Logic learning and optimized drawing: two hard combinatorial problems

Nowadays, information extraction from large datasets is a recurring operation in countless fields of applications. The purpose leading this thesis is to ideally follow the data flow along its journey, describing some hard combinatorial problems that arise from two key processes, one consecutive to the other: information extraction and representation. The approaches here considered will focus mainly on metaheuristic algorithms, to address the need for fast and effective optimization methods. The problems studied include data extraction instances, as Supervised Learning in Logic Domains and the Max Cut-Clique Problem, as well as two different Graph Drawing Problems. Moreover, stemming from these main topics, other additional themes will be discussed, namely two different approaches to handle Information Variability in Combinatorial Optimization Problems (COPs), and Topology Optimization of lightweight concrete structures

On the Use of Second Order Neighbors to Escape from Local Optima

Designing efficient local search based algorithms requires to consider the specific properties of the problems. We introduce a simple and effi- cient strategy, the Extended Reach, that escapes from local optima ob- tained from a best improvement local search and apply it to the linear ordering problem (LOP), the traveling salesperson problem (TSP) and the quadratic assignment problem (QAP). This strategy is based on two landscape properties observed in the literature. First, it considers that a local optimum is usually located in the frontier of its own attraction basin, and thus, it is enough to inspect the second order neighbors to reach a (better) solution inside an attraction basin of a better local optimum. Second, taking into account that for the LOP and specific neighborhoods it is possible to discard solutions without the need of being evaluated, we extend this result to the TSP with the 2-opt neighborhood to avoid the unnecessary evaluation of solutions. Efficient ways of evaluating the second order neighbors are also presented, based on the cost differences, reducing significantly the computation cost. Experimental results on ran- dom and benchmark instances show that our strategy, indeed, escapes from local optima despite its simplicity.PID2019-104966GB-I00 AXA Research Fun

Exploiting sets of independent moves in VRP

Most heuristic methods for VRP and its variants are based on the partial exploration of large neighborhoods, typically by means of single, simple moves applied to the current solution. In this paper we define an extended concept of independent moves and show how even a very standard heuristic method can significantly improve when considering the simultaneous application of carefully chosen sets of moves. We show in particular that, when choosing a set such that the total cost variation is equal to the sum of the variations induced by each single move, the quality of solutions obtained is in general very high. When compared with numerical results obtained by some of the best available heuristics on challenging, large scale, problems, our simple algorithm equipped with the application of optimally chosen independent moves displayed very good quality

Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learning

Recent works using deep learning to solve the Traveling Salesman Problem (TSP) have focused on learning construction heuristics. Such approaches find TSP solutions of good quality but require additional procedures such as beam search and sampling to improve solutions and achieve state-of-the-art performance. However, few studies have focused on improvement heuristics, where a given solution is improved until reaching a near-optimal one. In this work, we propose to learn a local search heuristic based on 2-opt operators via deep reinforcement learning. We propose a policy gradient algorithm to learn a stochastic policy that selects 2-opt operations given a current solution. Moreover, we introduce a policy neural network that leverages a pointing attention mechanism, which unlike previous works, can be easily extended to more general k-opt moves. Our results show that the learned policies can improve even over random initial solutions and approach near-optimal solutions at a faster rate than previous state-of-the-art deep learning methods.Comment: To appear in Proceedings Machine Learning Research - ACML 202

The Pickup and Delivery Problem with Split Loads

This dissertation focuses on improvements in vehicle routing that can be gained by allowing multiple vehicles to service a common load. We explore how costs can be reduced through the elimination of the constraint that a load must be serviced by only one vehicle. Specifically, we look at the problem of routing vehicles to service loads that have distinct origins and destinations, with no constraint on the amount of a load that a vehicle may service. We call this the Pickup and Delivery Problem with Split Loads (PDPSL). We model this problem as a dynamic program and introduce structural results that can help practitioners implement the use of split loads, including the definition of an upper bound on the benefit of split loads. This bound indicates that the routing cost can be reduced by at most one half when split loads are allowed. Furthermore, the most benefit occurs when load sizes are just above one half of vehicle capacity. We develop a heuristic for the solution of large scale problems, and apply this heuristic to randomly generated data sets. Various load sizes are tested, with the experimental results supporting the finding that most benefit with split loads occurs for load sizes just above one half vehicle capacity. Also, the average benefit of split loads is found to range from 6 to 7% for most data sets. The heuristic was also tested on a real world example from the trucking industry. These tests reveal the benefit of both using split loads and allowing fleet sharing. The benefit for split loads is not as significant as with the random data, and the various business rules added for this case are tested to find those that have the most impact. It is found that an additional cost for every stop the vehicle makes strictly limits the potential for benefit from split loads. Finally, we present a simplified version of the PDPSL in which all origins are visited prior to any destination on a route, generalizing structural results from the Split Delivery Vehicle Routing Problem for this problem.Ph.D.Committee Co-Chair: Ergun, Ozlem; Committee Co-Chair: White, Chelsea; Committee Member: Ellingwood, Bruce; Committee Member: Savelsbergh, Martin; Committee Member: Sokol, Joe

A Combined Adaptive Tabu Search and Set Partitioning Approach for the Crew Scheduling Problem with an Air Tanker Crew Application

This research develops the first metaheuristic approach to the complete air crew scheduling problem. It develops the first dynamic, integrated, set-partitioning based vocabulary scheme for metaheuristic search. Since no benchmark flight schedules exist for the tanker crew scheduling problem, this research defines and develops a Java™ based flight schedule generator. The robustness of the tabu search algorithms is judged by testing them using designed experiments. An integer program is developed to calculate lower bounds for the tanker crew scheduling problem objectives and to measure the overall quality of solutions produced by the developed algorithms

An Adaptive Tabu Search Heuristic for the Location Routing Pickup and Delivery Problem with Time Windows with a Theater Distribution Application

The time constrained pickup and delivery problem (PDPTW) is a problem of finding a set of routes for a fleet of vehicles in order to satisfy a set of transportation requests. Each request represents a user-specified pickup and delivery location. The PDPTW may be used to model many problems in logistics and public transportation. The location routing problem (LRP) is an extension of the vehicle routing problem where the solution identifies the optimal location of the depots and provides the vehicle schedules and distribution routes. This dissertation seeks to blend the PDPTW and LRP areas of research and formulate a location scheduling pickup and delivery problem with time windows (LPDPTW) in order to model the theater distribution problem and find excellent solutions. This research utilizes advanced tabu search techniques, including reactive tabu search and group theory applications, to develop a heuristic procedure for solving the LPDPTW. Tabu search is a metaheuristic that performs an intelligent search of the solution space. Group theory provides the structural foundation that supports the efficient search of the neighborhoods and movement through the solution space

Large-scale dynamic observation planning for unmanned surface vessels

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007.Includes bibliographical references (p. 129-134).With recent advances in research and technology, autonomous surface vessel capabilities have steadily increased. These autonomous surface vessel technologies enable missions and tasks to be performed without the direction of human operators, and have changed the way scientists and engineers approach problems. Because these robotic devices can work without manned guidance, they can execute missions that are too difficult, dangerous, expensive, or tedious for human operators to attempt. The United States government is currently expanding the use of autonomous surface vessel technologies through the United States Navy's Spartan Scout unmanned surface vessel (USV) and NASA's Ocean-Atmosphere Sensor Integration System (OASIS) USV. These USVs are well-suited to complete monotonous, dangerous, and time-consuming missions. The USVs provide better performance, lower cost, and reduced risk to human life than manned systems. In this thesis, we explore how to plan multiple USV observation schedules for two significant notional observation scenarios, collecting water temperatures ahead of the path of a hurricane, and collecting fluorometer readings to observe and track a harmful algal bloom.(cont.) A control system must be in place that coordinates a fleet of USVs to targets in an efficient manner. We develop three algorithms to solve the unmanned surface vehicle observation-planning problem. A greedy construction heuristic runs fastest, but produces suboptimal plans; a 3-phase algorithm which combines a greedy construction heuristic with an improvement phase and an insertion phase, requires more execution time, but generates significantly better plans; an optimal mixed integer programming algorithm produces optimal plans, but can only solve small problem instances.by John V. Miller.S.M

Metaheuristic approach for solving scheduling and financial derivative problems

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe objective of this thesis is to implement metaheuristic approaches to solve di erent types of combinatorial problems. The thesis is focused on neighborhood heuristic optimisation techniques such as Variable Neighborhood Search (VNS) and Ant Colony Optimisation (ACO) algorithms. The thesis will focus on two diverse combinatorial problems. A job shop scheduling problem, and a nancial derivative matching problem. The rst is a NP-hard 2-stage assembly problem, where we will be focussing on the rst stage. It consists of sequencing a set of jobs having multiple components to be processed. Each job has to be worked on independently on a speci c machine. We consider these jobs to form a vector of tasks. Our objective is to schedule jobs on the particular machines in order to minimise the completion time before the second stage starts. In this thesis, we have constructed a new hybrid metaheuristic approach to solve this unique job shop scheduling problem. The second problem has arisen in the nancial sector, where the nancial regulators collects transaction data across regulated assets classes. Our focus is to identify any unhedged derivative, Contract for Di erence (CFD), with its corresponding underlying asset that has been reported to the corresponding component authorities. The underlying asset and CFD transaction contain di erent variables, like volume and price. Therefore, we are looking for a combination of underlying asset variables that may hedge the equivalent CFD variables. Our aim is to identify unhedged or unmatched CFD's with their corresponding underlying asset. This problem closely relates to the goal programming problem with variable parameters. We have developed two new local search methods and embedded the newly constructed local search methods with basic VNS, to attain a new modi ed variant of the VNS algorithm. We then used these newly constructed VNS variants to solve this nancial matching problem. In tackling the Vector Job Scheduling problem, we developed a new hybrid optimisation heuristic algorithm by combining VNS and ACO. We then compared the results of this hybrid algorithm with VNS and ACO on their own. We found that the hybrid algorithm performance is better than the other two independent heuristic algorithms. In tackling the nancial derivative problem, our objective is to match the CFD trades with their corresponding underlying equity trades. Our goal is to identify the mismatched CFD trades while optimising the search process. We have developed two new local search techniques and we have implemented a VNS algorithm with the newly developed local search techniques to attain better solutions