A Tabu Search Heuristic for the Vehicle Routing Problem with Soft Time Windows

TLDR

The vehicle routing problem with soft time windows permits lateness at customer locations, incurring a penalty added to the objective. This paper proposes a tabu search heuristic for the vehicle routing problem with soft time windows. The heuristic constructs neighborhoods by swapping consecutive customer sequences between routes, uses an adaptive memory of the best routes, generates new starting points from combinations of stored routes, and applies large penalties to also address hard time windows. The method attains many best‑known solutions on classical test problems.

Abstract

This paper describes a tabu search heuristic for the vehicle routing problem with soft time windows. In this problem, lateness at customer locations is allowed although a penalty is incurred and added to the objective value. By adding large penalty values, the vehicle routing problem with hard time windows can be addressed as well. In the tabu search, a neighborhood of the current solution is created through an exchange procedure that swaps sequences of consecutive customers (or segments) between two routes. The tabu search also exploits an adaptive memory that contains the routes of the best previously visited solutions. New starting points for the tabu search are produced through a combination of routes taken from different solutions found in this memory. Many best-known solutions are reported on classical test problems.