Search Results (11)

This study establishes a novel mathematical framework for stochastic maintenance optimization in production systems by integrating Markov decision processes (MDPs) with convex programming theory. We develop a Z-transformation-based dual-space decomposition method to reconstruct MDPs into a solvable linear programming form, resolving the inherent instability of traditional models caused by uncertain initial conditions and non-stationary state transitions. The proposed approach introduces three mathematical innovations: (i) a spectral clustering mechanism that reduces state-space dimensionality while preserving Markovian properties, (ii) a Lagrangian dual formulation with adaptive penalty functions to handle operational constraints, and (iii) a warm start algorithm accelerating convergence in high-dimensional convex optimization. Theoretical analysis proves that the derived policy achieves stability in probabilistic transitions through martingale convergence arguments, demonstrating structural invariance to initial distributions. Experimental validations on production processes reveal that our model reduces long-term maintenance costs by 36.17% compared to Monte Carlo simulations (1500 vs. 2350 average cost) and improves computational efficiency by 14.29% over Q-learning methods. Sensitivity analyses confirm robustness across Weibull-distributed failure regimes (shape parameter $\beta \in$ [1.2, 4.8]) and varying resource constraints. Full article

This study proposes an Index-Based Neural Network (IBNN) framework for the static analysis of truss structures, employing a Lagrangian dual optimization technique grounded in the force method. A truss is a discrete structural system composed of linear members connected to nodes. Despite their geometric simplicity, analysis of large-scale truss systems requires significant computational resources. The proposed model simplifies the input structure and enhances the scalability of the model using member and node indices as inputs instead of spatial coordinates. The IBNN framework approximates member forces and nodal displacements using separate neural networks and incorporates structural equations derived from the force method as mechanics-informed constraints within the loss function. Training was conducted using the Augmented Lagrangian Method (ALM), which improves the convergence stability and learning efficiency through a combination of penalty terms and Lagrange multipliers. The efficiency and accuracy of the framework were numerically validated using various examples, including spatial trusses, square grid-type space frames, lattice domes, and domes exhibiting radial flow characteristics. Multi-index mapping and domain decomposition techniques contribute to enhanced analysis performance, yielding superior prediction accuracy and numerical stability compared to conventional methods. Furthermore, by reflecting the structured and discrete nature of structural problems, the proposed framework demonstrates high potential for integration with next-generation neural network models such as Quantum Neural Networks (QNNs). Full article

Algorithms involving kernel functions, such as support vector machine (SVM), have attracted huge attention within the artificial learning communities. The performance of these algorithms is greatly influenced by outliers and the choice of kernel functions. This paper introduces a new version of SVM named Deep Decomposition Neural Network Fuzzy SVM (DDNN-FSVM). To this end, we consider an auto-encoder (AE) deep neural network with three layers: input, hidden, and output. Unusually, the AE’s hidden layer comprises a number of neurons greater than the dimension of the input samples, which guarantees linear data separation. The encoder operator is then introduced into the FSVM’s dual to map the training samples to high-dimension spaces. To learn the support vectors and autoencoder parameters, we introduce the loss function and regularization terms in the FSVM dual. To learn from large-scale data, we decompose the resulting model into three small-dimensional submodels using Lagrangian decomposition. To solve the resulting problems, we use SMO, ISDA, and SCG for optimization problems involving large-scale data. We demonstrate that the optimal values of the three submodels solved in parallel provide a good lower bound for the optimal value of the initial model. In addition, thanks to its use of fuzzy weights, DDNN-FSVM is resistant to outliers. Moreover, DDNN-FSVM simultaneously learns the appropriate kernel function and separation path. We tested DDNN-FSVM on several well-known digital and image datasets and compared it to well-known classifiers on the basis of accuracy, precision, f-measure, g-means, and recall. On average, DDNN-FSVM improved on the performance of the classic FSVM across all datasets and outperformed several well-known classifiers. Full article

The main purpose of the work was examining various methods of decomposition of a network optimization problem of simultaneous routing and bandwidth allocation based on Lagrangian relaxation. The problem studied is an NP-hard mixed-integer nonlinear optimization problem. Multiple formulations of the optimization problem are proposed for the problem decomposition. The decomposition methods used several problem formulations and different choices of the dualized constraints. A simple gradient coordination algorithm, cutting-plane coordination algorithm, and their more sophisticated variants were used to solve dual problems. The performance of the proposed decomposition methods was compared to the commercial solver CPLEX and a heuristic algorithm. Full article

Bike sharing systems (BSSs) are widely adopted in major cities of the world due to traffic congestion and carbon emissions. Although there have been approaches to exploit either bike trailers via crowdsourcing or carrier vehicles to reposition bikes in the “right” stations in the “right” time, they did not jointly consider the usage of both bike trailers and carrier vehicles. In this paper, we aim to take advantage of both bike trailers and carrier vehicles to reduce the loss of demand by determining whether bike trailers or carrier vehicles (or both) should be used. In addition, we also would like to maximize the overall profit with regard to the crowdsourcing of bike trailers and the fuel cost of carrier vehicles. In the experiment, we exhibit that our approach outperforms baselines in multiple data sets from bike sharing companies. Full article

In this paper, we propose a mobile edge computing (MEC)-enabled unmanned aerial vehicle (UAV)-assisted vehicular ad hoc network (VANET) architecture, based on which a number of vehicles are served by UAVs equipped with computation resource. Each vehicle has to offload its computing tasks to the proper MEC server on the UAV due to the limited computation ability. To counter the problems above, we first model and analyze the transmission model and the security assurance model from the vehicle to the MEC server on UAV, and the task computation model of the local vehicle and the edge UAV. Then, the vehicle offloading problem is formulated as a multi-objective optimization problem by jointly considering the task offloading, the resource allocation, and the security assurance. For tackling this hard problem, we decouple the multi-objective optimization problem as two subproblems and propose an efficient iterative algorithm to jointly make the MEC selection decision based on the criteria of load balancing and optimize the offloading ratio and the computation resource according to the Lagrangian dual decomposition. Finally, the simulation results demonstrate that our proposed scheme achieves significant performance superiority compared with other schemes in terms of the successful task processing ratio and the task processing delay. Full article

The backbone of a conventional electrical power generation system relies on hydro-thermal coordination. Due to its intrinsic complex, large-scale and constrained nature, the feasibility of a direct approach is reduced. With this limitation in mind, decomposition methods, particularly Lagrangian relaxation, constitutes a consolidated choice to “simplify” the problem. Thus, translating a relaxed problem approach indirectly leads to solutions of the primal problem. In turn, the dual problem is solved iteratively, and Lagrange multipliers are updated between each iteration using subgradient methods. However, this class of methods presents a set of sensitive aspects that often require time-consuming tuning tasks or to rely on the dispatchers’ own expertise and experience. Hence, to tackle these shortcomings, a novel Lagrangian multiplier update adaptative algorithm is proposed, with the aim of automatically adjust the step-size used to update Lagrange multipliers, therefore avoiding the need to pre-select a set of parameters. A results comparison is made against two traditionally employed step-size update heuristics, using a real hydrothermal scenario derived from the Portuguese power system. The proposed adaptive algorithm managed to obtain improved performances in terms of the dual problem, thereby reducing the duality gap with the optimal primal problem. Full article

We consider a general problem of optimal allocation of limited resources in a wireless telecommunication network. The network users are divided into several different groups (or classes), which correspond to different levels of service. The network manager must satisfy these different users’ requirements. This approach leads to a convex optimization problem with balance and capacity constraints. We present several decomposition type methods to find a solution to this problem, which exploit its special features. We suggest applying first the dual Lagrangian method with respect to the total capacity constraint, which gives the one-dimensional dual problem. However, calculation of the value of the dual cost function requires solving several optimization problems. Our methods differ in approaches for solving these auxiliary problems. We consider three basic methods: Dual Multi Layer (DML), Conditional Gradient Dual Multilayer (CGDM) and Bisection (BS). Besides these methods we consider their modifications adjusted to different kind of cost functions. Our comparison of the performance of the suggested methods on several series of test problems show satisfactory convergence. Nevertheless, proper decomposition techniques enhance the convergence essentially. Full article

Recently, the simultaneous wireless information and power transfer (SWIPT) technique has been regarded as a promising approach to enhance performance of wireless sensor networks with limited energy supply. However, from a green communication perspective, energy efficiency optimization for SWIPT system design has not been investigated in Wireless Rechargeable Sensor Networks (WRSNs). In this paper, we consider the tradeoffs between energy efficiency and three factors including spectral efficiency, the transmit power and outage target rate for two different modes, i.e., power splitting (PS) and time switching modes (TS), at the receiver. Moreover, we formulate the energy efficiency maximization problem subject to the constraints of minimum Quality of Service (QoS), minimum harvested energy and maximum transmission power as non-convex optimization problem. In particular, we focus on optimizing power control and power allocation policy in PS and TS modes to maximize energy efficiency of data transmission. For PS and TS modes, we propose the corresponding algorithm to characterize a non-convex optimization problem that takes into account the circuit power consumption and the harvested energy. By exploiting nonlinear fractional programming and Lagrangian dual decomposition, we propose suboptimal iterative algorithms to obtain the solutions of non-convex optimization problems. Furthermore, we derive the outage probability and effective throughput from the scenarios that the transmitter does not or partially know the channel state information (CSI) of the receiver. Simulation results illustrate that the proposed optimal iterative algorithm can achieve optimal solutions within a small number of iterations and various tradeoffs between energy efficiency and spectral efficiency, transmit power and outage target rate, respectively. Full article

In this paper, we propose a novel automated double auction mechanism called convergent linear function submission-based double-auction (CLFS-DA) for a prosumers’ decentralized smart grid. The target decentralized smart grid is a regional electricity network that consists of many prosumers that have a battery and a renewable energy-based generator, such as photovoltaic cells. In the proposed double-auction mechanism, each intelligent software agent representing each prosumer submits linear demand and supply functions to an automated regional electricity market where they are registered. It is proven that the CLFS-DA mechanism is guaranteed to obtain one of the global optimal price profiles in addition to it achieving an exact balance between demand and supply, even through the learning period. The proof of convergence is provided on the basis of the theory of LFS-DA, which gives a clear bridge between a function submission-based double auction and a dual decomposition (DD)-based real-time pricing procedure. The performance of the proposed mechanism is demonstrated numerically through a simulation experiment. Full article

A linear function submission-based double auction (LFS-DA) mechanism for a regional electricity network is proposed in this paper. Each agent in the network is equipped with a battery and a generator. Each agent simultaneously becomes a producer and consumer of electricity, i.e., a prosumer, and trades electricity in the regional market at a variable price. In the LFS-DA, each agent uses linear demand and supply functions when they submit bids and asks to an auctioneer in the regional market. The LFS-DA can achieve an exact balance between electricity demand and supply for each time slot throughout the learning phase and was shown capable of solving the primal problem of maximizing the social welfare of the network without any central price setter, e.g., a utility or a large electricity company, in contrast with conventional real-time pricing (RTP). This paper presents a clarification of the relationship between the RTP algorithm derived on the basis of a dual decomposition framework and LFS-DA. Specifically, we proved that the changes in the price profile of the LFS-DA mechanism are equal to those achieved by the RTP mechanism derived from the dual decomposition framework, except for a constant factor. Full article