This paper proposes an interactive co-evolutionary genetic algorithm (IGA) for multi-objective optimization problems, specifically applied to the graph layout problem. The algorithm maintains two populations: one for graph layouts and another for weight sets. The graph layout population evolves using a genetic algorithm to find aesthetically pleasing layouts, while the weight set population evolves based on how well the weights reflect the user's preferences. The fitness of the layout population depends on the current set of weights, which in turn depends on the evolution of the weight population. The weight population's fitness is determined by how closely its ranking of the layout population matches the user's ranking. The algorithm uses a co-evolutionary approach where the user's preferences are incorporated into the fitness function. The user ranks a sample of layouts, and the weight population evolves to match this ranking. The layout population is then allowed to evolve using the newly found weights. This process is repeated until a satisfactory layout is achieved. The genetic algorithm for the weight population uses a rank-based selection scheme and evaluates the fitness of weight sets based on their ability to rank the layout population according to the user's preferences. The algorithm also includes mutation operators to perturb the weights and improve the fitness function. The genetic algorithm for the layout population uses a standard generational approach, where each candidate solution is encoded as a real vector of vertex coordinates. The algorithm optimizes for several aesthetic criteria, including energy functions and other metrics. Mutation operators are used to perturb the coordinates of vertices, and the algorithm avoids crossover due to the difficulty of combining equivalent layouts. The algorithm was tested on a simple planar graph, and the results showed that the proposed IGA can effectively incorporate user preferences into the layout process, leading to layouts that reflect the user's subjective preferences. The algorithm is able to handle multi-objective optimization problems by co-evolving the layout and weight populations, allowing for a more interactive and user-driven approach to optimization.This paper proposes an interactive co-evolutionary genetic algorithm (IGA) for multi-objective optimization problems, specifically applied to the graph layout problem. The algorithm maintains two populations: one for graph layouts and another for weight sets. The graph layout population evolves using a genetic algorithm to find aesthetically pleasing layouts, while the weight set population evolves based on how well the weights reflect the user's preferences. The fitness of the layout population depends on the current set of weights, which in turn depends on the evolution of the weight population. The weight population's fitness is determined by how closely its ranking of the layout population matches the user's ranking. The algorithm uses a co-evolutionary approach where the user's preferences are incorporated into the fitness function. The user ranks a sample of layouts, and the weight population evolves to match this ranking. The layout population is then allowed to evolve using the newly found weights. This process is repeated until a satisfactory layout is achieved. The genetic algorithm for the weight population uses a rank-based selection scheme and evaluates the fitness of weight sets based on their ability to rank the layout population according to the user's preferences. The algorithm also includes mutation operators to perturb the weights and improve the fitness function. The genetic algorithm for the layout population uses a standard generational approach, where each candidate solution is encoded as a real vector of vertex coordinates. The algorithm optimizes for several aesthetic criteria, including energy functions and other metrics. Mutation operators are used to perturb the coordinates of vertices, and the algorithm avoids crossover due to the difficulty of combining equivalent layouts. The algorithm was tested on a simple planar graph, and the results showed that the proposed IGA can effectively incorporate user preferences into the layout process, leading to layouts that reflect the user's subjective preferences. The algorithm is able to handle multi-objective optimization problems by co-evolving the layout and weight populations, allowing for a more interactive and user-driven approach to optimization.