Vibroseis Vehicle Routing Problem with Spatio-Temporal Coupled Constraints

Abstract

Simultaneous multi vibroseis vehicle operations are central to modern land seismic exploration and can be modeled as a Vehicle Routing Problem (VRP). A critical distinction from classical VRPs, however, is the need for a minimum start-time interval between nearby sources to prevent signal interference. This constraint introduces strong spatio-temporal coupling, as one vehicle's route directly impacts the schedules of others, leading to potential forced waits. This paper defines this novel problem as the Vibroseis Vehicle Routing Problem with Spatio-Temporal Coupled Constraints (STCVRP) and aims to minimize the makespan. To systematically investigate this problem, we first establish a Mixed-Integer Linear Programming (MILP) model to provide a precise mathematical description. As the MILP is intractable for realistic-scale instances, we subsequently develop a discrete-event simulation model. This model accurately calculates the true makespan of any candidate solution under all constraints, thereby serving as a high-fidelity fitness evaluation function for metaheuristics. To solve the problem, we design and implement a simulation-based Genetic Algorithm (GA) framework capable of searching the solution space efficiently. Finally, to validate the proposed framework and facilitate future research, we construct and release a new benchmark suite for the STCVRP. We solve the instances using both exact methods and our GA, with experimental results demonstrating the problem's high complexity and the effectiveness of the metaheuristic approach, providing a set of high-quality initial solutions for the benchmark.