One of the basic engineering optimization problems is the problem of improving a prototype. This problem is constantly encountered by industrial and academic organizations that produce and design various objects (e.g., motor vehicles, machine tools, ships, and aircraft). This paper presents an approach for improving a prototype by construction of the feasible and Pareto sets while performing multicriteria analysis. We introduce visualization methods that facilitate constructing the feasible and Pareto sets. Using these techniques, an expert can correctly state and solve the problem under consideration in a series of dialogs with the computer. Finally, we present a case study of applying these methods to a problem of improving a prototype of the ship.