370 research outputs found
DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization
Neural network-based Combinatorial Optimization (CO) methods have shown
promising results in solving various NP-complete (NPC) problems without relying
on hand-crafted domain knowledge. This paper broadens the current scope of
neural solvers for NPC problems by introducing a new graph-based diffusion
framework, namely DIFUSCO. Our framework casts NPC problems as discrete {0,
1}-vector optimization problems and leverages graph-based denoising diffusion
models to generate high-quality solutions. We investigate two types of
diffusion models with Gaussian and Bernoulli noise, respectively, and devise an
effective inference schedule to enhance the solution quality. We evaluate our
methods on two well-studied NPC combinatorial optimization problems: Traveling
Salesman Problem (TSP) and Maximal Independent Set (MIS). Experimental results
show that DIFUSCO strongly outperforms the previous state-of-the-art neural
solvers, improving the performance gap between ground-truth and neural solvers
from 1.76% to 0.46% on TSP-500, from 2.46% to 1.17% on TSP-1000, and from 3.19%
to 2.58% on TSP10000. For the MIS problem, DIFUSCO outperforms the previous
state-of-the-art neural solver on the challenging SATLIB benchmark. Our code is
available at "https://github.com/Edward-Sun/DIFUSCO"
Exact Models, Heuristics, and Supervised Learning Approaches for Vehicle Routing Problems
This dissertation presents contributions to the field of vehicle routing problems by utilizing exact methods, heuristic approaches, and the integration of machine learning with traditional algorithms. The research is organized into three main chapters, each dedicated to a specific routing problem and a unique methodology. The first chapter addresses the Pickup and Delivery Problem with Transshipments and Time Windows, a variant that permits product transfers between vehicles to enhance logistics flexibility and reduce costs. To solve this problem, we propose an efficient mixed-integer linear programming model that has been shown to outperform existing ones. The second chapter discusses a practical workforce scheduling problem, formulated as a specific type of vehicle routing problem. The objective here is to efficiently assign consultants to various clients and plan their trips. This computational challenge is addressed by using a two-stage approach: the first stage employs a mathematical model, while the second stage refines the solution with a heuristic algorithm. In the final chapter, we explore methods that integrate machine learning with traditional approaches to address the Traveling Salesman Problem, a foundational routing challenge. Our goal is to utilize supervised learning to predict information that boosts the efficiency of existing algorithms. Taken together, these three chapters offer a comprehensive overview of methodologies for addressing vehicle routing problems
Continuation Path Learning for Homotopy Optimization
Homotopy optimization is a traditional method to deal with a complicated
optimization problem by solving a sequence of easy-to-hard surrogate
subproblems. However, this method can be very sensitive to the continuation
schedule design and might lead to a suboptimal solution to the original
problem. In addition, the intermediate solutions, often ignored by classic
homotopy optimization, could be useful for many real-world applications. In
this work, we propose a novel model-based approach to learn the whole
continuation path for homotopy optimization, which contains infinite
intermediate solutions for any surrogate subproblems. Rather than the classic
unidirectional easy-to-hard optimization, our method can simultaneously
optimize the original problem and all surrogate subproblems in a collaborative
manner. The proposed model also supports real-time generation of any
intermediate solution, which could be desirable for many applications.
Experimental studies on different problems show that our proposed method can
significantly improve the performance of homotopy optimization and provide
extra helpful information to support better decision-making.Comment: Accepted by the 40th International Conference on Machine Learning
(ICML 2023
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Local search: A guide for the information retrieval practitioner
There are a number of combinatorial optimisation problems in information retrieval in which the use of local search methods are worthwhile. The purpose of this paper is to show how local search can be used to solve some well known tasks in information retrieval (IR), how previous research in the field is piecemeal, bereft of a structure and methodologically flawed, and to suggest more rigorous ways of applying local search methods to solve IR problems. We provide a query based taxonomy for analysing the use of local search in IR tasks and an overview of issues such as fitness functions, statistical significance and test collections when conducting experiments on combinatorial optimisation problems. The paper gives a guide on the pitfalls and problems for IR practitioners who wish to use local search to solve their research issues, and gives practical advice on the use of such methods. The query based taxonomy is a novel structure which can be used by the IR practitioner in order to examine the use of local search in IR
Data Driven Waste Management in Smart Cities
Bekreftelse fra programsansvarlig på at det holder kun med engelsk sammendrag. Grunnet masteroppgaven er skrevet på engelsk.Waste management is a critical issue worldwide. One of the major challenges in waste management is the efficient collection and transportation of waste from the source to the disposal facility. Research shows that systematic adoption of data-driven technologies (e.g. Machine Learning and Internet-of-Things) can assist public utilities (Kommune) by a) improving the waste collection management process, and b) minimizing the total incurred cost (Misra et al., 2018; Komninos, 2007). Thus, in this work, we show that systematic adoption of data-driven techniques can significantly improve the waste collection process and minimize the incurred cost to public utilities. In order to perform experiments, we generated a synthetic dataset motivated by a real-life urban environment. Also, we aimed to present different approaches to cost-benefit analysis in the targeted scenario. Our study shows that the systematic use of Internet-of-Things-based smart garbage bins, smart transportation algorithms, and Machine Learning can significantly reduce the total incurred cost of public utilities operating in this space
Traveling Salesman Problem
The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance
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