Efficient combinatorial optimization algorithms for logistic problems

The field of logistics and combinatorial optimization features a wealth of NP-hard problems that are of great practical importance. For this reason it is important that we have efficient algorithms to provide optimal or near-optimal solutions. In this work, we study, compare and develop Sampling-Based Metaheuristics and Exact Methods for logistic problems that are important for their applications in vehicle routing and scheduling. More specifically, we study two Stochastic Combinatorial Optimization Problems (SCOPs) and finally a Combinatorial Optimization Problem using methods related to the field of Metaheuristics, Monte Carlo Sampling, Experimental Algorithmics and Exact Algorithms. For the SCOPs studied, we emphasize studying the impact of approximating the objective function to the quality of the final solution found. We begin by examining Solution Methods for the Orienteering Problem with Stochastic Travel and Service Times (OPSTS). We introduce the state-of-the-art before our contributions and proceed to examining our suggested improvements. The core of our improvements stem from the approximation of the objective function using a combination of Monte Carlo sampling and Analytical methods. We present four new Evaluators (approximations) and discuss their advantages and disadvantages. We then demonstrate experimentally the advantages of the Evaluators over the previous state-of-the-art and explore their trade- offs. We continue by generating large reference datasets and embedding our Evaluators in two Metaheuristics that we use to find realistic near-optimal solutions to OPSTS. We demonstrate that our results are statistically significantly better than the previous state-of-the-art. In the next chapter, we present the 2-stage Capacitated Vehicle Routing Problem with Stochastic Demands inspired by an environmental use case. We propose four different solution approaches based on different approximations of the objective function and use the Ant Colony Metaheuristic to find solutions for the problem. We discuss the trade-offs of each proposed solution and finally argue about its potentially important environmental application. Finally, focus on exact methods for the Sequential Ordering Problem (SOP). Firstly, we make an extensive experimental comparison of two exact algorithms existing in the literature from different domains (cargo and transportation and the other compilers). From the experimental comparison and application of the algorithms in new contexts we were able to close nine previously open instances in the literature and improve seventeen more. It also led to insights for the improvement of one of the methods (The Branch-and-Bound Approach - B&B). We proceed with the presentation of the improved version that led to the closing of eight more instances and speeding up the previous version of the B&B algorithm by 4%-98%

Investigating heuristic and meta-heuristic algorithms for solving pickup and delivery problems

The development of effective decision support tools that can be adopted in the transportation industry is vital in the world we live in today, since it can lead to substantial cost reduction and efficient resource consumption. Solving the Vehicle Routing Problem (VRP) and its related variants is at the heart of scientific research for optimizing logistic planning. One important variant of the VRP is the Pickup and Delivery Problem (PDP). In the PDP, it is generally required to find one or more minimum cost routes to serve a number of customers, where two types of services may be performed at a customer location, a pickup or a delivery. Applications of the PDP are frequently encountered in every day transportation and logistic services, and the problem is likely to assume even greater prominence in the future, due to the increase in e-commerce and Internet shopping. In this research we considered two particular variants of the PDP, the Pickup and Delivery Problem with Time Windows (PDPTW), and the One-commodity Pickup and Delivery Problem (1-PDP). In both problems, the total transportation cost should be minimized, without violating a number of pre-specified problem constraints. In our research, we investigate heuristic and meta-heuristic approaches for solving the selected PDP variants. Unlike previous research in this area, though, we try to focus on handling the difficult problem constraints in a simple and effective way, without complicating the overall solution methodology. Two main aspects of the solution algorithm are directed to achieve this goal, the solution representation and the neighbourhood moves. Based on this perception, we tailored a number of heuristic and meta-heuristic algorithms for solving our problems. Among these algorithms are: Genetic Algorithms, Simulated Annealing, Hill Climbing and Variable Neighbourhood Search. In general, the findings of the research indicate the success of our approach in handling the difficult problem constraints and devising simple and robust solution mechanisms that can be integrated with vehicle routing optimization tools and used in a variety of real world applicationsEThOS - Electronic Theses Online ServiceGBUnited Kingdo

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Heuristic search under time and cost bounds

Intelligence is difficult to formally define, but one of its hallmarks is the ability find a solution to a novel problem. Therefore it makes good sense that heuristic search is a foundational topic in artificial intelligence. In this context search refers to the process of finding a solution to the problem by considering a large, possibly infinite, set of potential plans of action. Heuristic refers to a rule of thumb or a guiding, if not always accurate, principle. Heuristic search describes a family of techniques which consider members of the set of potential plans of action in turn, as determined by the heuristic, until a suitable solution to the problem is discovered. This work is concerned primarily with suboptimal heuristic search algorithms. These algorithms are not inherently flawed, but they are suboptimal in the sense that the plans that they return may be more expensive than a least cost, or optimal, plan for the problem. While suboptimal heuristic search algorithms may not return least cost solutions to the problem, they are often far faster than their optimal counterparts, making them more attractive for many applications. The thesis of this dissertation is that the performance of suboptimal search algorithms can be improved by taking advantage of information that, while widely available, has been overlooked. In particular, we will see how estimates of the length of a plan, estimates of plan cost that do not err on the side of caution, and measurements of the accuracy of our estimators can be used to improve the performance of suboptimal heuristic search algorithms

From metaheuristics to learnheuristics: Applications to logistics, finance, and computing

Un gran nombre de processos de presa de decisions en sectors estratègics com el transport i la producció representen problemes NP-difícils. Sovint, aquests processos es caracteritzen per alts nivells d'incertesa i dinamisme. Les metaheurístiques són mètodes populars per a resoldre problemes d'optimització difícils en temps de càlcul raonables. No obstant això, sovint assumeixen que els inputs, les funcions objectiu, i les restriccions són deterministes i conegudes. Aquests constitueixen supòsits forts que obliguen a treballar amb problemes simplificats. Com a conseqüència, les solucions poden conduir a resultats pobres. Les simheurístiques integren la simulació a les metaheurístiques per resoldre problemes estocàstics d'una manera natural. Anàlogament, les learnheurístiques combinen l'estadística amb les metaheurístiques per fer front a problemes en entorns dinàmics, en què els inputs poden dependre de l'estructura de la solució. En aquest context, les principals contribucions d'aquesta tesi són: el disseny de les learnheurístiques, una classificació dels treballs que combinen l'estadística / l'aprenentatge automàtic i les metaheurístiques, i diverses aplicacions en transport, producció, finances i computació.Un gran número de procesos de toma de decisiones en sectores estratégicos como el transporte y la producción representan problemas NP-difíciles. Frecuentemente, estos problemas se caracterizan por altos niveles de incertidumbre y dinamismo. Las metaheurísticas son métodos populares para resolver problemas difíciles de optimización de manera rápida. Sin embargo, suelen asumir que los inputs, las funciones objetivo y las restricciones son deterministas y se conocen de antemano. Estas fuertes suposiciones conducen a trabajar con problemas simplificados. Como consecuencia, las soluciones obtenidas pueden tener un pobre rendimiento. Las simheurísticas integran simulación en metaheurísticas para resolver problemas estocásticos de una manera natural. De manera similar, las learnheurísticas combinan aprendizaje estadístico y metaheurísticas para abordar problemas en entornos dinámicos, donde los inputs pueden depender de la estructura de la solución. En este contexto, las principales aportaciones de esta tesis son: el diseño de las learnheurísticas, una clasificación de trabajos que combinan estadística / aprendizaje automático y metaheurísticas, y varias aplicaciones en transporte, producción, finanzas y computación.A large number of decision-making processes in strategic sectors such as transport and production involve NP-hard problems, which are frequently characterized by high levels of uncertainty and dynamism. Metaheuristics have become the predominant method for solving challenging optimization problems in reasonable computing times. However, they frequently assume that inputs, objective functions and constraints are deterministic and known in advance. These strong assumptions lead to work on oversimplified problems, and the solutions may demonstrate poor performance when implemented. Simheuristics, in turn, integrate simulation into metaheuristics as a way to naturally solve stochastic problems, and, in a similar fashion, learnheuristics combine statistical learning and metaheuristics to tackle problems in dynamic environments, where inputs may depend on the structure of the solution. The main contributions of this thesis include (i) a design for learnheuristics; (ii) a classification of works that hybridize statistical and machine learning and metaheuristics; and (iii) several applications for the fields of transport, production, finance and computing