A Preprocessing Framework for Efficient Approximate Bi-Objective Shortest-Path Computation in the Presence of Correlated Objectives
This work addresses computational efficiency for multi-objective optimization in domains like road networks, though it is incremental as it builds on existing bounded sub-optimal solvers like A*pex.
The paper tackles the bi-objective shortest-path problem with correlated objectives by proposing a preprocessing framework that clusters correlated graph regions, enabling faster approximate solutions. It achieves up to five times speedup on DIMACS benchmark instances while maintaining theoretical guarantees on solution quality.
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.