Discrete Route/Trajectory Decision Making Problems

TL;DR

This paper explores discrete, multistage decision making problems for designing routes or trajectories across various domains, using combinatorial models and illustrating with practical examples like education, startups, and medical treatment.

Contribution

It introduces a comprehensive framework for modeling and solving complex multi-route decision problems with multiple goals and domains, expanding on existing routing methodologies.

Findings

Numerical examples demonstrate the approach's effectiveness.

Applications include educational, startup, and medical planning.

Modeling techniques facilitate design space construction.

Abstract

The paper focuses on composite multistage decision making problems which are targeted to design a route/trajectory from an initial decision situation (origin) to goal (destination) decision situation(s). Automobile routing problem is considered as a basic physical metaphor. The problems are based on a discrete (combinatorial) operations/states design/solving space (e.g., digraph). The described types of discrete decision making problems can be considered as intelligent design of a route (trajectory, strategy) and can be used in many domains: (a) education (planning of student educational trajectory), (b) medicine (medical treatment), (c) economics (trajectory of start-up development). Several types of the route decision making problems are described: (i) basic route decision making, (ii) multi-goal route decision making, (iii) multi-route decision making, (iv) multi-route decision making with route/trajectory change(s), (v) composite multi-route decision making (solution is a composition of several routes/trajectories at several corresponding domains), and (vi) composite multi-route decision making with coordinated routes/trajectories. In addition, problems of modeling and building the design spaces are considered. Numerical examples illustrate the suggested approach. Three applications are considered: educational trajectory (orienteering problem), plan of start-up company (modular three-stage design), and plan of medical treatment (planning over digraph with two-component vertices).