Constrained Fitness Landscape Analysis of Capacitated Vehicle Routing Problems

Vehicle Routing Problems (VRP) comprise many variants obtained by adding to the original problem constraints representing diverse system characteristics. Different variants are widely studied in the literature; however, the impact that these constraints have on the structure of the search space associated with the problem is unknown, and so is their influence on the performance of search algorithms used to solve it. This article explores how assignation constraints (such as a limited vehicle capacity) impact VRP by disturbing the network structure defined by the solution space and the local operators in use. This research focuses on Fitness Landscape Analysis for the multiple Traveling Salesman Problem (m-TSP) and Capacitated VRP (CVRP). We propose a new Fitness Landscape Analysis measure that provides valuable information to characterize the fitness landscape’s structure under specific scenarios and obtain several relationships between the fitness landscape’s structure and the algorithmic performance.

Matheuristics and Column Generation for a Basic Technician Routing Problem

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.