Solution Of Problem Research Articles

Existence of weak solutions for nonlocal Dirichlet problems via Young measure theory

This article investigates the existence of weak solutions for a class of nonlocal problems with Dirichlet boundary conditions. The proof of the existence result relies on Galerkin's approximation and Young's measure theory. For more information see https://ejde.math.txstate.edu/Volumes/2024/73/abstr.html

Optimum solution of power flow problem based on search and rescue algorithm

AbstractIn order to solve the optimal power flow (OPF) problem, a unique algorithm based on a search and rescue method is applied in this study. For the OPF problem under three objective functions, the SAR offers a straightforward and reliable solution. The three objective functions are used to minimize the fuel cost, power loss and voltage deviation as a single objective function. The OPF problem for benchmark test system, including the IEEE-14 bus, IEEE-30 bus, and IEEE-57 bus, are solved by the Search and Rescue algorithm (SAR) under specific objective functions that are determined by the operational and economic performance indices of the power system. To demonstrate the efficacy and possibilities of the SAR algorithm, SAR is contrasted with alternative optimization techniques such as harmony search algorithm, gradient method, adaptive genetic algorithm, biogeography-based optimization, Artificial bee colony, gravitational search algorithm, particle swarm optimization, Jaya algorithm, enhanced genetic algorithm, modified shuffle frog leaping algorithm, practical swarm optimizer, Moth flam optimizer, whale and moth flam optimizer, grey wolf optimizer, cheap optimization algorithm and differential evolution algorithm. The value of minimum power losses based on SAR technique is equal to 0.459733441487247 MW for IEEE-14 bus. The value of minimum total fuel cost based on SAR technique is equal to 8051.12225602148 $/h for IEEE-14 bus. The value of minimum voltage deviation based on SAR technique is equal to 0.0357680148269292 for IEEE-14 bus. The value of minimum power losses based on SAR technique is equal to 2.71286428848434 MW for IEEE-30 bus. The value of minimum total fuel cost based on SAR technique is equal to 798.197578585806 $/h for IEEE-30 bus. The value of minimum voltage deviation based on SAR technique is equal to 0.0978069572088536 for IEEE-30 bus. The value of minimum total fuel cost based on SAR technique is equal to 38017.7691758245 $/h for IEEE-57 bus. The acquired results for the OPF compared to all competitor algorithms in every case of fitness function demonstrate the superiority of the SAR method.

Accurate, Fast, and Non-Destructive Net Charge Measurement of Levitated Nanoresonators Based on Maxwell Speed Distribution Law

Nanoscale resonant devices based on optical tweezers are widely used in the field of precision sensing. In the process of driving the nanoresonator based on the Coulomb force, the real-time, precise regulation of the charge carried by the charged resonator is essential for continuous manipulation. However, the accuracy of the existing charge measurement methods for levitated particles is low, and these methods cannot meet the needs of precision sensing. In this study, a novel net charge measurement protocol for levitated particles based on spatial speed statistics is proposed. High-precision mass measurement based on Maxwell’s rate distribution law is the basis for improving the accuracy of charge measurement, and accurate measurement of net charge can be achieved by periodic electric field driving. The error of net charge measurement is less than 7.3% when the pressure is above 0.1 mbar, while it can be less than 0.76% at 10 mbar. This proposed method features real-time, high-precision, non-destructive, and in situ measurement of the net charge of particles in the medium vacuum, which provides new solutions for practical problems in the fields of high-precision sensing and nano-metrology based on levitated photodynamics.

Determination of the Thermal Conductivity and Volumetric Heat Capacity of Substance from Heat Flux

The study of nonlinear problems related to heat transfer in a substance is of great practical important. Earlier, this paper’s authors proposed an effective algorithm for determining the volumetric heat capacity and thermal conductivity of a substance based on experimental observations of the dynamics of the temperature field in the object. In this paper, the problem of simultaneous identification of temperature-dependent volumetric heat capacity and thermal conductivity of the substance under study from the heat flux at the boundary of the domain is investigated. The consideration is based on the first boundary value problem for a one-dimensional unsteady heat equation. The coefficient inverse problem under consideration is reduced to a variational problem, which is solved by gradient methods based on the application of fast automatic differentiation. The uniqueness of the solution of the inverse problem is investigated.

Quadratic Programming Problems and Its Solution Techniques With Neural Network Modeling

ABSTRACTThis paper presents a study on quadratic programming problems (QPP) and introduces a new neural network model with feasibility analysis. The stability analysis of QPP using neural network modeling is also discussed. The proposed neural network model has a simple form, and its optimal feasibility for both primal and dual QP problems is established. The model demonstrates a good convergence rate with a minimal number of iterations, achieving a very fast convergence to the exact solutions of both the primal and dual QP problems. The optimal solutions for the original QP problem and its dual QPP are obtained. Finally, two simple numerical examples are simulated to illustrate the findings.

Sequential Kalman Tuning of the t-preconditioned Crank-Nicolson algorithm: efficient, adaptive and gradient-free inference for Bayesian inverse problems

Abstract Ensemble Kalman Inversion (EKI) has been proposed as an efficient method for the approximate solution of Bayesian inverse problems with expensive forward models. However, when applied to the Bayesian inverse problem EKI is only exact in the regime of Gaussian target measures and linear forward models. In this work we propose embedding EKI and Flow Annealed Kalman Inversion (FAKI), its normalizing flow (NF) preconditioned variant, within a Bayesian annealing scheme as part of an adaptive implementation of the $t$-preconditioned Crank-Nicolson (tpCN) sampler. The tpCN sampler differs from standard pCN in that its proposal is reversible with respect to the multivariate $t$-distribution. The more flexible tail behaviour allows for better adaptation to sampling from non-Gaussian targets. Within our Sequential Kalman Tuning (SKT) adaptation scheme, EKI is used to initialize and precondition the tpCN sampler for each annealed target. The subsequent tpCN iterations ensure particles are correctly distributed according to each annealed target, avoiding the accumulation of errors that would otherwise impact EKI. We demonstrate the performance of SKT for tpCN on three challenging numerical benchmarks, showing significant improvements in the rate of convergence compared to adaptation within standard SMC with importance weighted resampling at each temperature level, and compared to similar adaptive implementations of standard pCN. The SKT scheme applied to tpCN offers an efficient, practical solution for solving the Bayesian inverse problem when gradients of the forward model are not available. Code implementing the SKT schemes for tpCN is available at \url{https://github.com/RichardGrumitt/KalmanMC}.

A Modified Simulated Annealing and Enhanced Harmony Search Algorithms for the Continuous Facility Layout Problem (CFLP)

This paper focuses on solving the Continuous Facility Layout Problem (CFLP), which aims to minimize material handling costs by strategically placing facilities in a known or unknown area. The objective is to find optimal or near-optimal facility arrangements while adhering to non-overlapping and spatial constraints, thus enhancing the efficiency of production systems. The study addresses various layout scenarios, including single-row facility layout (with and without clearance), continuous layout, and unequal-area facility layout problems. To achieve this, the authors propose a mixed-integer nonlinear programming (MINLP) model tailored for continuous layouts. Two meta-heuristic algorithms are developed to optimize this model: a hybrid Simulated Annealing-Genetic Algorithm (SA-GA), which leverages genetic crossover operations, and an Enhanced Harmony Search Algorithm (EHSA), featuring dynamic parameters and a novel improvisation technique. The proposed methods provide flexible and efficient solutions for both small and large-scale layout problems, offering decision-makers practical tools for real-world applications.

Promoted Osprey Optimizer: a solution for ORPD problem with electric vehicle penetration.

This paper proposes a new optimization technique to make an integration between the Optimal Reactive Power Dispatch (ORPD) problem and Electric Vehicles (EV). Here, a modified metaheuristic algorithm, called the Promoted Osprey Optimizer (POO) is used for this purpose. Inspired by the hunting behavior of ospreys, a predatory bird species, the POO algorithm employs various strategies like diving, soaring, and gliding to effectively explore the search space and avoid local optima. To evaluate its performance, the POO-based model has been applied to the IEEE 118-bus and IEEE 57-bus systems, considering different scenarios of EV penetration. The experimental findings demonstrate that the POO algorithm can effectively optimize the reactive power dispatch problem with EV integration, achieving significant reductions in active power losses and voltage deviations toward several existing metaheuristic optimization techniques in different terms. The POO algorithm demonstrates a significant reduction in power loss, achieving up to 22.2% and 16.2% in the 57-bus and 118-bus systems, respectively. This improvement is accompanied by reductions in voltage deviation of up to 20.6% and 15.7%. In the 57-bus system, power loss is reduced from 2.35MW to 1.93MW, while voltage deviation decreases from 0.034 p.u. to 0.027 p.u. For the 118-bus system, power loss is lowered from 4.21MW to 3.53MW, and voltage deviation is reduced from 0.051 p.u. to 0.043 p.u. Furthermore, the POO algorithm surpasses other optimization methods in minimizing voltage deviation, achieving reductions of up to 0.056 p.u. in the 57-bus system and up to 0.163 p.u. in the 118-bus system. Consequently, the POO algorithm holds great potential as a valuable tool for power system operators and planners to optimize reactive power dispatch and enhance power system performance with EV integration.

Local geometry of NAE-SAT solutions in the condensation regime

AbstractThe local behavior of typical solutions of random constraint satisfaction problems (csp) describes many important phenomena including clustering thresholds, decay of correlations, and the behavior of message passing algorithms. When the constraint density is low, studying the planted model is a powerful technique for determining this local behavior which in many examples has a simple Markovian structure. The work of Coja-Oghlan, Kapetanopoulos, Müller (Comb Prob Comput 29:346-422, 2020) showed that for a wide class of models, this description applies up to the so-called condensation threshold. Understanding the local behavior after the condensation threshold is more complex due to long-range correlations. In this work, we revisit the random regular nae-sat model in the condensation regime and determine the local weak limit which describes a random solution around a typical variable. This limit exhibits a complicated non-Markovian structure arising from the space of solutions being dominated by a small number of large clusters. This is the first description of the local weak limit in the condensation regime for any sparse random csps in the one-step replica symmetry breaking (1rsb) class. Our result is non-asymptotic and characterizes the tight fluctuation $$O(n^{-1/2})$$ O ( n - 1 / 2 ) around the limit. Our proof is based on coupling the local neighborhoods of an infinite spin system, which encodes the structure of the clusters, to a broadcast model on trees whose channel is given by the 1rsb belief-propagation fixed point. We believe that our proof technique has broad applicability to random csps in the 1rsb class.

Dynamic Supplier Selection and Its Optimal Strategy Considering Full Truck Load and Fuzzy Demand using Fuzzy Expected Value-Based Programming

This article proposes a linear integer optimization model incorporating fuzzy parameters to find the optimal solution for a dynamic supplier selection problem with uncertain demand. The uncertain demand value is represented using a fuzzy variable. A fuzzy expected value-based linear optimization solver is used to address the optimization problem, to minimize the total cost under fuzzy demand values. Several computational experiments were conducted to evaluate and analyze the model. The results show that the proposed model effectively identifies the optimal suppliers for each product. Additionally, the model determines the optimal purchase volumes for each product type from the selected suppliers, leading to the minimal total expected cost.

Multi-Objective Optimization of Three-Stage Turbomachine Rotor Based on Complex Transfer Matrix Method

This study presents the complex transfer matrix method (CTMM) as an advanced mathematical model, providing significant advantages over the finite element method (FEM) by yielding rapid solutions for complex optimization problems. In order to design a more efficient structure of a three-stage turbomachine rotor, we integrated this method with various optimization algorithms, including genetic algorithm (GA), differential evolution (DE), simulated annealing (SA), gravitational search algorithm (GSA), black hole (BH), particle swarm optimization (PSO), Harris hawk optimization (HHO), artificial bee colony (ABC), and non-metaheuristic pattern search (PS). Thus, the best rotor geometry can be obtained fast with minimum bearing forces and disk deflections within design limits. In the results, the efficiency of the CTMM for achieving optimized designs is demonstrated. The CTMM outperformed the FEM in both speed and applicability for complex rotordynamic problems. The CTMM was found to deliver results of comparable quality much faster than the FEM, especially with higher element quality. The use of the CTMM in the iterative optimization process is shown to be highly advantageous. Furthermore, it is noted that among the different optimization algorithms, ABC provided the best results for this multi-objective optimization problem.

An enhanced flower pollination algorithm with superiority of feasible solution for optimal power flow problem

An enhanced flower pollination algorithm with superiority of feasible solution for optimal power flow problem

Application of linear Legendre multi-wavelets collocation method for solution of fourth order boundary value problems

Application of linear Legendre multi-wavelets collocation method for solution of fourth order boundary value problems

Data-Driven Morozov Regularization of Inverse Problems

The solution of inverse problems is crucial in various fields such as medicine, biology, and engineering, where one seeks to find a solution from noisy observations. These problems often exhibit non-uniqueness and ill-posedness, resulting in instability under noise with standard methods. To address this, regularization techniques have been developed to balance data fitting and prior information. Recently, data-driven variational regularization methods have emerged, mainly analyzed within the framework of Tikhonov regularization, termed Network Tikhonov (NETT). This paper introduces Morozov regularization combined with a learned regularizer, termed DD-Morozov regularization. Our approach employs neural networks to define non-convex regularizers tailored to training data, enabling a convergence analysis in the non-convex context with noise-dependent regularizers. We also propose a refined training strategy that improves adaptation to ill-posed problems compared to NETT’s original strategy, which primarily focuses on addressing non-uniqueness. We present numerical results for attenuation correction in photoacoustic tomography, comparing DD-Morozov regularization with NETT using the same trained regularizer, both with and without an additional total variation regularizer.

On Deadlock Analysis and Characterization of Labeled Petri Nets with Undistinguishable and Unobservable Transitions

This work addresses the analysis and characterization of deadlocks in discrete-event systems modeled by labeled Petri nets (LPNs) with undistinguishable and unobservable transitions. To provide a solution for the notorious problem, it is essential to present an effective characterization in such a way that deadlock control and synthesis are technically and methodologically possible. To this end, we introduce the notion of dangerous implicit vectors (DIVs), which implicitly threaten the system deadlock-freedom. The set of dead markings is divided into two subsets: dead basis markings (DBMs) and dangerous implicit markings (DIMs). An algorithm is designed to compute the sets of DIVs and DIMs at a given basis state of a system. Moreover, by virtue of linear algebraic equations, we formulate sufficient conditions for identifying the existence of blocking markings in an LPN. Finally, an algorithm is developed to construct an observed graph that is a compendious presentation of the reachability graph of a net system, with respect to the existence of dead reaches. At the end of this paper, experiment results that illustrate the correctness and effectiveness of the reported solution are presented.

A Physics Informed Neural Network for Solving the Inverse Heat Transfer Problem in Gas Turbine Rotating Cavities

Abstract Recently, Physics-Informed Neural Networks have displayed great potential in delivering swift and accurate solutions for inverse problems. Here, a Physics-Informed Neural Network (PINN) was used to solve the inverse heat conduction problem in the rotating cavities of a aeroengine high-pressure compressor internal air system. The neural network was designed to receive experimentally captured radially distributed temperature profiles as inputs and predict the associated surface heat fluxes. The correctness of these predicted heat fluxes are assessed by numerically solving the direct heat conduction equation using a 2D Finite-Element model, thereby recovering the original temperature profiles. A comparative analysis is conducted between the predicted temperature profiles and the initial inputs. The physics informed neural network is trained using noise free synthetic data, created from a range of radial temperature curve fit coefficients, and subsequently tested on noisy experimental data at engine representative conditions. The predicted temperature values exhibit some good agreement with their respective actual counterparts. Furthermore, the sensitivity of model hyperparameters are explored to showcase the capability of the proposed approach. The results show that Physics- Informed Neural Networks exhibit reduced susceptibility to experimental uncertainties when addressing inverse problems, in contrast to inverse solution methods, and offer a possible new approach for analysis of experimental data if trained on a sufficiently large dataset.

Viscosity solutions of centralized control problems in measure spaces

This work focuses on a control problem in the Wasserstein space of probability measures over $\mathbb{R}^d$. Our aim is to link this control problem to a suitable Hamilton-Jacobi-Bellman (HJB) equation. We explore a notion of viscosity solution using test functions that are locally Lipschitz and locally semiconvex or semiconcave functions. This regularity allows to define a notion of viscosity and a Hamiltonian function relying on directional derivatives. Using a generalization of Ekeland's principle, we show that the corresponding HJB equation admits a comparison principle, and deduce that the value function is the unique solution in this viscosity sense. The PDE tools are developed in the general framework of Measure Differential Equations.

Adaptable and Generic Methods for Monitoring and Prognostics of Energy Assets

Monitoring and prognostics of energy assets are crucial for maintaining their reliability and efficiency. Effective monitoring ensures that potential issues are identified early, preventing unexpected failures and optimizing maintenance schedules. However, several challenges complicate this process in real-world scenarios, including poor data quality, low-fidelity and sparse data, the influence of external environmental factors, and diverse operating conditions and asset types. These challenges highlight the need for adaptable and generic solutions that can handle variability and complexity across different energy systems. This Ph.D. project aims to address these challenges by developing scalable, data-driven approaches for monitoring and prognostics. By focusing on creating adaptable and generic frameworks, the research seeks to provide robust solutions for real-world monitoring and prognostic problems for energy assets.

Robotic Warehousing Operations: A Learn-Then-Optimize Approach to Large-Scale Neighborhood Search

The rapid deployment of robotics technologies requires dedicated optimization algorithms to manage large fleets of autonomous agents. This paper supports robotic parts-to-picker operations in warehousing by optimizing order–workstation assignments, item–pod assignments, and the schedule of order fulfillment at workstations. The model maximizes throughput, managing human workload at the workstations and congestion in the facility. We solve it via large-scale neighborhood search with a novel learn-then-optimize approach to subproblem generation. The algorithm relies on an off-line machine learning procedure to predict objective improvements based on subproblem features and an online optimization model to generate a new subproblem at each iteration. In collaboration with Amazon Robotics, we show that our model and algorithm generate much stronger solutions for practical problems than state-of-the-art approaches. In particular, our solution enhances the utilization of robotic fleets by coordinating robotic tasks for human operators to pick multiple items at once and by coordinating robotic routes to avoid congestion in the facility. Funding: This research was partially funded by Amazon.com Services LLC under award number 2D-12552417. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2024.0033 .

Multitask scheduling on cloud additive manufacturing using NSGA-II

Purpose: Cloud manufacturing (CM) represents a new manufacturing paradigm that integrates distributed resources to provide on-demand services. The high consumer demand from various locations, coupled with the customizability and complexity of manufacturing, complicates task scheduling. In this context, 3D printers are crucial as innovative manufacturing technologies with significant potential in producing complex and custom products. Scheduling in CM falls under the non-deterministic polynomial time-hard category, where tasks must be scheduled and distributed rapidly. Considerations of distance, minimization of delays, and makespan become critical variables that must be considered. This research aims to schedule and distribute tasks in CM using the non-dominated sorting genetic algorithm II (NSGA-II) to minimize delays, reduce makespan, and decrease costs.Methodology: NSGA-II is employed to tackle the complexities of scheduling in CM. The strength of NSGA-II lies in its ability to determine optimal and efficient solutions for multiobjective problems. Tasks originating from requests at various locations are adjusted based on material parameters and dimensions and then distributed to providers while considering aspects such as makespan, delay minimization, and cost.Findings: The optimization results using NSGA-II demonstrate effective and efficient task distribution to providers. Across the four tested task distribution scenarios, the average computational time required was 5.59 seconds. Pareto analysis indicates a trade-off between various objective functions. Solutions with short distances tend to have increased maximum time and delays.Originality/value: NSGA-II is effective for task distribution with multiobjective considerations. Not all three objective functions can be optimized simultaneously, given the trade-offs between distance, maximum time, and lateness. The priority of the objective functions should be determined to achieve optimal results. If minimizing lateness is most important, the focus should be on points with low lateness values. Further development can be done by modifying the Pareto front to make data-driven decisions that consider these trade-offs.