Perturbations Of Operators Research Articles

A multi-strategy fruit fly optimization algorithm for the distributed permutation flowshop scheduling problem with sequence-dependent setup times

Distributed manufacturing has become one of the mainstream manufacturing modes today and is widely present in industries such as aviation and electronics. However, in actual production processes, unexpected situations such as machine failures and tool changes may occur, which require time. Based on practical needs, this paper studies a distributed permutation flow shop scheduling problem with sequence-dependent setup times (DPFSP/SDST) aimed at minimizing the makespan and proposes a hybrid multi-strategy fruit fly optimization algorithm (HMFOA) to solve it. In HMFOA, three strategies are constructed to initialize the positions of some individual flies in the solution space to improve population diversity. In the smell search phase, four problem-oriented neighborhood perturbation operators are designed, and sinusoidal optimization algorithm is introduced to control the search range, which improves the global search ability of the algorithm. In the visual search phase, a position reconstruction strategy is proposed to divide individual flies into different populations based on their mass. Through the interaction of individuals from different populations, the convergence is accelerated and the algorithm efficiency is improved. In addition, a local search strategy is designed to guide the flies to more promising areas. Based on well-known examples of DPFSP in the literature, a comprehensive test set was generated for DPFSP/SDST, taking into account various combinations of jobs, machines, factories, and SDST, resulting in 270 benchmark instances used to validate the performance of HMFOA, and compared to eight other advanced algorithms. The relative percentage deviation of HMFOA is 1.00%, which is significant improvement.

A Discrete Brain Storm Optimization Algorithm for Hybrid Flowshop Scheduling Problems with Batch Production at Last Stage in the Steelmaking-Refining-Continuous Casting Process.

The iron and steel industry is energy-intensive due to the large volume of steel produced and its high-temperature and high-weight characteristics, sensors such as high-temperature application sensors can be utilized to collect production data and support the process control and optimization. Steelmaking-refining-continuous casting (SRCC) is a bottleneck in the iron and steel production process. SRCC scheduling problems are worldwide problems and NP-hard. The problems are not only important for iron and steel enterprises to enhance production efficiency, but also play a significant role in saving energy and reducing resource consumption. SRCC scheduling problems can be modeled as hybrid flowshop scheduling problems with batch production at the last stage. In this paper, a Discrete Brain Storm Optimization (DBSO) algorithm is proposed to handle SRCC scheduling problems. In the proposed DBSO, population initialization and cluster center replacement are specially designed to enhance the intensification abilities. Moreover, a perturbation operator is devised to enhance its diversification abilities. Furthermore, a new individual generation operator is devised to improve the intensification and diversification abilities simultaneously. Experimental results have demonstrated that the proposed DBSO is an efficient method for solving SRCC scheduling problems.

An enhanced competitive swarm optimizer with strongly robust sparse operator for large-scale sparse multi-objective optimization problem

In the real world, the decision variables of large-scale sparse multi-objective problems are high-dimensional, and most Pareto optimal solutions are sparse. The balance of the algorithms is difficult to control, so it is challenging to deal with such problems in general. Therefore, An Enhanced Competitive Swarm Optimizer with Strongly Robust Sparse Operator (SR-ECSO) algorithm is proposed. Firstly, the strongly robust sparse functions which accelerate particles in the population better sparsity in decision space, are used in high-dimensional decision variables. Secondly, the diversity of sparse solutions is maintained, and the convergence balance of the algorithm is enhanced by the introduction of an adaptive random perturbation operator. Finally, the state of the particles is updated using a swarm optimizer to improve population competitiveness. To verify the proposed algorithm, we tested eight large-scale sparse benchmark problems, and the decision variables were set in three groups with 100, 500, and 1000 as examples. Experimental results show that the algorithm is promising for solving large-scale sparse optimization problems.

Computing the QRPA level density with the finite amplitude method

We describe a new algorithm to calculate the vibrational nuclear level density of an atomic nucleus. Fictitious perturbation operators that probe the response of the system are generated by drawing their matrix elements from some probability distribution function. We use the Finite Amplitude Method to explicitly compute the response for each such sample. With the help of the Kernel Polynomial Method, we build an estimator of the vibrational level density and provide the upper bound of the relative error in the limit of infinitely many random samples. The new algorithm can give accurate estimates of the vibrational level density. Since it is based on drawing multiple samples of perturbation operators, its computational implementation is naturally parallel and scales like the number of available processing units.

Superlinear Krylov convergence under streamline diffusion FEM for convection‐dominated elliptic operators

AbstractThis paper studies the superlinear convergence of Krylov iterations under the streamline‐diffusion preconditioning operator for convection‐dominated elliptic problems. First, convergence results are given involving the diffusion parameter . Then the limiting case is studied on the operator level, and the convergence results are extended to this situation under some conditions, in spite of the lack of compactness of the perturbation operators. An explicit rate is also given.

QuanTest: Entanglement-Guided Testing of Quantum Neural Network Systems

Quantum Neural Network (QNN) combines the Deep Learning (DL) principle with the fundamental theory of quantum mechanics to achieve machine learning tasks with quantum acceleration. Recently, QNN systems have been found to manifest robustness issues similar to classical DL systems. There is an urgent need for ways to test their correctness and security. However, QNN systems differ significantly from traditional quantum software and classical DL systems, posing critical challenges for QNN testing. These challenges include the inapplicability of traditional quantum software testing methods to QNN systems due to differences in programming paradigms and decision logic representations, the dependence of quantum test sample generation on perturbation operators, and the absence of effective information in quantum neurons. In this paper, we propose QuanTest, a quantum entanglement-guided adversarial testing framework to uncover potential erroneous behaviors in QNN systems. We design a quantum entanglement adequacy criterion to quantify the entanglement acquired by the input quantum states from the QNN system, along with two similarity metrics to measure the proximity of generated quantum adversarial examples to the original inputs. Subsequently, QuanTest formulates the problem of generating test inputs that maximize the quantum entanglement adequacy and capture incorrect behaviors of the QNN system as a joint optimization problem and solves it in a gradient-based manner to generate quantum adversarial examples. Experimental results demonstrate that QuanTest possesses the capability to capture erroneous behaviors in QNN systems (generating 67.48%-96.05% more high-quality test samples than the random noise under the same perturbation size constraints). The entanglement-guided approach proves effective in adversarial testing, generating more adversarial examples (maximum increase reached 21.32%).

The constrained permutation flowshop problem: An effective two-stage iterated greedy algorithm to minimize weighted tardiness

In the domain of just-in-time permutation flowshop scheduling, most studies typically assume that all jobs either have their own soft due date or none of them do. However, in practice, scheduling a combination of hard and soft due date jobs, particularly with the context of emergency order insertion, remains a significant research topic. This paper addresses a constrained permutation flowshop scheduling problem with a mix of hard and soft due date jobs under total weighted tardiness criterion (CPFSP-TWT). We establish a mathematical model and propose an effective Two-Stage Iterated Greedy (ETSIG) algorithm tailored to the problem's characteristics, incorporating a two-stage constructive heuristic to generate a high-quality initial solution. We introduce problem-specific acceleration mechanisms based on position-bound considerations to enhance operational efficiency. We propose three knowledge-based repair strategies for handling infeasible solutions, along with a dynamic self-adjustment mechanism. Additionally, three efficient local search procedures integrate several specific perturbation operators to balance algorithmic exploitation and exploration abilities. Experimental evaluations affirm ETSIG's superiority over five state-of-the-art metaheuristics from closely related literature, establishing its efficacy in addressing CPFSP-TWT.

Local well-posedness of abstract hyperbolic equation with Lipschitz perturbation and non-autonomous operator

Based on the local well-posedness for the homogeneous abstract problem, the existence and uniqueness of the local mild and classical solutions have been presented by using Kato’s variable norm technique for the Cauchy problem of abstract hyperbolic equation with Lipschitz perturbation and non-autonomous operator.

HTQ: Exploring the High-Dimensional Trade-Off of mixed-precision quantization

Mixed-precision quantization, where more sensitive layers are kept at higher precision, can achieve the trade-off between accuracy and complexity of neural networks. However, the search space for mixed-precision grows exponentially with the number of layers, making the brute force approach infeasible on deep networks. To reduce this exponential search space, recent efforts use Pareto frontier or integer linear programming to select the bit-precision of each layer. Unfortunately, we find that these prior works rely on a single constraint. In practice, model complexity includes space complexity and time complexity, and the two are weakly correlated, thus using simply one as a constraint leads to sub-optimal results. Besides this, they require manually set constraints, making them only pseudo-automatic. To address the above issues, we propose High-dimensional Trade-off Quantization (HTQ), which automatically determines the bit-precision in the high-dimensional space of model accuracy, space complexity, and time complexity without any manual intervention. Specifically, we use the saliency criterion based on connection sensitivity to indicate the accuracy perturbation after quantization, which performs similarly to Hessian information but can be calculated quickly (more than 1000× speedup). The bit-precision is then automatically selected according to the three-dimensional (3D) Pareto frontier of the total perturbation, model size, and bit operations (BOPs) without manual constraints. Moreover, HTQ allows for the joint optimization of weights and activations, and thus the bit-precisions of both can be computed concurrently. Compared to state-of-the-art methods, HTQ achieves higher accuracy and lower space/time complexity on various model architectures for image classification and object detection tasks. Code is available at: https://github.com/zkkli/HTQ.

An Iterated Local Search Heuristic for the Multi-Trip Vehicle Routing Problem with Multiple Time Windows

This paper studies the multi-trip vehicle routing problem with multiple time windows, which extends the multi-trip vehicle routing problem by deciding not only the sequence of customers that each vehicle serves but also the service time window of each customer. It also requires that the delivery service time is within the selected time windows and that the total demand of the customers served by the vehicle on each trip does not exceed the maximum carrying capacity. For solving the studied problem, we develop a mixed integer linear programming model with the objective of minimizing the total travel distance of vehicles and design a tailored iterative local search heuristic. Within the framework of the iterative local search, an improved Solomon greedy insertion algorithm suitable for multiple time windows and multi-trip scenarios is designed to generate the initial solution, and local search operators such as Or-opt and Relocate, as well as Random Exchange perturbation operations, are also developed. The experiment results demonstrate the effectiveness of the proposed model and algorithm and confirm that by providing customers with multiple time windows option, carriers can flexibly plan vehicle routes and select appropriate service time windows, thereby reducing the number of vehicles used and the total distance travelled and improve delivery success.

Semi-chiral operators in 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 gauge theories

We discuss the properties of quarter-BPS local operators in four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supersymmetric Yang-Mills theory using the formalism of holomorphic twists. We study loop corrections both to the space of local operators and to algebraic operations which endow the twisted theory with an infinite symmetry algebra. We classify all single-trace quarter-BPS operators in the planar approximation for SU(N) gauge theory and propose a holographic dual description for the twisted theory. We classify perturbative quarter-BPS operators in SU(2) and SU(3) gauge theories with sufficiently small quantum numbers and discuss possible non-perturbative corrections to the answer. We set up analogous calculations for some theories with matter.

Collaborative orchard pesticide spraying routing problem with multi-vehicles supported multi-UAVs

The application of UAVs in orchard management presents a substantial opportunity to enhance efficiency and promote environmentally friendly agricultural production. While individual UAVs encounter limitations, such as endurance constraints, these challenges can be mitigated through collaborative efforts involving multiple vehicles and UAVs. This study addresses the issue of multi-UAV cooperative orchard path planning with multiple vehicles by formulating a mathematical optimization model aimed at minimizing the maximum UAV operation time. In the proposed model, the vehicle solely provides batteries and supplies to the UAV. To efficiently solve this model, we propose an improved Simulated Annealing-Lin Kernighan Helsgaun (SA-LKH) algorithm. The proposed algorithm utilizes the K-means and convex hull algorithm to generate the initial solution. Subsequently, the paths of each group of UAVs and vehicles are optimized based on the LKH algorithm. Additionally, we construct a directed perturbation operator that perturbs the maximum and minimum time-consuming paths to achieve fast convergence of the algorithm. The results from four different cases demonstrate that, compared to the general variable neighborhood search algorithm, the improved Ant Colony Algorithm and Improved Genetic Algorithm, the proposed algorithm has demonstrated an average improvement in solution quality of 3.41%, 5.72% and 9.67%, respectively. The proposed method effectively enhances the solution quality, which can provide valuable insights into green cleaning management of orchards.

Coupled cluster finite temperature simulations of periodic materials via machine learning

Density functional theory is the workhorse of materials simulations. Unfortunately, the quality of results often varies depending on the specific choice of the exchange-correlation functional, which significantly limits the predictive power of this approach. Coupled cluster theory, including single, double, and perturbative triple particle-hole excitation operators, is widely considered the ‘gold standard' of quantum chemistry as it can achieve chemical accuracy for non-strongly correlated applications. Because of the high computational cost, the application of coupled cluster theory in materials simulations is rare, and this is particularly true if finite-temperature properties are of interest for which molecular dynamics simulations have to be performed. By combining recent progress in machine learning models with low data requirements for energy surfaces and in the implementation of coupled cluster theory for periodic materials, we show that chemically accurate simulations of materials are practical and could soon become significantly widespread. As an example of this numerical approach, we consider the calculation of the enthalpy of adsorption of CO2 in a porous material.

Team orienteering with possible multiple visits: Mathematical model and solution algorithms

This study addresses a new team orienteering problem in which each point can be visited possibly multiple times with decreasing scores. The problem is to determine a set of routes from a starting to a finishing point within an allowed travel time limit for the objective of maximizing the total collected score. A mixed integer programming model is developed to represent the problem mathematically. Then, due to the complexity of the problem, a basic iterated local search (ILS) algorithm is proposed that incorporates the ordinary perturbation and local search operators. Then, it is improved in two ways: (a) an extended ILS algorithm with multi-visit based local search operators and (b) a hybrid ILS algorithm with a simulated annealing technique to permit non-improving moves in the local search step. To test the performance of the ILS algorithms, computational experiments were done on modified benchmark instances under the cases of linear, convex and concave score decreases, and the results show that the hybrid ILS algorithm improves the others significantly and also gives near optimal solutions for small sized test instances. Finally, a case study was done for a naval warship reconnaissance operation, and the results are reported.

Active Distribution Network Fault Diagnosis Based on Improved Northern Goshawk Search Algorithm

Timely and accurate fault location in active distribution networks is of vital importance to ensure the reliability of power grid operation. However, existing intelligent algorithms applied in fault location of active distribution networks possess slow convergence speed and low accuracy, hindering the construction of new power systems. In this paper, a new regional fault localization method based on an improved northern goshawk search algorithm is proposed. The population quality of the samples was improved by using the chaotic initialization strategy. Meanwhile, the positive cosine strategy and adaptive Gaussian–Cauchy hybrid variational perturbation strategy were introduced to the northern goshawk search algorithm, which adopted the perturbation operation to interfere with the individuals to increase the diversity of the population, contributing to jumping out of the local optimum to strengthen the ability of local escape. Finally, simulation verification was carried out in a multi-branch distribution network containing distributed power sources. Compared with the traditional regional localization models, the new method proposed possesses faster convergence speed and higher location accuracy under different fault locations and different distortion points.

Fractional-Order PID Control of Permanent Magnet Synchronous Motors Based on Based on Improved Squirrel Algorithm

An adaptive differential squirrel algorithm fractional order PID controller is proposed to address the problems of instability and poor accuracy of Permanent Magnet Synchronous Motor PID control systems. In order to improve the global optimisation of the squirrel search algorithm, the crossover operation of the difference algorithm was combined, adaptive predation probability factor, dynamic crossover probability and Gaussian distribution perturbation operation are added to the squirrel search algorithm to improve its exploration and exploitation capability. In the comparative experiment of PMSM speed control, ADESA fractional-order PID was contrasted with conventional PID and other intelligent optimization algorithms. The results indicate that the PMSM control utilizing fractional-order PID through ADESA demonstrated minimal overshoot, the fastest response time, and superior anti-disturbance capabilities compared to PID and other intelligent optimization algorithms. This significantly enhanced the control performance of the permanent magnet synchronous motor.

Iterated Local Search with Linkage Learning

In pseudo-Boolean optimization, a variable interaction graph represents variables as vertices, and interactions between pairs of variables as edges. In black-box optimization, the variable interaction graph may be at least partially discovered by using empirical linkage learning techniques. These methods never report false variable interactions, but they are computationally expensive. The recently proposed local search with linkage learning discovers the partial variable interaction graph as a side-effect of iterated local search. However, information about the strength of the interactions is not learned by the algorithm. We propose local search with linkage learning 2, which builds a weighted variable interaction graph that stores information about the strength of the interaction between variables. The weighted variable interaction graph can provide new insights about the optimization problem and behavior of optimizers. Experiments with NK landscapes, knapsack problem, and feature selection show that local search with linkage learning 2 is able to efficiently build weighted variable interaction graphs. In particular, experiments with feature selection show that the weighted variable interaction graphs can be used for visualizing the feature interactions in machine learning. Additionally, new transformation operators that exploit the interactions between variables can be designed. We illustrate this ability by proposing a new perturbation operator for iterated local search.

Adaptive population-based simulated annealing for resource constrained job scheduling with uncertainty

Transporting ore from mines to ports is of significant interest in mining supply chains. These operations are commonly associated with growing costs and a lack of resources. Large mining companies are interested in optimally allocating resources to reduce operational costs. This problem has been previously investigated as resource constrained job scheduling (RCJS). While a number of optimisation methods have been proposed to tackle the deterministic problem, the uncertainty associated with resource availability, an inevitable challenge in mining operations, has received less attention. RCJS with uncertainty is a hard combinatorial optimisation problem that is challenging for existing optimisation methods. We propose an adaptive population-based simulated annealing algorithm that can overcome existing limitations of methods for RCJS with uncertainty, including pre-mature convergence, excessive number of hyper-parameters, and the inefficiency in coping with different uncertainty levels. This new algorithm effectively balances exploration and exploitation, by using a population, modifying the cooling schedule in the Metropolis-Hastings algorithm, and using an adaptive mechanism to select perturbation operators. The results show that the proposed algorithm outperforms existing methods on a benchmark RCJS dataset considering different uncertainty levels. Moreover, new best known solutions are discovered for all but one problem instance across all uncertainty levels.

On second order differential inclusion driven by quasi-variational–hemivariational inequalities

In this paper we investigate an evolution problem (SDQHVI) which constitutes of the second order differential inclusion driven by a quasi-variational–hemivariational inequality (QHVI) with perturbation operator in Banach spaces. Unlike the existing literature on differential inclusions, on the one hand, the second order differential operator is not assumed to be compact; on the other hand, the solvability of the inequality is proved under non-coercive condition. More precisely, first, it is shown that the solution set of the QHVI with perturbation operator is nonempty, bounded, closed and convex under the KKM theorem and the Minty formulation. Then, an associated multivalued map with the solution set of the QHVI with perturbation operator is introduced, and we prove that it is upper semicontinuous and measurable. Finally, by utilizing Kakutani–Fan–Glicksberg fixed point theorem, a weak topology technique and properties of strong continuous cosine operators, we prove the existence of mild solutions for SDQHVI.

Intramolecular rate-constant calculations based on the correlation function using temperature dependent quantum Green's functions.

A theoretical method for calculating rate constants for internal conversion (IC), intersystem crossing (ISC) and radiative (R) electronic transitions is presented. The employed method uses temperature-dependent quantum Green's functions, which give the opportunity to consider almost any nth-order polynomial perturbation operator and the influence of external electromagnetic fields on the rate constants. The rate constants of the IC, ISC and R processes are calculated for two important indocyanine molecules namely indocyanine green (ICG) and heptamethine cyanine (IR808) at the Franck-Condon level using the temperature-dependent quantum Green's function approach. Calculations at the time-dependent density functional theory level with the MN15 functional show that ICG and IR808 have only one triplet state below the S1 state. The main deactivation channel of the S1 state is the IC process with a large (kIC(S1 → S0)) rate constant of ∼109-1011 s-1. The estimated quantum yield of fluorescence (φfl) is ∼0.001-0.24 for the two studied molecules, which agrees rather well with experimental values. Thus, the present approach enables calculations of the three kinds of rate constants and the quantum yield of fluorescence using the same computational methodology.