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Fairness Driven Multi-Agent Path Finding Problem

Aditi Anand, Dildar Ali, Suman Banerjee

TL;DR

Considering the agents are rational, a mechanism is developed and demonstrated that it is a dominant strategy, incentive compatible, and individually rational and a heuristic solution for this problem is proposed.

Abstract

The Multi-Agent Path Finding (MAPF) problem aims at finding non-conflicting paths for multiple agents from their respective sources to destinations. This problem arises in multiple real-life situations, including robot motion planning and airspace assignment for unmanned aerial vehicle movement. The problem is computationally expensive, and adding to it, the agents are rational and can misreport their private information. In this paper, we study both variants of the problem under the realm of fairness. For the non-rational agents, we propose a heuristic solution for this problem. Considering the agents are rational, we develop a mechanism and demonstrate that it is a dominant strategy, incentive compatible, and individually rational. We employ various solution methodologies to highlight the effectiveness and efficiency of the proposed solution approaches.

Fairness Driven Multi-Agent Path Finding Problem

TL;DR

Considering the agents are rational, a mechanism is developed and demonstrated that it is a dominant strategy, incentive compatible, and individually rational and a heuristic solution for this problem is proposed.

Abstract

The Multi-Agent Path Finding (MAPF) problem aims at finding non-conflicting paths for multiple agents from their respective sources to destinations. This problem arises in multiple real-life situations, including robot motion planning and airspace assignment for unmanned aerial vehicle movement. The problem is computationally expensive, and adding to it, the agents are rational and can misreport their private information. In this paper, we study both variants of the problem under the realm of fairness. For the non-rational agents, we propose a heuristic solution for this problem. Considering the agents are rational, we develop a mechanism and demonstrate that it is a dominant strategy, incentive compatible, and individually rational. We employ various solution methodologies to highlight the effectiveness and efficiency of the proposed solution approaches.
Paper Structure (24 sections, 5 theorems, 5 equations, 2 figures, 1 table, 5 algorithms)

This paper contains 24 sections, 5 theorems, 5 equations, 2 figures, 1 table, 5 algorithms.

Table of Contents

  1. Introduction
  2. Background and Problem Set Up
  3. Basic Notations and Terminologies.
  4. Agents and Problem Instance.
  5. Welfare of an Agent.
  6. Conflict Constraints.
  7. Fairness in MAPF Problem
  8. Proposed Solution Approaches
  9. Fair Increasing Cost Tree Search
  10. Fair Conflict-Based Search
  11. Fairness Verification
  12. Mechanism for Rational Agents
  13. Mechanism Settings
  14. Mechanism.
  15. Experimental Evaluation
  16. ...and 9 more sections

Key Result

Theorem 1

Let $\mathcal{F}_{fair}$ denote the set of all fair and feasible joint plans. If there exists at least one feasible MAPF solution, then the Fair-ICTS algorithm terminates and returns an optimal fair joint plan $\Pi^\ast = \arg\max_{\Pi \in \mathcal{F}_{fair}} \sum_{i=1}^{\ell} W_i(\pi_i)$.

Figures (2)

  • Figure 1: (a) Environment graph $\mathcal{G}$, (b) individual agent DAGs $\mathcal{D}_1$ and $\mathcal{D}_2$, and (c) their joint DAG $\mathcal{D} = \mathcal{D}_1 \times \mathcal{D}_2$, with step bound 2.
  • Figure 2: Experimental results for the proposed algorithms on four benchmark MAPF environments. (a)--(e) correspond to the random32-32-20 map, (f)--(i) to empty48-48, (j) to den312d, and (k)--(l) to empty16-16. Specifically: (a) proportional fairness (success fraction), (b) proportional fairness (runtime), (c) $\epsilon$-envy fairness (runtime), (d) max--min fairness (success fraction), (e) max--min fairness (runtime) on random32-32-20; (f) proportional fairness (success fraction), (g) proportional fairness (runtime), (h) max--min fairness (success fraction), (i) max--min fairness (runtime) on empty48-48; (j) proportional fairness (runtime) on den312d; (k) max--min fairness (success fraction), and (l) max--min fairness (runtime) on empty16-16.

Theorems & Definitions (17)

  • Definition 1: Social Welfare
  • Definition 2: Feasible Path Assignment
  • Definition 3: Optimal Path Assignment
  • Definition 4: $\epsilon$-Envy Freeness
  • Definition 5: Max-min fairness
  • Definition 6: Proportional Fairness
  • Theorem 1
  • proof
  • Theorem 2
  • Theorem 3
  • ...and 7 more