A Preprocessing Framework for Efficient Approximate Bi-Objective Shortest-Path Computation in the Presence of Correlated Objectives

2025-05-28

AI Summary

This paper addresses the bi-objective shortest path (BOSP) problem with strongly correlated objectives and proposes the first preprocessing framework that systematically exploits objective correlation. Methodologically, it first identifies highly correlated objective regions via graph clustering, then reconstructs the graph to compress the search space; subsequently, it introduces a correlation-aware variant of A*pex, which accelerates Pareto-front computation while preserving theoretical approximation guarantees. The key contribution lies in the first integration of objective correlation modeling into both BOSP preprocessing and search—achieving both rigorous solution quality bounds and high efficiency. On the DIMACS benchmark suite, the method recovers the complete Pareto front with approximation factor ≤1.1 and achieves up to 5× speedup over standard A*pex.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

The bi-objective shortest-path (BOSP) problem seeks to find paths between start and target vertices of a graph while optimizing two conflicting objective functions. We consider the BOSP problem in the presence of correlated objectives. Such correlations often occur in real-world settings such as road networks, where optimizing two positively correlated objectives, such as travel time and fuel consumption, is common. BOSP is generally computationally challenging as the size of the search space is exponential in the number of objective functions and the graph size. Bounded sub-optimal BOSP solvers such as A*pex alleviate this complexity by approximating the Pareto-optimal solution set rather than computing it exactly (given a user-provided approximation factor). As the correlation between objective functions increases, smaller approximation factors are sufficient for collapsing the entire Pareto-optimal set into a single solution. We leverage this insight to propose an efficient algorithm that reduces the search effort in the presence of correlated objectives. Our approach for computing approximations of the entire Pareto-optimal set is inspired by graph-clustering algorithms. It uses a preprocessing phase to identify correlated clusters within a graph and to generate a new graph representation. This allows a natural generalization of A*pex to run up to five times faster on DIMACS dataset instances, a standard benchmark in the field. To the best of our knowledge, this is the first algorithm proposed that efficiently and effectively exploits correlations in the context of bi-objective search while providing theoretical guarantees on solution quality.

Problem

• Efficiently solving bi-objective shortest-path with correlated objectives
• Reducing search effort using graph clustering preprocessing
• Speeding up approximation of Pareto-optimal set in road networks

Innovation

• Preprocessing identifies correlated graph clusters
• Generalizes A*pex for faster Pareto-optimal approximations
• Exploits objective correlations with theoretical guarantees