Real ship structural design problems are usually characterized by presence of many conflicting objectives. Simultaneously, a complete definition of the optimum structural design requires a formulation of size-topology-shape-material optimization task unifying the optimization problems of the four areas and giving an effective solution of the problem. So far, a significant progress towards the solution of the problem has not been obtained. An objective of the present paper was to develop an evolutionary algorithm for multiobjective optimization of structural elements of large spatial sections of ships. Selected elements of the multi-criteria optimization theory have been presented in detail. Methods for solution of the multi-criteria optimization problems have been discussed with the focus on the evolutionary optimization algorithms. In the paper an evolutionary algorithm where selection takes place based on the aggregated objective function combined with domination attributes as well as distance to the asymptotic solution, is proposed and applied to solve the problem of optimizing structural elements with respect to their weight and surface area on a high speed vehicle-passenger catamaran structure, with several design variables, such as plate thickness, scantlings of longitudinal stiffeners and transverse frames, and spacing between longitudinal and transversal members, taken into account. Details of the computational models were at the level typical for conceptual design. Scantlings were analyzed by using selected rules of a classification society. The results of numerical experiments with the use of the developed algorithm, are presented. They show that the proposed genetic algorithm can be an efficient tool for multi-objective optimization of ship structures. The paper is published in three parts: Part I: Theoretical background on evolutionary multi-objective optimization, Part II: Computational investigations, and Part III: Analysis of the results