The paper proposes an interactive co-evolutionary genetic algorithm (IGA) for multi-objective optimization problems, particularly focusing on the graph layout problem. The IGA maintains two populations: a graph layout population and a weight-set population. Each population evolves independently but is coupled through fitness evaluation, which involves user intervention. The fitness of the layout population is determined by how well it meets user preferences, while the fitness of the weight-set population is based on how closely it ranks the layouts according to the user's preferences. The process is repeated until a satisfactory graph layout is achieved. The paper discusses the background of multi-objective optimization, interactive evolutionary computation, and co-evolutionary algorithms. It also details the specific genetic algorithms used for each population and presents numerical experiments to demonstrate the approach's feasibility and performance. The results show that the IGA can effectively balance user preferences and objective criteria, leading to visually appealing graph layouts.The paper proposes an interactive co-evolutionary genetic algorithm (IGA) for multi-objective optimization problems, particularly focusing on the graph layout problem. The IGA maintains two populations: a graph layout population and a weight-set population. Each population evolves independently but is coupled through fitness evaluation, which involves user intervention. The fitness of the layout population is determined by how well it meets user preferences, while the fitness of the weight-set population is based on how closely it ranks the layouts according to the user's preferences. The process is repeated until a satisfactory graph layout is achieved. The paper discusses the background of multi-objective optimization, interactive evolutionary computation, and co-evolutionary algorithms. It also details the specific genetic algorithms used for each population and presents numerical experiments to demonstrate the approach's feasibility and performance. The results show that the IGA can effectively balance user preferences and objective criteria, leading to visually appealing graph layouts.