https://sci2s.ugr.es/sites/default/files/files/Teaching/GraduatesCourses/Metaheuristicas/Bibliography/VNS.pdf

Variable neighborhood search

This paper considers the design and analysis of algorithms for vehicle routing and scheduling problems with time window constraints. Given the intrinsic difficulty of this problem class, approximation methods seem to offer the most promise for practical size problems. After describing a variety of heuristics, we conduct an extensive computational study of their performance. The problem set includes routing and scheduling environments that differ in terms of the type of data used to generate the problems, the percentage of customers with time windows, their tightness and positioning, and the scheduling horizon. We found that several heuristics performed well in different problem environments; in particular an insertion-type heuristic consistently gave very good results.

https://www.jstor.org/stable/pdfplus/170697.pdf

Algorithms for the vehicle routing and scheduling problems with time window constraints

Variable Neighborhood Search.

We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch-and-bound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. We then discuss computational issues and implementation of column generation, branch-and-bound algorithms, including special branching rules and efficient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality.

/pdf/branch-and-price-column-generation-for-solving-huge-integer-4jvlny6blr.pdf

Branch-And-Price: Column Generation for Solving Huge Integer Programs

Variable neighborhood search: Principles and applications

The vehicle routing problem with time windows VRPTW is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest and the latest times when the customer will permit the start of service. In this paper, we present the development of a new optimization algorithm for its solution. The LP relaxation of the set partitioning formulation of the VRPTW is solved by column generation. Feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming. The LP solution obtained generally provides an excellent lower bound that is used in a branch-and-bound algorithm to solve the integer set partitioning formulation. Our results indicate that this algorithm proved to be successful on a variety of practical sized benchmark VRPTW test problems. The algorithm was capable of optimally solving 100-customer problems. This problem size is six times larger than any reported to date by other published research.

A new optimization algorithm for the vehicle routing problem with time windows

A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows

Dantzig-Wolfe decomposition and column generation, devised for linear programs, is a success story in large-scale integer programming. We outline and relate the approaches, and survey mainly recent contributions, not yet found in textbooks. We emphasize the growing understanding of the dual point of view, which has brought considerable progress to the column generation theory and practice. It stimulated careful initializations, sophisticated solution techniques for the restricted master problem and subproblem, as well as better overall performance. Thus, the dual perspective is an ever recurring concept in our "selected topics."

/pdf/selected-topics-in-column-generation-hx3sv5ci8j.pdf

Jacques Desrosiers

Papers

A new optimization algorithm for the vehicle routing problem with time windows

A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows

Selected Topics in Column Generation

Time Constrained Routing and Scheduling

The pickup and delivery problem with time windows