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Multi-Objective Search: Algorithms, Applications, and Emerging Directions

Oren Salzman, Carlos Hernández Ulloa, Ariel Felner, Sven Koenig

TL;DR

This paper addresses the challenge of balancing multiple objectives in decision-making by surveying the MOS landscape, including exact, approximate, anytime, and dynamic variants, as well as extensions beyond deterministic MOS. It clarifies foundational notions (e.g., PF, dominance, and epsilon-approximation) and details algorithmic progress (MO-A*, NAMOA-dr, A^*pex, MVH/BO-DHs), along with practical toolbox applications in MO-MST, MO-MAPF, and CSP. The authors review emerging applications in automated design, multi-modal planning, and robotics, and identify open challenges such as scalability, dynamic environments, preference elicitation, cross-domain cross-fertilization, and benchmarks. The work highlights the practical significance of MOS for real-world systems, where trade-offs between time, cost, safety, and other criteria must be navigated, and argues for greater cross-community collaboration and benchmark development to accelerate progress.

Abstract

Multi-objective search (MOS) has emerged as a unifying framework for planning and decision-making problems where multiple, often conflicting, criteria must be balanced. While the problem has been studied for decades, recent years have seen renewed interest in the topic across AI applications such as robotics, transportation, and operations research, reflecting the reality that real-world systems rarely optimize a single measure. This paper surveys developments in MOS while highlighting cross-disciplinary opportunities, and outlines open challenges that define the emerging frontier of MOS

Multi-Objective Search: Algorithms, Applications, and Emerging Directions

TL;DR

This paper addresses the challenge of balancing multiple objectives in decision-making by surveying the MOS landscape, including exact, approximate, anytime, and dynamic variants, as well as extensions beyond deterministic MOS. It clarifies foundational notions (e.g., PF, dominance, and epsilon-approximation) and details algorithmic progress (MO-A*, NAMOA-dr, A^*pex, MVH/BO-DHs), along with practical toolbox applications in MO-MST, MO-MAPF, and CSP. The authors review emerging applications in automated design, multi-modal planning, and robotics, and identify open challenges such as scalability, dynamic environments, preference elicitation, cross-domain cross-fertilization, and benchmarks. The work highlights the practical significance of MOS for real-world systems, where trade-offs between time, cost, safety, and other criteria must be navigated, and argues for greater cross-community collaboration and benchmark development to accelerate progress.

Abstract

Multi-objective search (MOS) has emerged as a unifying framework for planning and decision-making problems where multiple, often conflicting, criteria must be balanced. While the problem has been studied for decades, recent years have seen renewed interest in the topic across AI applications such as robotics, transportation, and operations research, reflecting the reality that real-world systems rarely optimize a single measure. This paper surveys developments in MOS while highlighting cross-disciplinary opportunities, and outlines open challenges that define the emerging frontier of MOS

Paper Structure

This paper contains 39 sections, 3 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Scope.
  3. Problem Setting & Variants
  4. Notation
  5. MOS---Problem definition and variants
  6. Exact MOS.
  7. Approximate MOS.
  8. Anytime MOS.
  9. Incremental & Dynamic MOS.
  10. Beyond MOS
  11. Handling uncertainty.
  12. Learning.
  13. Multi-objective Optimization.
  14. Algorithmic Advances
  15. Brief historical overview
  16. ...and 24 more sections

Figures (1)

  • Figure 1: Visualization of key MOS concepts for the special case of a bi-objective problem. Solutions on and not on the PF are visualized as purple and black dots, respectively. Visualization of all solutions dominated and approximately dominated by solutions $\pi_1$ and $\pi_2$ are visualized by turquoise and orange regions respectively. Example for sets of solutions that approximate the PF which lie and which do not lie on the PF are depicted with purple squares and red diamonds, respective. Finally, the dominance factor $\textsc{Df}(\pi_1, \pi_2)$ in this example is $\max(\max(8/3-1,0),\max(1/7-1,0))=5/3$.