A multi-vehicle covering tour problem with speed optimization

TL;DR

This paper introduces a new multi-vehicle covering tour problem with speed and energy constraints, formulates it as a MISOCP model, and develops a specialized algorithm for its solution.

Contribution

It extends existing vehicle routing models by incorporating coverage, time windows, and energy restrictions, and proposes a novel solution approach for a special case.

Findings

Formulated the problem as a MISOCP model.

Developed a labeling algorithm for the Lagrangian relaxation.

Demonstrated the effectiveness of the approach on problem instances.

Abstract

The multi-vehicle covering tour problem with time windows (MCTPTW) aims to construct a set of maximal coverage routes for a fleet of vehicles that serve (observe) a secondary set of sites given a fixed time schedule, coverage requirements, and energy restrictions. The problem is formulated as a mixed-integer second-order cone programming (MISOCP) model and is an extension of both the multi-covering tour problem and the vehicle routing problem with time windows under energy constraints. Further, we study a special case of the proposed model and develop a labeling algorithm to solve its Lagrangian relaxation problem, which exploits the combinatorial structure exhibited by an optimal solution to the Lagrangian relaxation.