The Machine Learning and Traveling Repairman Problem

Second International Conference, ADT 2011, Piscataway, NJ, USA, October 26-28, 2011. ProceedingsThe goal of the Machine Learning and Traveling Repairman Problem (ML&TRP) is to determine a route for a “repair crew,” which repairs nodes on a graph. The repair crew aims to minimize the cost of failures at the nodes, but the failure probabilities are not known and must be estimated. If there is uncertainty in the failure probability estimates, we take this uncertainty into account in an unusual way; from the set of acceptable models, we choose the model that has the lowest cost of applying it to the subsequent routing task. In a sense, this procedure agrees with a managerial goal, which is to show that the data can support choosing a low-cost solution.Fulbright Program (International Fulbright Science and Technology Award)Massachusetts Institute of Technology. Energy InitiativeNational Science Foundation (U.S.) (Grant IIS-1053407

A Deep Reinforcement Learning - based Hyperheuristic for the Flexible Traveling Repairman Problem with Drones

Masteroppgave i informatikkINF399MAMN-PROGMAMN-IN

Enhancing Understanding of Discrete Event Simulation Models Through Analysis

Simulation is used increasingly throughout research, development, and planning for many purposes. While model output is often the primary interest, insights gained through the simulation process can also be valuable. Insights can come from building and validating the model as well as analyzing its behaviors and output; however, much that could be informative may not be easily discernible through these existing traditional approaches, particularly as models continue to increase in complexity. This research extends current work in model analysis and program understanding to assist modelers in obtaining more insight into their models and the systems they represent. A primary technique for model understanding is analysis of model output; this research has developed new, complementary techniques. A significant point of this research is that the created tools do not necessitate that a modeler or model user be able to encode the model or have any coding expertise. Some of the information presented here could be produced by existing software development tools; however, most modelers today do not have the technical background to use such tools or to make use of the reports they can produce. Additionally, one of the significant details of this research is the focus on model aspects rather than simulation aspects: the tools developed here detail the model embedded in implementation code, not the code necessary for implementation. Source code tends to involve many issues unrelated to the model itself, such as data collection, animation, and tricks for efficient run-time behavior. Even when the modeler is an expert programmer, this other code often can obscure features of the model as implemented. Results indicate these tools and techniques, when applied to even modest simulation models, can reveal aspects of those models not readily apparent to the builders or users of the models. This work provides both model builders and model users with additional techniques that can give them improved understanding of their models

The Multi-Depot Minimum Latency Problem with Inter-Depot Routes

The Minimum Latency Problem (MLP) is a class of routing problems that seeks to minimize the wait times (latencies) of a set of customers in a system. Similar to its counterparts in the Traveling Salesman Problem (TSP) and Vehicle Routing Problem (VRP), the MLP is NP-hard. Unlike these other problem classes, however, the MLP is customer-oriented and thus has impactful potential for better serving customers in settings where they are the highest priority. While the VRP is very widely researched and applied to many industry settings to reduce travel times and costs for service-providers, the MLP is a more recent problem and does not have nearly the body of literature supporting it as found in the VRP. However, it is gaining significant attention recently because of its application to such areas as disaster relief logistics, which are a growing problem area in a global context and have potential for meaningful improvements that translate into reduced suffering and saved lives. An effective combination of MLP\u27s and route minimizing objectives can help relief agencies provide aid efficiently and within a manageable cost. To further the body of literature on the MLP and its applications to such settings, a new variant is introduced here called the Multi-Depot Minimum Latency Problem with Inter-Depot Routes (MDMLPI). This problem seeks to minimize the cumulative arrival times at all customers in a system being serviced by multiple vehicles and depots. Vehicles depart from one central depot and have the option of refilling their supply at a number of intermediate depots. While the equivalent problem has been studied using a VRP objective function, this is a new variant of the MLP. As such, a mathematical model is introduced along with several heuristics to provide the first solution approaches to solving it. Two objectives are considered in this work: minimizing latency, or arrival times at each customer, and minimizing weighted latency, which is the product of customer need and arrival time at that customer. The case of weighted latency carries additional significance as it may correspond to a larger number of customers at one location, thus adding emphasis to the speed with which they are serviced. Additionally, a discussion on fairness and application to disaster relief settings is maintained throughout. To reflect this, standard deviation among latencies is also evaluated as a measure of fairness in each of the solution approaches. Two heuristic approaches, as well as a second-phase adjustment to be applied to each, are introduced. The first is based on an auction policy in which customers bid to be the next stop on a vehicle\u27s tour. The second uses a procedure, referred to as an insertion technique, in which customers are inserted one-by-one into a partial routing solution such that each addition minimizes the (weighted) latency impact of that single customer. The second-phase modification takes the initial solutions achieved in the first two heuristics and considers the (weighted) latency impact of repositioning nodes one at a time. This is implemented to remove potential inefficient routing placements from the original solutions that can have compounding effects for all ensuing stops on the tour. Each of these is implemented on ten test instances. A nearest neighbor (greedy) policy and previous solutions to these instances with a VRP objective function are used as benchmarks. Both heuristics perform well in comparison to these benchmarks. Neither heuristic appears to perform clearly better than the other, although the auction policy achieves slightly better averages for the performance measures. When applying the second-phase adjustment, improvements are achieved and lead to even greater reductions in latency and standard deviation for both objectives. The value of these latency reductions is thoroughly demonstrated and a call for further research regarding customer-oriented objectives and evaluation of fairness in routing solutions is discussed. Finally, upon conclusion of the results presented in this work, several promising areas for future work and existing gaps in the literature are highlighted. As the body of literature surrounding the MLP is small yet growing, these areas constitute strong directions with important relevance to Operations Research, Humanitarian Logistics, Production Systems, and more

Several approaches for the traveling salesman problem

We characterize both approaches, mldp and k-mldp, with several methodologies; both a linear and a non-linear mathematical formulation are proposed. Additionally, the design and implementation of an exact methodology to solve both linear formulations is implemented and with it we obtained exact results. Due to the large computation time these formulations take to be solved with the exact methodology proposed, we analyse the complexity each of these approaches and show that both problems are NP-hard. As both problems are NP-hard, we propose three metaheuristic methods to obtain solutions in shorter computation time. Our solution methods are population based metaheuristics which exploit the structure of both problems and give good quality solutions by introducing novel local search procedures which are able to explore more efficiently their search space and to obtain good quality solutions in shorter computation time. Our main contribution is the study and characterization of a bi-objective problematic involving the minimization of two objectives: an economic one which aims to minimize the total travel distance, and a service-quality objective which aims to minimize of the waiting time of the clients to be visited. With this combination of objectives, we aim to characterize the inclusion of the client in the decision-making process to introduce service-quality decisions alongside a classic routing objective.This doctoral dissertation studies and characterizes of a combination of objectives with several logistic applications. This combination aims to pursue not only a company benefit but a benefit to the clients waiting to obtain a service or a product. In classic routing theory, an economic approach is widely studied: the minimization of traveled distance and cost spent to perform the visiting is an economic objective. This dissertation aims to the inclusion of the client in the decision-making process to bring out a certain level of satisfaction in the client set when performing an action. We part from having a set of clients demanding a service to a certain company. Several assumptions are made: when visiting a client, an agent must leave from a known depot and come back to it at the end of the tour assigned to it. All travel times among the clients and the depot are known, as well as all service times on each client. This is to say, the agent knows how long it will take to reach a client and to perform the requested service in the client location. The company is interested in improving two characteristics: an economic objective as well as a servicequality objective by minimizing the total travel distance of the agent while also minimizing the total waiting time of the clients. We study two main approaches: the first one is to fulfill the visits assuming there is a single uncapacitated vehicle, this is to say that such vehicle has infinite capacity to attend all clients. The second one is to fulfill the visits with a fleet of k-uncapacitated vehicles, all of them restricted to an strict constraint of being active and having at least one client to visit. We denominate the single-vehicle approach the minimum latency-distance problem (mldp), and the k-sized fleet the k-minimum latency-distance problem (k-mldp). As previously stated, this company has two options: to fulfil the visits with a single-vehicle or with a fixed-size fleet of k agents to perform the visits