Matheuristics and Column Generation for a Basic Technician Routing Problem

Abstract

This paper considers a variant of the Vehicle Routing Problem with Time Windows, with site dependencies, multiple depots and outsourcing costs. This problem is the basis for many technician routing problems. Having both site-dependency and time window constraints lresults in difficulties in finding feasible solutions and induces highly constrained instances. Matheuristics based on Mixed Integer Linear Programming compact formulations are firstly designed. Column Generation matheuristics are then described by using previous matheuristics and machine learning techniques to stabilize and speed up the convergence of the Column Generation algorithm. The computational experiments are analyzed on public instances with graduated difficulties in order to analyze the accuracy of algorithms for ensuring feasibility and the quality of solutions for weakly to highly constrained instances. The results emphasize the interest of the multiple types of hybridization between mathematical programming, machine learning and heuristics inside the Column Generation framework. This work offers perspectives for many extensions of technician routing problems.

Matheuristics: survey and synthesis

“…Several other works apply column generation for heuristic search without explicitly mentioning Dantzig–Wolfe (DW) decomposition. The addressed range of problems is wide, including technician routing (Dupin et al., 2021), train timetabling (Martin‐Iradi and Ropke, 2022), electric vehicle routing (Echeverri et al., 2019), city logistics (Boschetti and Maniezzo, 2015) and planning in bulk ports (de Andrade and Menezes, 2023) among others.…”

Integer Linear Programming Reformulations for the Linear Ordering Problem

“…Indeed, c i = j =i x i,j counts the number of items after i, so that there is the invariant 22) have a positive impact on the quality of the LP relaxation. As big M constraints are reputed to be weak and inducing poor LP relaxations (we refer to [5]), a numerical issue is to determine the difference with the continuous relaxation when relaxing also constraints (21) and ( 22). One note that this relaxation has a trivial optimal solution, considering for i = j the value x i,j = 1 if and only if w i,j w j,i ).…”

“…A bridge between optimization and Machine Learning (ML) exists to optimize training parameters of ML models, using continuous optimization and metaheuristics [17,18]. Discrete and exact optimization, especially Integer Linear Programming (ILP), is also useful to model and solve specific variants of clustering or selection problems [5,6]. In this paper, another application of ILP to learning is studied: the Linear Ordering Problem (LOP).…”

“…Constraints ( 16) are sub-tour cuts between node 0 and item i > 0. Subtours between two cities may have a crucial impact in the resolution, as in [5]. Having variables x and constraints (6) and the tighter variants implies the other sub-tours between two items.…”

Special Issue “2021 Selected Papers from Algorithms’ Editorial Board Members”

“…The paper [11] investigates a variant of the vehicle routing problem including time windows, site dependencies, multiple depots and outsourcing costs. The authors develop matheuristics based on column generation.…”