In view of the problem of uneven load distribution and energy consumption among nodes in a multi-hop wireless sensor network, this research constructs the routing schedule problem as a MOP (Multi-objective Optimization Problem), and proposed an energy-aware routing optimization scheme RDSEGA based on multi-objective optimization. In this scheme, in order to avoid the searching space explosion problem caused by the increase of nodes, KSP Yen's algorithm was applied to prune the searching space, and the candidate paths selected after pruning are recoded based on priority. Then adopted the improved strengthen elitist genetic algorithm to get the entire network routing optimization scheme with the best energy efficiency. At the same time, in view of the problem of routing discontinuity in the process of path crossover and mutation, new crossover and mutation method was proposed that based on the gene fragments connected by the adjacent node or the same node to maximize the effectiveness of the evolution result. The experimental results prove that the scheme reduced the energy consumption of nodes in the network, the load between nodes becomes more balanced, and the working time of the network has been prolonged nearly 40% after the optimization. This brings convenience to practical applications, especially for those that are inconvenient to replace nodes.