High field superconducting magnets are used in different power applications, such as nuclear magnetic resonance systems, thermonuclear fusion technologies and energy storage. These magnets have to fulfill high quality standards in terms of field uniformity and stability, by keeping construction costs and size as low as possible while respecting superconducting critical state constraints. The subject of this Thesis is the statement of models and resolution strategies for the optimal engineering design of such superconducting power devices. It is shown here that the design of such magnets can have a great benefit by the adoption of the multi-objectives optimisation techniques, in particular the evolutionary approaches such as the Genetic Algorithms. Stateof- the-art models and methods of multi-objective optimisation are presented and discussed and new strategies are proposed, able to be applied to industrial relevant problems. Beside the classical approach based on the definition of a scalar weighted-sum objective function to minimise, another strategy exploiting the concept of Pareto optimality is adopted in addition. A parallel optimisation environment is exploited to increase the computing performances of the proposed algorithms and to implement a distributed multi-populations Genetic Algorithm with migration and aggression genetic operators using new population indices. The concept of solution robustness in the design process is introduced to deal with the effect of manufacturing and assembling tolerances and suitable corrective strategies are proposed by adopting a new expression of the objective function and Monte Carlo analysis. The resolution strategy of inverse problems is similar to multi-objectives optimisation problems by properly defining an error functional: the attention is focused on non-destructive testing, where the task is to identify flaws in critical structural parts by using external measures of physical parameters. A benchmark for the eddy current testing problem is solved with the use of the concept of evolution by biological diversity. The previous methodologies are exploited with the development of two prototypes, a software tool (Marides) and a cluster computing environment (Beosun). The presented strategies have been then applied to test cases and real world industrial problems. In particular, to the design of an energy storage system and of both low and high critical temperature superconducting magnets used for magnetic resonance imaging.