SEA was analyzed by homogeneous finite Markov chain to improve the theoretical system of SEA and promote the application research in engineering optimization problems of SEA. It was proved that SEA is not global convergent. Modified Elastic Evolutionary Algorithm based on State-space model (MESEA) was presented by limiting the value ranges of elements in state evolution matrix of SEA and introducing the elastic search. The analytical results show that search efficiency of SEA can be enhanced by introducing elastic search. The conclusion that MESEA is global convergent is drawn, and it provides theory basis for the application of algorithm in engineering optimization problems.