Among the approaches to multi-criteria decision making, Pareto navigation is a powerful, interactive tool that has been successfully applied to a variety of real-world problems with continuous decision variables, including chemical process design, drug manufacturing, logistical vehicle routing problems, and radiotherapy treatment planning. However, many real-life problems are formulated using both continuous and binary decision variables. In this work, we introduce patch navigation as an algorithmic concept that extends Pareto navigation to this type of problem where the number of binary variables is relatively small. The underlying idea is the navigation across a finite set of individual, convex fronts each associated with a specific configuration of the binary variables (patches). We show how the user interactions employed in current Pareto front navigation, namely selection and restriction, can be adopted to handle multiple patches. These routines enable the decision maker (DM) to change the solution in small increments while controlling the related trade-offs. We also describe additional, patch-specific routines that enable the DM to consider only an individually chosen subset of patches in the navigation. To illustrate patch navigation, and to demonstrate its usefulness for real-life problems, we present numerical examples of patch navigation along with an application motivated by radiotherapy planning.

中文翻译：

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多个凸面块的交互式导航

在多准则决策方法中，帕累托导航是一种强大的交互式工具，已成功应用于具有连续决策变量的各种现实问题，包括化学工艺设计、药物制造、物流车辆路线问题和放射治疗计划。然而，许多现实生活中的问题都是使用连续和二元决策变量来制定的。在这项工作中，我们引入补丁导航作为一种算法概念，将帕累托导航扩展到这种类型的问题，其中二进制变量的数量相对较少。基本思想是在一组有限的单个凸前沿上导航，每个凸前沿都与二进制变量的特定配置相关联（补丁）。我们展示了如何采用当前 Pareto 前端导航中使用的用户交互，即选择和限制，来处理多个补丁。这些例程使决策者 (DM) 能够在控制相关权衡的同时以小增量更改解决方案。我们还描述了额外的、特定于补丁的例程，使 DM 能够在导航中仅考虑单独选择的补丁子集。为了说明贴片导航并证明其对现实问题的有用性，我们提供了贴片导航的数值示例以及由放射治疗计划推动的应用程序。