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Group Trip Planning Query Problem with Multimodal Journey

Dildar Ali, Suman Banerjee, Yamuna Prasad

TL;DR

This work extends the Group Trip Planning Query Problem by incorporating multimodal journey options, formulating a formal model with PoI categories and multiple transport modalities. It presents a dynamic programming–based algorithm that builds a multi-graph, computes a common intermediate path across categories, and minimizes a group-specific cost that accounts for individual and shared legs. The approach is analyzed theoretically for time and space complexity and validated on real GTFS datasets from Switzerland and Helsinki, showing consistent cost reductions over baseline methods (RPRM, RPCM, NNCM) and providing insights into modality usage and scalability. The results underscore the practical value of jointly optimizing PoI selections and travel modalities for group routing in multimodal urban networks, with future work addressing fairness and broader applicability.

Abstract

In Group Trip Planning (GTP) Query Problem, we are given a city road network where a number of Points of Interest (PoI) have been marked with their respective categories (e.g., Cafeteria, Park, Movie Theater, etc.). A group of agents want to visit one PoI from every category from their respective starting location and once finished, they want to reach their respective destinations. This problem asks which PoI from every category should be chosen so that the aggregated travel cost of the group is minimized. This problem has been studied extensively in the last decade, and several solution approaches have been proposed. However, to the best of our knowledge, none of the existing studies have considered the different modalities of the journey, which makes the problem more practical. To bridge this gap, we introduce and study the GTP Query Problem with Multimodal Journey in this paper. Along with the other inputs of the GTP Query Problem, we are also given the different modalities of the journey that are available and their respective cost. Now, the problem is not only to select the PoIs from respective categories but also to select the modality of the journey. For this problem, we have proposed an efficient solution approach, which has been analyzed to understand their time and space requirements. A large number of experiments have been conducted using real-life datasets and the results have been reported. From the results, we observe that the PoIs and modality of journey recommended by the proposed solution approach lead to much less time and cost than the baseline methods.

Group Trip Planning Query Problem with Multimodal Journey

TL;DR

This work extends the Group Trip Planning Query Problem by incorporating multimodal journey options, formulating a formal model with PoI categories and multiple transport modalities. It presents a dynamic programming–based algorithm that builds a multi-graph, computes a common intermediate path across categories, and minimizes a group-specific cost that accounts for individual and shared legs. The approach is analyzed theoretically for time and space complexity and validated on real GTFS datasets from Switzerland and Helsinki, showing consistent cost reductions over baseline methods (RPRM, RPCM, NNCM) and providing insights into modality usage and scalability. The results underscore the practical value of jointly optimizing PoI selections and travel modalities for group routing in multimodal urban networks, with future work addressing fairness and broader applicability.

Abstract

In Group Trip Planning (GTP) Query Problem, we are given a city road network where a number of Points of Interest (PoI) have been marked with their respective categories (e.g., Cafeteria, Park, Movie Theater, etc.). A group of agents want to visit one PoI from every category from their respective starting location and once finished, they want to reach their respective destinations. This problem asks which PoI from every category should be chosen so that the aggregated travel cost of the group is minimized. This problem has been studied extensively in the last decade, and several solution approaches have been proposed. However, to the best of our knowledge, none of the existing studies have considered the different modalities of the journey, which makes the problem more practical. To bridge this gap, we introduce and study the GTP Query Problem with Multimodal Journey in this paper. Along with the other inputs of the GTP Query Problem, we are also given the different modalities of the journey that are available and their respective cost. Now, the problem is not only to select the PoIs from respective categories but also to select the modality of the journey. For this problem, we have proposed an efficient solution approach, which has been analyzed to understand their time and space requirements. A large number of experiments have been conducted using real-life datasets and the results have been reported. From the results, we observe that the PoIs and modality of journey recommended by the proposed solution approach lead to much less time and cost than the baseline methods.

Paper Structure

This paper contains 20 sections, 3 theorems, 8 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Problem Definition
  3. Road Network
  4. Group Trip Planning Query Problem
  5. Multi Modal Journey
  6. GTP Query Problem with Multi Modal Journey
  7. Proposed Approach
  8. Complexity Analysis of Algorithm \ref{['Alg:optimal_journey']}
  9. An Illustrative Example
  10. Experimental Evaluation
  11. Dataset Description.
  12. Environment and Key Parameter Setup.
  13. Baseline Methodologies.
  14. Goals of our Experiments.
  15. Experimental Results and Discussions.
  16. ...and 5 more sections

Key Result

theorem thmcountertheorem

The Algorithm Alg:optimal_journey always terminates within a finite number of steps for any valid input graph $\mathcal{G}$.

Figures (3)

  • Figure 1: Road network with categories $C_1$ to $C_5$.
  • Figure 2: Varying $|\mathcal{U}|$ Vs. Usage of transport medium in Switzerland $(a,b,c,d,e)$ and in Finland $(f,g,h,i,j)$, Varying No. of PoI Vs. Cost (k) and Varying No. of PoI Vs. Time $(\ell)$ for Switzerland dataset
  • Figure 3: Varying $|\mathcal{U}|$ in Switzerland $(a,b)$ and in Finland $(c,d)$

Theorems & Definitions (14)

  • definition thmcounterdefinition: Valid Path
  • definition thmcounterdefinition: GTP Query Problem
  • definition thmcounterdefinition: Route
  • definition thmcounterdefinition: Journey Planning
  • definition thmcounterdefinition: Cost of a Journey Planning
  • definition thmcounterdefinition: Minimum Cost Journey Planning
  • definition thmcounterdefinition: The Cost of the Group
  • definition thmcounterdefinition: GTP Query with Multi Modal Journey Problem
  • theorem thmcountertheorem
  • proof
  • ...and 4 more