of prosthesis--limb interfaces, surrogate modelling and optimisation. Genetic Algorithms are chosen due to their ability to effectively search large and complex design spaces, which is the problem presented by the continually variable distribution of possible limb--socket shape rectifications. These methods rely on thousands of function calls, and using FE models would not be feasible beyond single cases due to the time required for each simulation. However, by leveraging the speed increases of the surrogate model (Steer et al. [@CR37]), it becomes technically feasible to perform automated socket optimisation based upon structural analysis of the limb--prosthesis system. This provides the motivation for the current study, to perform a first-of-kind, subject-specific, multi-objective design optimisation of the prosthetic socket using the previously reported surrogate model. The result will be a series of personalised 'candidate' transtibial prosthetic socket designs, to which the prosthetist would add local modifications based upon their knowledge and conventional patient consultation. Finally, equipped with these results, a prosthetist would then further refine these concepts to achieve a desired pattern of prosthesis--limb load transfer, by using these designs to augment their experience-based decision-making.

Optimisation of transtibial prosthetic sockets {#Sec2}
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Population-based surrogate model {#Sec3}
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A detailed description of the population-based surrogate model is found in Part 1 of this paper (Steer et al. [@CR37]). In short, a generic residual limb was generated by producing a volume mesh from an MRI scan and imposing radial basis function mesh morphing to apply parametric variation in residuum length and profile (conical to bulbous) obtained from principal modes of variation from a population of 3D surface scans. These were varied by ± 1 $\documentclass[12pt]{minimal}
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