# Progressive Focus Search for the Static and Stochastic VRPTW with both Random Customers and Reveal Times

## TL;DR

This paper introduces a new meta-heuristic called Progressive Focus Search for solving the static stochastic VRPTW with random customers and reveal times, improving vehicle routing by efficiently handling uncertainty and reducing unsatisfied requests.

## Contribution

The paper presents a novel recourse strategy and the PFS meta-heuristic, enhancing solution quality and computational efficiency for the SS-VRPTW-CR problem.

## Key findings

- PFS accelerates the search process significantly.
- The new recourse strategy improves vehicle route efficiency.
- Results on real-world benchmark demonstrate effectiveness.

## Abstract

Static stochastic VRPs aim at modeling real-life VRPs by considering uncertainty on data. In particular, the SS-VRPTW-CR considers stochastic customers with time windows and does not make any assumption on their reveal times, which are stochastic as well. Based on customer request probabilities, we look for an a priori solution composed preventive vehicle routes, minimizing the expected number of unsatisfied customer requests at the end of the day. A route describes a sequence of strategic vehicle relocations, from which nearby requests can be rapidly reached. Instead of reoptimizing online, a so-called recourse strategy defines the way the requests are handled, whenever they appear. In this paper, we describe a new recourse strategy for the SS-VRPTW-CR, improving vehicle routes by skipping useless parts. We show how to compute the expected cost of a priori solutions, in pseudo-polynomial time, for this recourse strategy. We introduce a new meta-heuristic, called Progressive Focus Search (PFS), which may be combined with any local-search based algorithm for solving static stochastic optimization problems. PFS accelerates the search by using approximation factors: from an initial rough simplified problem, the search progressively focuses to the actual problem description. We evaluate our contributions on a new, real-world based, public benchmark.