Algorithme glouton

Résumé

Un algorithme glouton (greedy algorithm en anglais, parfois appelé aussi algorithme gourmand, ou goulu) est un algorithme qui suit le principe de réaliser, étape par étape, un choix optimum local, afin d'obtenir un résultat optimum global. Par exemple, dans le problème du rendu de monnaie (donner une somme avec le moins possible de pièces), l'algorithme consistant à répéter le choix de la pièce de plus grande valeur qui ne dépasse pas la somme restante est un algorithme glouton. Dans les cas où l'algorithme ne fournit pas systématiquement la solution optimale, il est appelé une heuristique gloutonne. L'illustration ci-contre montre un cas où ce principe est mis en échec. Description Exemples de problèmes Rendu de monnaie Problème du rendu de monnaie Suivant le système de pièces, l'algorithme glouton est optimal ou pas. Dans le système de pièces européen (en centimes : 1, 2, 5, 10, 20, 50, 100, 200), où l'algorithme glouton donne la somme suivante

Source officielle

https://fr.wikipedia.org/wiki/Algorithme_glouton

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A Reinforcement Learning Approach to Train Routing and Scheduling

Zora Oswald

Good train scheduling for a big network with many trains is very hard to achieve. As the trains are competing for the tracks with one another, the number of constraints grows rapidly. Trying to take advantage of emerging technologies in the areas of optimization and machine learning, the Swiss Federal Railways have created a challenge to find the best algorithm to solve this problem. Two algorithms to solve this task were implemented in this project. First, a greedy strategy trying to schedule all trains at their earliest possible and then solving conflict after conflict was reproduced. It is shown that this algorithm is able to keep up with the best methods existing. With the objective of generalizing and improving the result, a policy gradient method is then added to take on the most critical decisions that have to be made in every iteration of the first algorithm. Even though this second enhanced algorithm does not obtain optimal solutions, it is able to outperform the first one in a generalized task. Hence, it can be shown that reinforcement learning is applicable to the train routing and scheduling task and, more generally, in environments with an open structure.

2020

Chargement

In this thesis we consider two optimal routing problems in networks. Both are NP-hard and are often used to modelize real life problems of large size. We first present the capacitated arc routing problem (CARP). In this problem, we have to serve a set of customers represented by the arcs of a network with vehicles of restricted capacity. The aim is to design a set of vehicle routes of least total cost. We describe two heuristic methods for the CARP based on local search techniques. The first one is a Tabu Search heuristic using an original post-optimization procedure. Principles appearing in this procedure are used to define a class of neighborhoods we combine in a Variable Neighborhood Descent method. Our algorithms compare favorably with some of her methods. They were initially developed to deal with the undirected CARP. We describe how to transform them so that they can be applied to the directed CARP. We also propose an adaptation to the directed case of a lower bound originally developed for the undirected CARP. This lower bound is used to evaluate the quality of the solutions produced by our algorithms for the directed CARP. Our methods obtain solutions whose value is, on average, close to known lower bounds. We use the CARP to tackle a real life problem of boat routing and scheduling. This problem can be viewed as a directed CARP with time windows. We describe in detail its modeling process and we analyze our first results. We obtain solutions that require less boats than the present schedule. Nevertheless, these solutions are not completely feasible in practice. We suggest some ways to improve them. The second problem treated in this thesis is the shortest capacitated paths problem (SCPP). We present a Tabu Search heuristic and some post-optimization procedures for the SCPP. These procedures are called in our Tabu Search algorithm. Two versions of this algorithm are considered. In the first one, post-optimization procedures are intensively used. In the second one, they are less frequently applied. This second version is faster. Compared with a greedy approach, the two versions of our Tabu Search heuristic obtain solutions which are, on average, of better quality. The SCPP was proposed to us by EDF (Electricité de France) in order to minimize the total length of the paths followed by cables in a nuclear power-station. It can also be viewed as a subproblem of the bandwidth packing problem (BWP) appearing in telecommunications.

EPFL2000

Chargement

Localizing Polygonal Objects in Man-Made Environments

Xiaolu Sun

Object detection is a significant challenge in Computer Vision and has received a lot of attention in the field. One such challenge addressed in this thesis is the detection of polygonal objects, which are prevalent in man-made environments. Shape analysis is an important cue to detect these objects. We propose a contour-based object detection framework to deal with the related challenges, including how to efficiently detect polygonal shapes and how to exploit them for object detection. First, we propose an efficient component tree segmentation framework for stable region extraction and a multi-resolution line segment detection algorithm, which form the bases of our detection framework. Our component tree segmentation algorithm explores the optimal threshold for each branch of the component tree, and achieves a significant improvement over image thresholding segmentation, and comparable performance to more sophisticated methods but only at a fraction of computation time. Our line segment detector overcomes several inherent limitations of the Hough transform, and achieves a comparable performance to the state-of-the-art line segment detectors. However, our approach can better capture dominant structures and is more stable against low-quality imaging conditions. Second, we propose a global shape analysis measurement for simple polygon detection and use it to develop an approach for real-time landing site detection in unconstrained man-made environments. Since the task of detecting landing sites must be performed in a few seconds or less, existing methods are often limited to simple local intensity and edge variation cues. By contrast, we show how to efficiently take into account the potential sitesâ global shape, which is a critical cue in man-made scenes. Our method relies on component tree segmentation algorithm and a new shape regularity measure to look for polygonal regions in video sequences. In this way we enforce both temporal consistency and geometric regularity, resulting in reliable and consistent detections. Third, we propose a generic contour grouping based object detection approach by exploring promising cycles in a line fragment graph. Previous contour-based methods are limited to use additive scoring functions. In this thesis, we propose an approximate search approach that eliminates this restriction. Given a weighted line fragment graph, we prune its cycle space by removing cycles containing weak nodes or weak edges, until the upper bound of the cycle space is less than the threshold defined by the cyclomatic number. Object contours are then detected as maximally scoring elementary circuits in the pruned cycle space. Furthermore, we propose another more efficient algorithm, which reconstructs the graph by grouping the strongest edges iteratively until the number of the cycles reaches the upper bound. Our approximate search approaches can be used with any cycle scoring function. Moreover, unlike other contour grouping based approaches, our approach does not rely on a greedy strategy for finding multiple candidates and is capable of finding multiple candidates sharing common line fragments. We demonstrate that our approach significantly outperforms the state-of-the-art.

EPFL2015

Chargement

EPFL2000

Localizing Polygonal Objects in Man-Made Environments

Xiaolu Sun

EPFL2015