Path planning for surgical tools in minimally invasive surgery is a multi-objective optimization problem consisting in searching the best compromise between multiple placement constraints to find an optimal insertion point for the tool. Many works have been proposed to automate the decision-making process. Most of them use an aggregative approach that transforms the problem into a mono-objective problem. However, despite its intuitiveness, this approach is known for its incapacity to find all optimal solutions. In this work, we aim at maximizing the range of optimal solutions proposed to the surgeon. Our study compares three different optimization approaches: an aggregative method using a weighted sum of the multiple constraints, an evolutionary multi-objective method, and an exhaustive dominance-based method used as ground truth. For each approach, we extract the set of all optimal insertion points based on dominance rules, and analyze the common and differing solutions by comparing the surfaces they cover. The experiments have been performed on 30 images datasets from patients who underwent a Deep Brain Stimulation electrode implant in the brain. It can be observed that the areas covered by the optimal insertion points obtained by the three methods differ significantly. The obtained results show that the traditional weighted sum approach is not sufficient to find the totality of the optimal solutions. The Pareto-based approaches provide extra solutions, but neither of them could find the complete optimal solution space. Further works should investigate either hybrid or extended methods such as adaptive weighted sum, or hybrid visualization of the solutions in the GUI.
