This paper presents VORRT-COLREGs, a hybrid technique that combines velocity obstacles (VO) and rapidly-exploring random trees (RRT) to generate safe trajectories for autonomous surface vessels (ASVs) while following nautical rules of the road. RRT generates a set of way points and the velocity obstacles method ensures safe travel between way points. We also ensure that the actions of ASVs do not violate maritime collision guidelines. Earlier work has used RRT and VO separately to generate paths for ASVs. However, RRT does not handle highly dynamic situations well and and VO seems most suitable as a local path planner. Combining both approaches, VORRT-COLREGs is a global path planner that uses a joint forward simulation to ensure that generated paths remain valid and collision free as the situation changes. Experiments were conducted in different types of collision scenarios and with different numbers of ASVs. Results show that VORRT-COLREGS generated collision regulations (COLREGs) complaint paths in open ocean scenarios. Furthermore, VORRT-COLREGS successfully generated compliant paths within traffic separation schemes. These results show the applicability of our technique for generating paths for ASVs in different collision scenarios. To the best of our knowledge, this is the first work that combines velocity obstacles and RRT to produce safe and COLREGs complaint path for ASVs.

Mobile Edge Learning (MEL) is a collaborative learning paradigm that features distributed training of Machine Learning (ML) models over edge devices (e.g., IoT devices). In MEL, possible coexistence of multiple learning tasks with different datasets may arise. The heterogeneity in edge devices' capabilities will require the joint optimization of the learners-orchestrator association and task allocation. To this end, we aim to develop an energy-efficient framework for learners-orchestrator association and learning task allocation, in which each orchestrator gets associated with a group of learners with the same learning task based on their communication channel qualities and computational resources, and allocate the tasks accordingly. Therein, a multi objective optimization problem is formulated to minimize the total energy consumption and maximize the learning tasks' accuracy. However, solving such optimization problem requires centralization and the presence of the whole environment information at a single entity, which becomes impractical in large-scale systems. To reduce the solution complexity and to enable solution decentralization, we propose lightweight heuristic algorithms that can achieve near-optimal performance and facilitate the trade-offs between energy consumption, accuracy, and solution complexity. Simulation results show that the proposed approaches reduce the energy consumption significantly while executing multiple learning tasks compared to recent state-of-the-art methods.

It is reported that the number of online payment users in China has reached 854 million; with the emergence of community e-commerce platforms, the trend of integration of e-commerce and social applications is increasingly intense. Community e-commerce is not a mature and sound comprehensive e-commerce with fewer categories and low brand value. To effectively retain community users and fully explore customer value has become an important challenge for community e-commerce operators. Given the above problems, this paper uses the data-driven method to study the prediction of community e-commerce customers' repurchase behaviour. The main research contents include 1. Given the complex problem of feature engineering, the classic model RFM in the field of customer relationship management is improved, and an improved model is proposed to describe the characteristics of customer buying behaviour, which includes five indicators. 2. In view of the imbalance of machine learning training samples in SMOTE-ENN, a training sample balance using SMOTE-ENN is proposed. The experimental results show that the machine learning model can be trained more effectively on balanced samples. 3. Aiming at the complexity of the parameter adjustment process, an automatic hyperparameter optimization method based on the TPE method was proposed. Compared with other methods, the model's prediction performance is improved, and the training time is reduced by more than 450%. 4. Aiming at the weak prediction ability of a single model, the soft voting based RF-LightgBM model was proposed. The experimental results show that the RF-LighTGBM model proposed in this paper can effectively predict customer repurchase behaviour, and the F1 value is 0.859, which is better than the single model and previous research results.

Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. It aims to find a low rank approximation for nonnegative data M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to solve while it can be solved efficiently under separability assumption, which requires the columns of factor matrix are equal to columns of the input matrix. In this paper, we generalize separability assumption based on 3-factor NMF M=P_1SP_2, and require that S is a sub-matrix of the input matrix. We refer to this NMF as a Co-Separable NMF (CoS-NMF). We discuss some mathematics properties of CoS-NMF, and present the relationships with other related matrix factorizations such as CUR decomposition, generalized separable NMF(GS-NMF), and bi-orthogonal tri-factorization (BiOR-NM3F). An optimization model for CoS-NMF is proposed and alternated fast gradient method is employed to solve the model. Numerical experiments on synthetic datasets, document datasets and facial databases are conducted to verify the effectiveness of our CoS-NMF model. Compared to state-of-the-art methods, CoS-NMF model performs very well in co-clustering task, and preserves a good approximation to the input data matrix as well.

Promotions and discounts are essential components of modern e-commerce platforms, where they are often used to incentivize customers towards purchase completion. Promotions also affect revenue and may incur a monetary loss that is often limited by a dedicated promotional budget. We study the Online Constrained Multiple-Choice Promotions Personalization Problem, where the optimization goal is to select for each customer which promotion to present in order to maximize purchase completions, while also complying with global budget limitations. Our work formalizes the problem as an Online Multiple Choice Knapsack Problem and extends the existent literature by addressing cases with negative weights and values. We provide a real-time adaptive method that guarantees budget constraints compliance and achieves above 99.7% of the optimal promotional impact on various datasets. Our method is evaluated on a large-scale experimental study at one of the leading online travel platforms in the world.

In a previous post, we introduced the method of Lagrange multipliers to find local minima or local maxima of a function with equality constraints. The same method can be applied to those with inequality constraints as well. In this tutorial, you will discover the method of Lagrange multipliers applied to find the local minimum or maximum of a function when inequality constraints are present, optionally together with equality constraints. Lagrange Multiplier Approach with Inequality Constraints Photo by Christine Roy, some rights reserved. You can review these concepts by clicking on the links above.

We focus on the election manipulation problem through social influence, where a manipulator exploits a social network to make her most preferred candidate win an election. Influence is due to information in favor of and/or against one or multiple candidates, sent  by seeds and spreading through the network according to the independent cascade model.  We provide a comprehensive theoretical study of the election control problem, investigating  two forms of manipulations: seeding to buy influencers given a social network and removing  or adding edges in the social network given the set of the seeds and the information sent.  In particular, we study a wide range of cases distinguishing in the number of candidates or  the kind of information spread over the network. Our main result shows that the election manipulation problem is not affordable in  the worst-case, even when one accepts to get an approximation of the optimal margin of  victory, except for the case of seeding when the number of hard-to-manipulate voters is not  too large, and the number of uncertain voters is not too small, where we say that a voter  that does not vote for the manipulator's candidate is hard-to-manipulate if there is no way  to make her vote for this candidate, and uncertain otherwise. We also provide some results showing the hardness of the problems in special cases.  More precisely, in the case of seeding, we show that the manipulation is hard even if the  graph is a line and that a large class of algorithms, including most of the approaches  recently adopted for social-influence problems (e.g., greedy, degree centrality, PageRank, VoteRank), fails to compute a bounded approximation even on elementary networks, such  as undirected graphs with every node having a degree at most two or directed trees. In the  case of edge removal or addition, our hardness results also apply to election manipulation  when the manipulator has an unlimited budget, being allowed to remove or add an arbitrary  number of edges, and to the basic case of social influence maximization/minimization in  the restricted case of finite budget. Interestingly, our hardness results for seeding and edge removal/addition still hold  in a re-optimization variant, where the manipulator already knows an optimal solution  to the problem and computes a new solution once a local modification occurs, e.g., the  removal/addition of a single edge.

FLAML is a lightweight Python library from Microsoft Research that finds accurate machine learning models in an efficient and economical way using cutting edge algorithms designed to be resource-efficient and easily parallelizable. FLAML can also utilize Ray Tune for distributed hyperparameter tuning to scale up these AutoML methods across a cluster. AutoML is known to be a resource and time consuming operation as it involves trials and errors to find a hyperparameter configuration with good performance. Since the space of possible configuration values is often very large, there is a need for an economical AutoML method that can more effectively search them. To address both of these factors, Microsoft Researchers have developed FLAML (Fast Lightweight AutoML).

In this paper, given a small bag of images, each containing a common but latent predicate, we are interested in localizing visual subject-object pairs connected via the common predicate in each of the images. We refer to this novel problem as visual relationship co-localization or VRC as an abbreviation. VRC is a challenging task, even more so than the well-studied object co-localization task. This becomes further challenging when using just a few images, the model has to learn to co-localize visual subject-object pairs connected via unseen predicates. To solve VRC, we propose an optimization framework to select a common visual relationship in each image of the bag. The goal of the optimization framework is to find the optimal solution by learning visual relationship similarity across images in a few-shot setting. To obtain robust visual relationship representation, we utilize a simple yet effective technique that learns relationship embedding as a translation vector from visual subject to visual object in a shared space. Further, to learn visual relationship similarity, we utilize a proven meta-learning technique commonly used for few-shot classification tasks. Finally, to tackle the combinatorial complexity challenge arising from an exponential number of feasible solutions, we use a greedy approximation inference algorithm that selects approximately the best solution. We extensively evaluate our proposed framework on variations of bag sizes obtained from two challenging public datasets, namely VrR-VG and VG-150, and achieve impressive visual co-localization performance.

This is a two-part case study where we define the optimization problem in part one, and we use the Pulp python library as a tool to solve the business problem in part two. Optimization problems are the dilemma of any business. This can come in two decision-making: either maximation and minimization, be it profit or cost. A typical optimization problem can be solved with an optimization method which in itself is mathematical. Therefore we need to represent our above component definitions mathematically.