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1) The OE-MLPG penalty meshfree method is developed to solve cracked structure.(2) Smartening the numerical meshfree method by combining the particle swarm optimization (PSO) optimization algorithms and Voronoi computational geometric algorithm. (3). Selection of base functions, finding optimal penalty factor and distribution of appropriate nodal points to the accuracy of calculation in the meshless local Petrov–Galekrin (MLPG) meshless method.

Using appropriate shape functions and distribution of nodal points in local domains and sub-domains and choosing an approximation or interpolation method has an effective role in the application of meshless methods for the analysis of computational fracture mechanics problems, especially problems with geometric discontinuity and cracks. In this research, computational geometry technique, based on the Voronoi diagram (VD) and Delaunay triangulation and PSO algorithm, are used to distribute nodal points in the sub-domain of analysis (crack line and around it on the crack plane).

By doing this process, the problems caused by too closeness of nodal points in computationally sensitive areas that exist in general methods of nodal point distribution are also solved. Comparing the effect of the number of sentences of basic functions and their order in the definition of shape functions, performing the mono-objective PSO algorithm to find the penalty factor, the coefficient, convergence, arrangement of nodal points during the three stages of VD implementation and the accuracy of the answers found indicates, the efficiency of V-E-MLPG method with Ns = 7 and ß = 0.0037–0.0075 to estimation of 3D-stress intensity factors (3D-SIFs) in computational fracture mechanics.

The present manuscript is a continuation of the studies (Ref. [33]) carried out by the authors, about; feasibility assessment, improvement and solution of challenges, introduction of more capacities and capabilities of the numerical MLPG method have been used. In order to validate the modeling and accuracy of calculations, the results have been compared with the findings of reference article [34] and [35].

Nonlinear dynamic analyses are employed for seismic collapse risk evaluation of existing steel moment frame buildings. The standards, such as ASCE 41-17, often define collapse thresholds based on plastic deformations; however, the collapse process involves several factors, and plastic deformation is only one of them. An energy-based approach employs deformation and resistance responses simultaneously, so it can consider various factors such as excessive deformation, stiffness and resistance degradation, and low-cycle fatigue as cumulative damage for seismic assessment. In this paper, an efficient energy-based methodology is proposed to estimate the collapse threshold responses of steel moment frame buildings.

This methodology uses a new criterion based on the energy balance concept and computes the structural responses for different seismic hazard levels. Meanwhile, a pre-processing phase is introduced to find the records that lead to the collapse of buildings. Furthermore, the proposed methodology can detect failure-prone hinges with a straightforward probability-based definition.

The findings show that the proposed methodology can estimate reasonably accurate responses against the results of the past experiment on the collapse threshold. Based on past studies, ASCE 41-17 results differ from experimental results and are even overly conservative in some cases. The authors believe that the proposed methodology can improve it. In addition, the failure-prone hinges detected by the proposed methodology are similar to the predicted collapse mechanism of three mid-rise steel moment frame buildings.

In the proposed methodology, new definitions based on energy and probability are employed to find out the structural collapse threshold and failure-prone hinges. Also, comparing the proposed methodology results against the experimental outcomes shows that this methodology efficiently predicts the collapse threshold responses.

Do luxury consumers negatively evaluate digital interactions (website and social media) by international luxury brands? The topic has received much debate. The authors argue that luxury brand personality (modern vs. traditional), which encompasses a more stable form of brand identity in global markets, affects evaluations of digital interactions. They further investigate the role of self-brand connection in this process.

Three experiments on Prolific use a European sample and manipulate a single factor between subjects (modernity: less vs. more; traditionality: less vs. more) of French luxury brands and measure evaluations as the dependent variable. Two studies assesses self-brand connection (continuous) as a moderator (studies 2a, 2b). Study 2b rules out some alternative explanations, with culture (independent vs. collectivist) as an independent variable. A fourth study, using a North American sample on CloudResearch, assesses the effect of personality manipulation (more modernity vs. more traditionality) on consumer evaluations of an Italian brand, and assesses ubiquity perceptions as a mediator.

Consumers evaluate digital interactions of international luxury brands less favorably when luxury brand personality exhibits more (vs. less) modernity or less (vs. more) traditionality. Perceptions of ubiquity mediate these relationships. When self-brand connection is high, this effect is attenuated.

The research sheds light on the debate on whether luxury brands should create digital interactions in international markets, given that these global brands operate in multiple channels. Findings show that luxury brands can develop strategies based on aspects of their brand identity, a less malleable feature of brand identity within global markets. Additionally, the research contributes to the conversation about a global luxury market. In short, the findings offer evidence in favor of brand identity (personality) influencing the digital channel strategy a brand should undertake in international markets, first, followed by consumer needs.

The study aims to optimize truck routes by minimizing social and economic costs. It introduces a strategy involving diverse drones and their potential for reusing at DNs based on flight range. In HTDRP-DC, trucks can select and transport various drones to LDs to reduce deprivation time. This study estimates the nonlinear deprivation cost function using a linear two-piece-wise function, leading to MILP formulations. A heuristic-based Benders Decomposition approach is implemented to address medium and large instances. Valid inequalities and a heuristic method enhance convergence boundaries, ensuring an efficient solution methodology.

Research has yet to address critical factors in disaster logistics: minimizing the social and economic costs simultaneously and using drones in relief distribution; deprivation as a social cost measures the human suffering from a shortage of relief supplies. The proposed hybrid truck-drone routing problem minimizing deprivation cost (HTDRP-DC) involves distributing relief supplies to dispersed demand nodes with undamaged (LDs) or damaged (DNs) access roads, utilizing multiple trucks and diverse drones. A Benders Decomposition approach is enhanced by accelerating techniques.

Incorporating deprivation and economic costs results in selecting optimal routes, effectively reducing the time required to assist affected areas. Additionally, employing various drone types and their reuse in damaged nodes reduces deprivation time and associated deprivation costs. The study employs valid inequalities and the heuristic method to solve the master problem, substantially reducing computational time and iterations compared to GAMS and classical Benders Decomposition Algorithm. The proposed heuristic-based Benders Decomposition approach is applied to a disaster in Tehran, demonstrating efficient solutions for the HTDRP-DC regarding computational time and convergence rate.

Current research introduces an HTDRP-DC problem that addresses minimizing deprivation costs considering the vehicle’s arrival time as the deprivation time, offering a unique solution to optimize route selection in relief distribution. Furthermore, integrating heuristic methods and valid inequalities into the Benders Decomposition approach enhances its effectiveness in solving complex routing challenges in disaster scenarios.

The purpose of the paper is to propose and demonstrate a novel approach for addressing the challenges of path planning and obstacle avoidance in the context of mobile robots (MR). The specific objectives and purposes outlined in the paper include: introducing a new methodology that combines Q-learning with dynamic reward to improve the efficiency of path planning and obstacle avoidance. Enhancing the navigation of MR through unfamiliar environments by reducing blind exploration and accelerating the convergence to optimal solutions and demonstrating through simulation results that the proposed method, dynamic reward-enhanced Q-learning (DRQL), outperforms existing approaches in terms of achieving convergence to an optimal action strategy more efficiently, requiring less time and improving path exploration with fewer steps and higher average rewards.

The design adopted in this paper to achieve its purposes involves the following key components: (1) Combination of Q-learning and dynamic reward: the paper’s design integrates Q-learning, a popular reinforcement learning technique, with dynamic reward mechanisms. This combination forms the foundation of the approach. Q-learning is used to learn and update the robot’s action-value function, while dynamic rewards are introduced to guide the robot’s actions effectively. (2) Data accumulation during navigation: when a MR navigates through an unfamiliar environment, it accumulates experience data. This data collection is a crucial part of the design, as it enables the robot to learn from its interactions with the environment. (3) Dynamic reward integration: dynamic reward mechanisms are integrated into the Q-learning process. These mechanisms provide feedback to the robot based on its actions, guiding it to make decisions that lead to better outcomes. Dynamic rewards help reduce blind exploration, which can be time-consuming and inefficient and promote faster convergence to optimal solutions. (4) Simulation-based evaluation: to assess the effectiveness of the proposed approach, the design includes a simulation-based evaluation. This evaluation uses simulated environments and scenarios to test the performance of the DRQL method. (5) Performance metrics: the design incorporates performance metrics to measure the success of the approach. These metrics likely include measures of convergence speed, exploration efficiency, the number of steps taken and the average rewards obtained during the robot’s navigation.

The findings of the paper can be summarized as follows: (1) Efficient path planning and obstacle avoidance: the paper’s proposed approach, DRQL, leads to more efficient path planning and obstacle avoidance for MR. This is achieved through the combination of Q-learning and dynamic reward mechanisms, which guide the robot’s actions effectively. (2) Faster convergence to optimal solutions: DRQL accelerates the convergence of the MR to optimal action strategies. Dynamic rewards help reduce the need for blind exploration, which typically consumes time and this results in a quicker attainment of optimal solutions. (3) Reduced exploration time: the integration of dynamic reward mechanisms significantly reduces the time required for exploration during navigation. This reduction in exploration time contributes to more efficient and quicker path planning. (4) Improved path exploration: the results from the simulations indicate that the DRQL method leads to improved path exploration in unknown environments. The robot takes fewer steps to reach its destination, which is a crucial indicator of efficiency. (5) Higher average rewards: the paper’s findings reveal that MR using DRQL receive higher average rewards during their navigation. This suggests that the proposed approach results in better decision-making and more successful navigation.

The paper’s originality stems from its unique combination of Q-learning and dynamic rewards, its focus on efficiency and speed in MR navigation and its ability to enhance path exploration and average rewards. These original contributions have the potential to advance the field of mobile robotics by addressing critical challenges in path planning and obstacle avoidance.

This study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in engineering and the electrostatic potential theory, using the modified Lagrange polynomial interpolation technique combined with the biconjugate gradient stabilized method (BiCGSTAB). The framework for the existence of the unique solutions of the integral equations is provided in the context of the Banach contraction principle and Bielecki norm.

The authors have applied the modified Lagrange polynomial method to approximate the numerical solutions of the second kind of weakly singular Volterra and Fredholm integral equations.

Approaching the interpolation of the unknown function using the aforementioned method generates an algebraic system of equations that is solved by an appropriate classical technique. Furthermore, some theorems concerning the convergence of the method and error estimation are proved. Some numerical examples are provided which attest to the application, effectiveness and reliability of the method. Compared to the Fredholm integral equations of weakly singular type, the current technique works better for the Volterra integral equations of weakly singular type. Furthermore, illustrative examples and comparisons are provided to show the approach’s validity and practicality, which demonstrates that the present method works well in contrast to the referenced method. The computations were performed by MATLAB software.

The convergence of these methods is dependent on the smoothness of the solution, it is challenging to find the solution and approximate it computationally in various applications modelled by integral equations of non-smooth kernels. Traditional analytical techniques, such as projection methods, do not work well in these cases since the produced linear system is unconditioned and hard to address. Also, proving the convergence and estimating error might be difficult. They are frequently also expensive to implement.

There is a great need for fast, user-friendly numerical techniques for these types of equations. In addition, polynomials are the most frequently used mathematical tools because of their ease of expression, quick computation on modern computers and simple to define. As a result, they made substantial contributions for many years to the theories and analysis like approximation and numerical, respectively.

This work presents a useful method for handling weakly singular integral equations without involving any process of change of variables to eliminate the singularity of the solution.

To the best of the authors’ knowledge, the authors claim the originality and effectiveness of their work, highlighting its successful application in addressing weakly singular Volterra and Fredholm integral equations for the first time. Importantly, the approach acknowledges and preserves the possible singularity of the solution, a novel aspect yet to be explored by researchers in the field.

Driven by sustainable production, mobile robots are introduced as a new clean-energy material handling tool for mixed-model assembly lines (MMALs), which reduces energy consumption and lineside inventory of workstations (LSI). Nevertheless, the previous part feeding scheduling method was designed for conventional material handling tools without considering the flexible spatial layout of the robotic mobile fulfillment system (RMFS). To fill this gap, this paper focuses on a greening mobile robot part feeding scheduling problem with Just-In-Time (JIT) considerations, where the layout and number of pods can be adjusted.

A novel hybrid-load pod (HL-pod) and mobile robot are proposed to carry out part feeding tasks between material supermarkets and assembly lines. A bi-objective mixed-integer programming model is formulated to minimize both total energy consumption and LSI, aligning with environmental and sustainable JIT goals. Due to the NP-hard nature of the proposed problem, a chaotic differential evolution algorithm for multi-objective optimization based on iterated local search (CDEMIL) algorithm is presented. The effectiveness of the proposed algorithm is verified by dealing with the HL-pod-based greening part feeding scheduling problem in different problem scales and compared to two benchmark algorithms. Managerial insights analyses are conducted to implement the HL-pod strategy.

The CDEMIL algorithm's ability to produce Pareto fronts for different problem scales confirms its effectiveness and feasibility. Computational results show that the proposed algorithm outperforms the other two compared algorithms regarding solution quality and convergence speed. Additionally, the results indicate that the HL-pod performs better than adopting a single type of pod.

This study proposes an innovative solution to the scheduling problem for efficient JIT part feeding using RMFS and HL-pods in automobile MMALs. It considers both the layout and number of pods, ensuring a sustainable and environmental-friendly approach to production.

This study aims to propose a more precise method for robust design optimization of mechanical structures with black-box problems, while also considering the efficiency of uncertainty analysis.

The method first introduces a dual adaptive chaotic flower pollination algorithm (DACFPA) to overcome the shortcomings of the original flower pollination algorithm (FPA), such as its susceptibility to poor accuracy and convergence efficiency when dealing with complex optimization problems. Furthermore, a DACFPA-Kriging model is developed by optimizing the relevant parameter of Kriging model via DACFPA. Finally, the dual Kriging model is constructed to improve the efficiency of uncertainty analysis, and a robust design optimization method based on DACFPA-Dual-Kriging is proposed.

The DACFPA outperforms the FPA, particle swarm optimization and gray wolf optimization algorithms in terms of solution accuracy, convergence speed and capacity to avoid local optimal solutions. Additionally, the DACFPA-Kriging model exhibits superior prediction accuracy and robustness contrasted with the original Kriging and FPA-Kriging. The proposed method for robust design optimization based on DACFPA-Dual-Kriging is applied to the motor hanger of the electric multiple units as an engineering case study, and the results confirm a significant reduction in the fluctuation of the maximum equivalent stress.

This study represents the initial attempt to enhance the prediction accuracy of the Kriging model using the improved FPA and to combine the dual Kriging model for uncertainty analysis, providing an idea for the robust optimization design of mechanical structure with black-box problem.

The main purpose of this paper is to introduce the gradient discretisation method (GDM) to a system of reaction diffusion equations subject to non-homogeneous Dirichlet boundary conditions. Then, the authors show that the GDM provides a comprehensive convergence analysis of several numerical methods for the considered model. The convergence is established without non-physical regularity assumptions on the solutions.

In this paper, the authors use the GDM to discretise a system of reaction diffusion equations with non-homogeneous Dirichlet boundary conditions.

The authors provide a generic convergence analysis of a system of reaction diffusion equations. The authors introduce a specific example of numerical scheme that fits in the gradient discretisation method. The authors conduct a numerical test to measure the efficiency of the proposed method.

This work provides a unified convergence analysis of several numerical methods for a system of reaction diffusion equations. The generic convergence is proved under the classical assumptions on the solutions.

Small business capabilities and customer interactions are particularly susceptible to market disruptions. Small businesses must pivot quickly to build or grow their capabilities and manage diverse strategies to deal with crises. This ability to quickly adapt and formulate strategies is necessary to help small businesses maintain sales and continue to engage with their clients, especially in light of disruption and crises. This work uses design thinking strategies to provide insight into how businesses can navigate such disruptions.

This research investigates how design thinking can help small businesses address crises. The focus is on leveraging design thinking strategies such as empathizing, defining, ideating, prototyping and testing (EDIPT), divergence/convergence and customer journey mapping design thinking tools.

The authors provide propositions and strategies to help firms adapt their strategies to the demands of clients during crises.

This piece provides an accessible introduction to three design thinking strategies (general EDIPT model, convergence/divergence and consumer journey mapping). The authors present this in the context of disruption, especially the recent pandemic, specifically focusing on small businesses.