Diversifying Multi-Objective Gradient Techniques and their Role in Hybrid Multi-Objective Evolutionary Algorithms for Deformable Medical Image Registration

摘要

htmlabstractGradient methods and their value in single-objective, real-valued\udoptimization are well-established. As such, they play\uda key role in tackling real-world, hard optimization problems\udsuch as deformable image registration (DIR). A key question\udis to which extent gradient techniques can also play a role in\uda multi-objective approach to DIR. We therefore aim to exploit\udgradient information within an evolutionary-algorithm-based\udmulti-objective optimization framework for DIR. Although an\udanalytical description of the multi-objective gradient (the set\udof all Pareto-optimal improving directions) is\udavailable, it is nontrivial how to best choose the most\udappropriate direction per solution because these directions are\udnot necessarily uniformly distributed in objective space. To\udaddress this, we employ a Monte-Carlo method to obtain\uda discrete, spatially-uniformly distributed approximation of\udthe set of Pareto-optimal improving directions. We then\udapply a diversification technique in which each solution is\udassociated with a unique direction from this set based on its\udmulti- as well as single-objective rank. To assess its utility,\udwe compare a state-of-the-art multi-objective evolutionary\udalgorithm with three different hybrid versions thereof on\udseveral benchmark problems and two medical DIR problems.\udResults show that the diversification strategy successfully\udleads to unbiased improvement, helping an adaptive hybrid\udscheme solve all problems, but the evolutionary algorithm\udremains the most powerful optimization method, providing\udthe best balance between proximity and diversity.