Neur2RO: Neural Two-Stage Robust Optimization

Robust optimization provides a mathematical framework for modeling and solving decision-making problems under worst-case uncertainty. This work addresses two-stage robust optimization (2RO) problems (also called adjustable robust optimization), wherein first-stage and second-stage decisions are made before and after uncertainty is realized, respectively. This results in a nested min-max-min optimization problem which is extremely challenging computationally, especially when the decisions are discrete. We propose Neur2RO, an efficient machine learning-driven instantiation of column-and-constraint generation (CCG), a classical iterative algorithm for 2RO. Specifically, we learn to estimate the value function of the second-stage problem via a novel neural network architecture that is easy to optimize over by design. Embedding our neural network into CCG yields high-quality solutions quickly as evidenced by experiments on two 2RO benchmarks, knapsack and capital budgeting. For knapsack, Neur2RO finds solutions that are within roughly $2\%$ of the best-known values in a few seconds compared to the three hours of the state-of-the-art exact branch-and-price algorithm; for larger and more complex instances, Neur2RO finds even better solutions. For capital budgeting, Neur2RO outperforms three variants of the $k$-adaptability algorithm, particularly on the largest instances, with a 5 to 10-fold reduction in solution time. Our code and data are available at https://github.com/khalil-research/Neur2RO

Machine Learning for K-adaptability in Two-stage Robust Optimization

Two-stage robust optimization problems constitute one of the hardest optimization problem classes. One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the uncertainty set of scenarios into K subsets, and optimizes decisions corresponding to each of these subsets. In general case, it is solved using the K-adaptability branch-and-bound algorithm, which requires exploration of exponentially-growing solution trees. To accelerate finding high-quality solutions in such trees, we propose a machine learning-based node selection strategy. In particular, we construct a feature engineering scheme based on general two-stage robust optimization insights that allows us to train our machine learning tool on a database of resolved B&B trees, and to apply it as-is to problems of different sizes and/or types. We experimentally show that using our learned node selection strategy outperforms a vanilla, random node selection strategy when tested on problems of the same type as the training problems, also in case the K-value or the problem size differs from the training ones

Notes on the Markowitz portfolio selection method

Portfolio Investment;management science

A concise history of analytical accounting: examining the use of mathematical notions in our discipline.

Este trabajo ofrece una sucinta revisión de los métodos de matemática analítica empleados en teneduría de libros y contabilidad durante los últimos cinco milenios. The paper offers a succinct survey of analytical-mathematical methods as employed in bookkeeping and accounting during some five millennia.Historia de la contabilidad analítica, uso de nociones matemáticas, álgebra matricial, information perspectiva, clean surplus theory, teoría matemática de la agencia. History of analytical accounting, use of mathematical notions, matrix algebra, information perspective, clean surplus theory, mathematical agency theory.

An intelligent system for risk classification of stock investment projects

The proposed paper demonstrates that a hybrid fuzzy neural network can serve as a risk classifier of stock investment projects. The training algorithm for the regular part of the network is based on bidirectional incremental evolution proving more efficient than direct evolution. The approach is compared with other crisp and soft investment appraisal and trading techniques, while building a multimodel domain representation for an intelligent decision support system. Thus the advantages of each model are utilised while looking at the investment problem from different perspectives. The empirical results are based on UK companies traded on the London Stock Exchange

An Extensive Exploration of Techniques for Resource and Cost Management in Contemporary Cloud Computing Environments

Resource and cost optimization techniques in cloud computing environments target minimizing expenditure while ensuring efficient resource utilization. This study categorizes these techniques into three primary groups: Cloud and VM-focused strategies, Workflow techniques, and Resource Utilization and Efficiency techniques. Cloud and VM-focused strategies predominantly concentrate on the allocation, scheduling, and optimization of resources within cloud environments, particularly virtual machines. These strategies aim at a balance between cost reduction and adhering to specified deadlines, while ensuring scalability and adaptability to different cloud models. However, they may introduce complexities due to their dynamic nature and continuous optimization requirements. Workflow techniques emphasize the optimal execution of tasks in distributed systems. They address inconsistencies in Quality of Service (QoS) and seek to enhance the reservation process and task scheduling. By employing models, such as Integer Linear Programming, these techniques offer precision. But they might be computationally demanding, especially for extensive problems. Techniques focusing on Resource Utilization and Efficiency attempts to maximize the use of available resources in an energy-efficient and cost-effective manner. Considering factors like current energy levels and application requirements, these models aim to optimize performance without overshooting budgets. However, a continuous monitoring mechanism might be necessary, which can introduce additional complexities