Dynamic Programming Methodologies in Very Large Scale Neighborhood Search Applied to the Traveling Salesman Problem

We provide two different neighborhood construction techniques for creating exponentially large neighborhoods that are searchable in polynomial time using dynamic programming. We illustrate both of these approaches on very large scale neighborhood search techniques for the traveling salesman problem. Our approaches are intended both to unify previously known results as well as to offer schemas for generating additional exponential neighborhoods that are searchable in polynomial time. The first approach is to define the neighborhood recursively. In this approach, the dynamic programming recursion is a natural consequence of the recursion that defines the neighborhood. In particular, we show how to create the pyramidal tour neighborhood, the twisted sequences neighborhood, and dynasearch neighborhoods using this approach. In the second approach, we consider the standard dynamic program to solve the TSP. We then obtain exponentially large neighborhoods by selecting a polynomially bounded number of states, and restricting the dynamic program to those states only. We show how the Balas and Simonetti neighborhood and the insertion dynasearch neighborhood can be viewed in this manner. We also show that one of the dynasearch neighborhoods can be derived directly from the 2-exchange neighborhood using this approach

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based on sequential/cyclic moves and a cyclic transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world data sets for high school timetabling in the Netherlands and England.We present results of the cyclic transfer algorithm with different settings on these data sets. The costs decrease by 8–28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based\ud on sequential/cyclic moves and a Cyclic Transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world datasets for high school timetabling in the Netherlands and England. We present results of the cyclic transfer algorithm with different settings on these datasets. The costs decrease by 8% to 28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

Search in the Universe of Big Networks and Data

Searching in the Internet for some object characterised by its attributes in the form of data, such as a hotel in a certain city whose price is less than something, is one of our most common activities when we access the Web. We discuss this problem in a general setting, and compute the average amount of time and the energy it takes to find an object in an infinitely large search space. We consider the use of N search agents which act concurrently. Both the case where the search agent knows which way it needs to go to find the object, and the case where the search agent is perfectly ignorant and may even head away from the object being sought. We show that under mild conditions regarding the randomness of the search and the use of a time-out, the search agent will always find the object despite the fact that the search space is infinite. We obtain a formula for the average search time and the average energy expended by N search agents acting concurrently and independently of each other. We see that the time-out itself can be used to minimise the search time and the amount of energy that is consumed to find an object. An approximate formula is derived for the number of search agents that can help us guarantee that an object is found in a given time, and we discuss how the competition between search agents and other agents that try to hide the data object, can be used by opposing parties to guarantee their own success.Comment: IEEE Network Magazine - Special Issue on Networking for Big Data, July-August 201

A large-scale neighborhood search approach to vehicle routing pick-up and delivery problem with time windows under uncertainty

The vehicle routing problem with shipment pick-up and delivery with time windows (VRPPDTW) is one of the core problems that is addressed by a package delivery company in its operations. Most often, this problem has been addressed from the point of view of cost-cutting, to achieve the lowest cost possible under a given/predicted demand and service time scenario. This thesis aims to study a real-world VRPPDTW problem with side-constraints and build solutions that are cost-effective as well as robust to stochasticity in demands and service times. Even without the additional side constraints, the VRPPDTW is NP-hard. In particular, we consider the solution of VRPPDTW with side-constraints adopted by a carrier. Because of the nature as well as the size of the problem and the network, we demonstrate that the problem is combinatorially explosive. We therefore develop a large-scale neighbourhood search heuristic combined with a break-and-join heuristic and a clustering heuristic. We use this heuristic to build a set of schedules with far lower operating costs than the existing solution and effectively decrease the costs by 15% by reducing the number of routes needed to serve the shipments. We then build a framework to evaluate the performance of the solutions under stochasticity, and present results related to under stochasticity in service times