Class Of Problems Research Articles

An optimization-based method for sign-changing elliptic PDEs

We study the numerical approximation of sign-shifting problems of elliptic type. We fully analyze and assess the method briefly introduced in [Abdulle, Huber, Lemaire; CRAS, 17]. Our method is based on domain decomposition and optimization. Upon an extra integrability assumption on the exact normal flux trace along the sign-changing interface, our method is proved to be convergent as soon as, for a given loading, the PDE admits a unique solution of finite energy. Departing from the T-coercivity approach, which relies on the use of geometrically fitted mesh families, our method works for arbitrary (interface-compliant) mesh sequences. Moreover, it is shown convergent for a class of problems for which T-coercivity is not applicable. A comprehensive set of test-cases complements our analysis.

Bayesian reinforcement learning: A basic overview

We and other animals learn because there is some aspect of the world about which we are uncertain. This uncertainty arises from initial ignorance, and from changes in the world that we do not perfectly know; the uncertainty often becomes evident when our predictions about the world are found to be erroneous. The Rescorla-Wagner learning rule, which specifies one way that prediction errors can occasion learning, has been hugely influential as a characterization of Pavlovian conditioning and, through its equivalence to the delta rule in engineering, in a much wider class of learning problems. Here, we review the embedding of the Rescorla-Wagner rule in a Bayesian context that is precise about the link between uncertainty and learning, and thereby discuss extensions to such suggestions as the Kalman filter, structure learning, and beyond, that collectively encompass a wider range of uncertainties and accommodate a wider assortment of phenomena in conditioning.

Offline Planning and Online Learning Under Recovering Rewards

Motivated by emerging applications, such as live-streaming e-commerce, promotions, and recommendations, we introduce and solve a general class of nonstationary multi-armed bandit problems that have the following two features: (i) the decision maker can pull and collect rewards from up to [Formula: see text] out of N different arms in each time period and (ii) the expected reward of an arm immediately drops after it is pulled and then nonparametrically recovers as the arm’s idle time increases. With the objective of maximizing the expected cumulative reward over T time periods, we design a class of purely periodic policies that jointly set a period to pull each arm. For the proposed policies, we prove performance guarantees for both the offline and the online problems. For the offline problem when all model parameters are known, the proposed periodic policy obtains a long-run approximation ratio that is at the order of [Formula: see text], which is asymptotically optimal when K grows to infinity. For the online problem when the model parameters are unknown and need to be dynamically learned, we integrate the offline periodic policy with the upper confidence bound procedure to construct on online policy. The proposed online policy is proved to approximately have [Formula: see text] regret against the offline benchmark. Our framework and policy design may shed light on broader offline planning and online learning applications with nonstationary and recovering rewards. This paper was accepted by J. George Shanthikumar, data science. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.04202 .

Energy-Efficiency Optimization With Model Convexification for Wireless Ad Hoc Networks With Multi-Packet Reception Capability

Energy efficiency is a significant requirement of resource management and design optimization in information networks. In this work, we propose an iterative fractional programming framework embedded with a distributed primal-dual extra-gradient projection algorithm, which addresses a wide class of the energy-efficiency optimization problems in wireless ad hoc networks with full-duplex radios and multi-packet reception capability. Specifically, we propose a model convexification mechanism by joining an affine transformation and an exponential transformation into the nonlinear fractional programming, which enables us to deal with the challenge arising from the complexity and non-convex structure of the original problem. With the model convexification, we can map the non-convex power control space into a convex space and equivalently derive a sequence of convex subproblems, which relaxes the convexity assumption widely adopted in the existing literature. We further propose a distributed primal-dual algorithm based on extra-gradient projection to solve the convex subproblem at each iteration of the fractional programming. The convergence of the proposed iterative fractional programming and the distributed optimization method is theoretically proven. Numerical results also verify the proposed method and demonstrate its superior performance over other representative distributed and centralized schemes in terms of achieving global energy efficiency.

Bernstein collocation technique for a class of Sturm-Liouville problems

Sturm-Liouville problems have yielded the biggest achievement in the spectral theory of ordinary differential operators. Sturm-Liouville boundary value issues appear in many key applications in natural sciences. All the eigenvalues for the standard Sturm-Liouville problem are guaranteed to be real and simple, and the related eigenfunctions form a basis in a suitable Hilbert space. This article uses the weighted residual collocation technique to numerically compute the eigenpairs of both regular and singular Strum Liouville problems. Bernstein polynomials over [0,1] has been used to develop a weighted residual collocation approach to achieve an improved accuracy. The properties of Bernstein polynomials and the differentiation formula based on the Bernstein operational matrix are used to simplify the given singular boundary value problems into a matrix-based linear algebraic system. Keeping this fact in mind such a polynomial with space defined collocation scheme has been studied for Strum Liouville problems. The main reasons to use the collocation technique are its affordability, ease of use, well-conditioned matrices, and flexibility. The weighted residual collocation method is found to be more appealing because Bernstein polynomials vanish at the two interval ends, providing better versatility. A multitude of test problems are offered along with computation errors to demonstrate how the suggested method behaves. The numerical algorithm and its applicability to particular situations are described in detail, along with the convergence behavior and precision of the current technique.

Rank-1 transition uncertainties in constrained Markov decision processes

We consider an infinite-horizon discounted constrained Markov decision process (CMDP) with uncertain transition probabilities. We assume that the uncertainty in transition probabilities has a rank-1 matrix structure and the underlying uncertain parameters belong to a polytope. We formulate the uncertain CMDP problem using a robust optimization framework. To derive reformulation of the robust CMDP problem, we restrict to the class of stationary policies and show that it is equivalent to a bilinear programming problem. We provide a simple example where a Markov policy performs better than the optimal policy in the class of stationary policies, implying that, unlike in classical CMDP problem, an optimal policy of the robust CMDP problem need not be present in the class of stationary policies. For the case of a single uncertain parameter, we propose sufficient conditions under which an optimal policy of the restricted robust CMDP problem is unaffected by uncertainty. The numerical experiments are performed on randomly generated instances of a machine replacement problem and a well-known class of problems called Garnets.

Generally Applicable Q-Table Compression Method and Its Application for Constrained Stochastic Graph Traversal Optimization Problems

We analyzed a special class of graph traversal problems, where the distances are stochastic, and the agent is restricted to take a limited range in one go. We showed that both constrained shortest Hamiltonian pathfinding problems and disassembly line balancing problems belong to the class of constrained shortest pathfinding problems, which can be represented as mixed-integer optimization problems. Reinforcement learning (RL) methods have proven their efficiency in multiple complex problems. However, researchers concluded that the learning time increases radically by growing the state- and action spaces. In continuous cases, approximation techniques are used, but these methods have several limitations in mixed-integer searching spaces. We present the Q-table compression method as a multistep method with dimension reduction, state fusion, and space compression techniques that project a mixed-integer optimization problem into a discrete one. The RL agent is then trained using an extended Q-value-based method to deliver a human-interpretable model for optimal action selection. Our approach was tested in selected constrained stochastic graph traversal use cases, and comparative results are shown to the simple grid-based discretization method.

A Classification Algorithm Inspired by the Chromatographic Separation Mechanism Dedicated to the Classification of Variable-length and Multi-class Vectors

Nowadays, one of the critical problems related to data mining is the processing of large data sets. This article presents an algorithm that may apply to the issues associated with classifying large-volume data sets. The motivation behind defining this type of algorithm was that the methods used to process this data type are subject to several significant limitations. The first considerable limitation of using classical classification methods is ensuring a constant data size. The second type of constraint is related to the data dimension. The last limitation in using classic classification algorithms is associated with the situation in which a given input vector may contain data belonging to many classes simultaneously, in which case we are talking about so-called multi-class vectors. The presented algorithm is inspired by the method of chromatographic separation of chemical substances. This method is widely and successfully used in analytical chemistry. As we know, in the case of chromatographic separation, we are dealing with a similar class of problems that occur when processing large data sets, firstly: the molecules of a chemical substance have a different number of molecules - i.e., they have different lengths, which corresponds to the situation that occurs when processing large data sets. In this work, a classification algorithm inspired by the mechanism of resolution chromatography is presented. The article presents the results of calculations for sample data sets. It discusses issues related to the properties of the defined algorithm, which concern the algorithm training process and the classification of single-class and multi-class data.

Route Planning Algorithms for Fleets of Connected Vehicles: State of the Art, Implementation, and Deployment

The introduction of 5G technologies has enabled the possibility of designing and building several new classes of networked information systems that were previously impossible to implement due to limitations on data throughput or the reliability of transmission channels. Among them, one of the most interesting and successful examples with a highly positive impact in terms of the quality of urban environments and societal and economical welfare is a system of semi-autonomous connected vehicles, where IoT devices, data centers, and fleets of smart vehicles equipped with communication and computational resources are combined into a heterogeneous and distributed infrastructure, unifying hardware, networks, and software. In order to efficiently provide various services (e.g., patrolling, pickup and delivery, monitoring), these systems typically rely on collecting and broadcasting large amounts of data (e.g., sensor data, GPS traces, or maps), which need to be properly collected and processed in a timely manner. As is well documented in the literature, one of the most effective ways to achieve this purpose, especially in a real-time context, is to adopt a graph model of the data (e.g., to model communication networks, roads, or interactions between vehicles) and to employ suitable graph algorithms to solve properly defined computational problems of interest (e.g., shortest paths or distributed consensus). While research in this context has been extensive from a theoretical perspective, works that have focused on the implementation, deployment, and evaluation of the practical performance of graph algorithms for real-world systems of autonomous vehicles have been much rarer. In this paper, we present a study of this kind. Specifically, we first describe the main features of a real-world information system employing semi-autonomous connected vehicles that is currently being tested in the city of L’Aquila (Italy). Then, we present an overview of the computational challenges arising in the considered application domain and provide a systematic survey of known algorithmic results for one of the most relevant classes of computational problems that have to be addressed in said domain, namely, pickup and delivery problems. Finally, we discuss implementation issues, adopted software tools, and the deployment and testing phases concerning one of the algorithmic components of the mentioned real-world system dedicated to handling a specific problem of the above class, namely, the pickup and delivery multi-vehicle problem with time windows.

Непрерывная зависимость решений линеаризованной начально-краевой задачи транспорта многокомпонентных наносов от входных данных задачи

We consider a chain of problems linearized on a time grid that describe the processes of transport of multicomponent sediments in relation to coastal marine systems. In the author's previous works, the conditions for the existence and uniqueness of a solution to this class of problems were determined, while simultaneously determining the requirements for the smoothness classes of the input data of the problem. The result of this study is related to obtaining an a priori estimate of the norm for solving the problem depending on the integral esti-mates of the right-hand side, boundary conditions and the norm of the initial condition. The obtained a priori estimates allow us to further carry out computationally stable calculations with respect to small errors in the initial data and to errors that arise during calculations.

METHOD OF ORGANIZING INTER-MODULE DATA EXCHANGE

The purpose of this article is the development and description of the method of organizing inter-module data exchange, that is based on the parametric presented subsystems, as well as the evaluation of the effectiveness of the developed multiprocessor computing systems. The authors propose a method of organizing inter-modular exchanges, which is based on the parametric presented subsystem. When developing programs using parallelization algorithms, parameters are used that set specific values for the subsystem. These values are determined during the formation of the subsystem. This makes the program independent of the graph of subsystem inter-module connections, on the basis of which this program will be implemented. The effectiveness of the computer system depends on a set of characteristics, which include: performance, reliability, probability of results, stability, manufacturability and others. To compare computer systems as a criterion of efficiency, it is necessary to adopt a comprehensive indicator that will take into account the main indicators. The real efficiency of a computer system is determined by the time it fulfils its functional purpose. Accordingly, the more reliable the system, the more relative time it is used for its intended purpose and the greater its efficiency. Thus, when comparing computer systems, it is necessary to compare their performance taking into account the real reliability of the system. At the same time, depending on the classes of problems being solved, the influence of various indicators (including reliability) on the efficiency of the system changes. Based on the results of the research, the following conclusions can be drawn: the most effective are the computer systems that are implemented on the developed MO. This fact is clearly visible from the comparison of the time spent on calculating not only the test task, but also when calculating the test equation with the test parameters.

DYNAMIC PROGRAMMING FOR SOLVE THE INVENTORY MANAGEMENT PROBLEM IN LOGISTICS

Currently, there is a problem of methods insufficient efficiency for finding solutions to the inventory management problem. The research object is the process of solving inventory management problems. The research subject is methods for finding a solution to the inventory management problem based on dynamic programming. The research goal is to increase the efficiency of finding a solution to the inventory management problem through dynamic programming. A method based on deterministic dynamic programming, a method based on stochastic dynamic programming, a method based on Q-learning, and a method based on SARSA were applicated for the inventory management problem. There are advantages of the methods. of Methods modification of deterministic and stochastic dynamic programming, Q-learning, and SARSA due to dynamic parameters makes it possible to increase the learning speed while maintaining the root-mean-square error of the method. The numerical study made it possible to evaluate the methods (for modifying the deterministic and stochastic dynamic programming methods, the number of iterations is close to the number of stages; for both methods of deterministic and stochastic dynamic programming, the root mean square error was 0.02; for modifying the Q-learning and SARSA methods, the number of iterations was 300, for both methods of Q-learning and SARSA, the root mean square error was 0.05). These methods make it possible to expand the scope of dynamic programming, which is confirmed by their adaptation to the inventory management problem and helps to increase the intelligent computer systems efficiency for general and special purposes. The application of these methods for a wide class of artificial intelligence problems are the prospects for further research.

Multi-objective Optimization for Green Delivery Routing Problems with Flexible Time Windows

ABSTRACT This paper presents a model and heuristic solution algorithms for the Green Vehicle Routing Problem with Flexible Time Windows. A scenario of new vehicle routing is analyzed in which customers are asked to provide alternative time windows to offer flexibility to help route planners find more fuel-efficient routes (“green delivery”). Customers can rank their preferred time windows as first, second, and third. The optimization model aims to reduce tour costs, promote electromobility over fossil fuels, such as diesel, and meet customer preferences when possible and affordable. The study incorporates a multi-objective optimization model with three objectives, which are overall cost, use of fossil fuel, and customer satisfaction. For the new problem, a set of realistic benchmark problems is created and four mainstream solvers are applied for the Pareto front approximation: NSGA-II, NSGA-III, MOEA/D, and SMS-EMOA. These algorithms are compared in terms of their effectiveness in achieving the objectives of minimizing travel costs, promoting electromobility, and meeting customer preferences. The study uses five different problems of single-vehicle route planning. Two major findings are that the selection of the metaheuristic can make a big difference in terms of algorithm performance. The resulting 3-D Pareto fronts reveal the nature of this new class of problems: Interestingly, in the new model with flexible time windows, most users can still be delivered in their most preferred time windows with only small concessions to the other objectives. However, using only one time window per user can lead to an increasingly drastic cost and fossil fuel consumption.

Integration of Efficient Techniques Based on Endpoints in Solution Method for Lifelong Multiagent Pickup and Delivery Problem

We investigate the integration of several additional efficient techniques that improve a solution method for the lifelong multiagent pickup-and-delivery (MAPD) problem to reduce the redundancy in the concurrent task execution and space usage of a warehouse map. The lifelong MAPD problem is an extended class of iterative multiagent pathfinding problems where a set of shortest collision-free travel paths of multiple agents is iteratively planned. This problem models a system in automated warehouses with robot-carrier agents that are allocated to pickup-and-delivery tasks generated on demand. In the task allocation to agents, several solution methods for lifelong MAPD problems consider the endpoints of the agents’ travel paths to avoid the deadlock situations among the paths due to the conflict of the endpoints. Since redundancies are found in the problem settings themselves and the concurrency of allocated tasks, several additional techniques have been proposed to reduce them in solution methods. However, there should be opportunities to investigate the integration of additional techniques with improvements for more practical solution methods. As analysis and an improved understanding of the additional solution techniques based on endpoints, we incrementally integrate the techniques and experimentally investigate their contributions to the quality of task allocation and the paths of the agents. Our result reveals significant complementary effects of the additionally integrated techniques and trade-offs among them in several different problem settings.

CMOS plus stochastic nanomagnets enabling heterogeneous computers for probabilistic inference and learning

Extending Moore’s law by augmenting complementary-metal-oxide semiconductor (CMOS) transistors with emerging nanotechnologies (X) has become increasingly important. One important class of problems involve sampling-based Monte Carlo algorithms used in probabilistic machine learning, optimization, and quantum simulation. Here, we combine stochastic magnetic tunnel junction (sMTJ)-based probabilistic bits (p-bits) with Field Programmable Gate Arrays (FPGA) to create an energy-efficient CMOS + X (X = sMTJ) prototype. This setup shows how asynchronously driven CMOS circuits controlled by sMTJs can perform probabilistic inference and learning by leveraging the algorithmic update-order-invariance of Gibbs sampling. We show how the stochasticity of sMTJs can augment low-quality random number generators (RNG). Detailed transistor-level comparisons reveal that sMTJ-based p-bits can replace up to 10,000 CMOS transistors while dissipating two orders of magnitude less energy. Integrated versions of our approach can advance probabilistic computing involving deep Boltzmann machines and other energy-based learning algorithms with extremely high throughput and energy efficiency.

К вопросу об особенностях и проблемах использования искусственного интеллекта: Сhat GPT в юридической деятельности

The subject of research in this article is the features and patterns of legal activity in comparison with the features and patterns of functioning of artificial intelligence systems, including systems based on Chat GPT technology. The purpose of the study is to analyze the features and patterns of legal activity, the features and patterns of functioning of artificial intelligence systems, including systems based on the Chat GPT technology, compare these patterns, and based on the comparison of these patterns, draw a conclusion about the degree applicability of artificial intelligence technologies for solving a particular class of legal problems. Research methods include the social experiment method, when Chat GPT was asked certain questions of a legal nature, answers to them were received and analyzed. Also during the study, general scientific research methods were used, such as analysis, synthesis, deduction, abstraction, generalization. These research methods were used to reveal the features and patterns of legal activity, the features and patterns of the functioning of artificial intelligence systems, as well as to draw conclusions about the degree of applicability of artificial intelligence technologies for solving a particular class of problems in jurisprudence.
 During the study, it was found that artificial intelligence technologies based on Chat GPT in some cases are not very suitable for solving problems related to the application of legal norms to specific situations, due to the specific “thinking” of artificial intelligence systems, which in some cases does not allow one to distinguish so-called legal circumstances that are significant in a given situation, from legal circumstances that are not significant in a given situation, the inability in some cases to correctly qualify the legal relations of the parties and make the correct legal decision with reference to current legislation. The study also analyzed the capabilities of artificial intelligence based on Chat GPT technologies for solving problems in the field of lawmaking, application and interpretation of legal norms. It is concluded that in these areas, artificial intelligence technologies, including those based on Chat GPT, have a certain potential, provided that the associative connection built by artificial intelligence between the elements of legal reality contained in the texts corresponds to the ontological connection between the objects of legal reality.

Reduced Desensitization Formulation for Optimal Control Problems

Solutions to nonlinear optimal control problems (OCPs) exhibit dispersions under model uncertainties and it is desirable to generate optimal solutions that exhibit less sensitivity to model uncertainties. We propose a novel solution desensitization method dubbed “Reduced Desensitization Formulation (RDF)” by leveraging non-uniqueness of the solution of the costate differential equations when a hybrid indirect-direct optimization method is used. A key property of the RDF method is a significant reduction in the number of differential equations needed for generating desensitized solutions. This feature facilitates the generation of open-loop desensitized trajectories and makes the methodology applicable to OCPs with a larger number of uncertain parameters. To demonstrate the utility of the RDF method, three important classes of trajectory optimization problems are considered with uncertainty in the thrust magnitude of the propulsion system: (1) minimum-fuel low-thrust interplanetary rendezvous maneuvers, (2) low-thrust orbit-raising maneuvers, and (3) minimum-fuel high-thrust rocket-landing problems. For the considered problems with bang-bang control profiles, an analysis is presented on the change in the number of control switches between sensitive and desensitized optimal solutions. Numerical results demonstrate desensitization of the considered performance indices with respect to the thrust magnitude of the propulsion system.

A high-order B-spline collocation method for solving a class of nonlinear singular boundary value problems

A high-order B-spline collocation method for solving a class of nonlinear singular boundary value problems

Simultaneous analysis and design optimization for seismic retrofitting of hysteretic structures with fluid viscous dampers

Fluid viscous dampers, if properly sized and placed, can significantly improve the performance and safety of existing structures during an earthquake. This has motivated the development of several approaches to optimize the design of fluid viscous dampers. The optimization approaches available typically have an iterative nature, and in every iteration, expensive time-history analyses are performed. This paper presents a novel optimization-based approach for retrofitting hysteretic structures with fluid viscous dampers that does not require the computation of time-history analyses. The sizing and placement of the dampers are defined using a simultaneous analysis and design optimization approach based on nonlinear programming. In this approach, the equations of motion are treated as equality constraints of the optimization problem. As a consequence, design sensitivity analysis methods are not needed to calculate the gradients of the objective and constraint functions. Two design scenarios are considered: structures with hysteretic behavior retrofitted with linear or nonlinear fluid viscous dampers. The optimization variables include the damping coefficients of the dampers and the structural response over time. The manufacturing cost of the dampers is minimized, with constraints on the inter-story drifts. A continuation scheme on the design-driving inter-story drift constraints is proposed to effectively solve the class of problems considered. The numerical results demonstrate that the proposed approach can solve complex design optimization problems using reasonable computational resources and time. It is also shown that, thanks to the proposed approach, additional constraints can be incorporated in the problem formulation with minimal modeling effort, and without the need to develop additional sensitivity analyses for computing the gradients of the added constraints. The Julia codes used in this study are freely available on GitHub: https://github.com/pollinico/SAND_opt_nonlinFVDs.

A Graph-Based Approach for Relating Integer Programs

This paper presents a framework for classifying and comparing instances of integer linear programs (ILPs) based on their mathematical structure. It has long been observed that the structure of ILPs can play an important role in determining the effectiveness of certain solution techniques; those that work well for one class of ILPs are often found to be effective in solving similarly structured problems. In this work, the structure of a given ILP instance is captured via a graph-based representation, where decision variables and constraints are described by nodes, and edges denote the presence of decision variables in certain constraints. Using machine learning techniques for graph-structured data, we introduce two approaches for leveraging the graph representations for relating ILPs. In the first approach, a graph convolutional network (GCN) is used to classify ILP graphs as having come from one of a known number of problem classes. The second approach makes use of latent features learned by the GCN to compare ILP graphs to one another directly. As part of the latter approach, we introduce a formal measure of graph-based structural similarity. A series of empirical studies indicate strong performance for both the classification and comparison procedures. Additional properties of ILP graphs, namely, losslessness and permutation invariance, are also explored via computational experiments. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0255 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0255 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .