Restricted Problem Research Articles

Pickup capacitated vehicle routing problem with three-dimensional loading constraints: Model and algorithms

This study addresses the pickup capacitated vehicle routing problem with three-dimensional loading constraints (3L-PCVRP), which combined the container loading problem (CLP) and the capacitated vehicle routing problem (CVRP). A mixed-integer linear programming model for 3L-PCVRP is designed with the objective of minimizing the total transportation cost. The basic constraints of CLP and CVRP as well as the practical constraints imposed by the pickup operations are incorporated in 3L-PCVRP. An improved branch-and-price-based (B&P) algorithm is proposed to solve 3L-PCVRP. The 3L-PCVRP model is decomposed into the restricted master problem (RMP) for selecting routes and the subproblem (SP) for generating routes that satisfy the loading and routing constraints. A label-correcting-based algorithm (LCA) is presented to solve the SP, which employs a two-stage method and two enhanced loading algorithms to ensure the loading feasibility of the routes. The two loading algorithms (tree search and greedy heuristic algorithms) are improved by a new evaluation function and an improved space-merging method. The two-stage method is designed to call the two loading algorithms at different frequencies to investigate the route feasibility accurately and efficiently. Numerical experiments are designed to test the performance of the proposed algorithms. The efficiency and effectiveness of the improved loading algorithms are demonstrated in hundreds randomly generated instances. For small-scale 3L-PCVRP instances, the B&P algorithm can generate solutions that are not worse than those of the solver within 0.14% of the solver’s running time. The efficiency and effectiveness of the improved B&P algorithm are also validated in large-scale benchmark instances.

Strong simulation of linear optical processes

In this paper, we provide an algorithm and general framework for the simulation of photons passing through linear optical interferometers. Given n photons at the input of an m-mode interferometer, our algorithm computes the probabilities of all possible output states with time complexity O(n(n+m−1m−1)), linear in the number of output states (n+m−1m−1). It outperforms the permanent-based method by an exponential factor, and for the restricted problem of computing the probability for one given output it improves the time complexity over the state-of-the-art for the permanent of matrices with multiple rows or columns, with a tradeoff in the memory usage. Our algorithm also has additional versatility by virtue of its use of memorisation – the storing of intermediate results – which is advantageous in situations where several input states may be of interest. Additionally it allows for hybrid simulations, in which outputs are sampled from output states whose probability exceeds a given threshold, or from a restricted set of states. We consider a concrete, optimised implementation, and we benchmark the efficiency of our approach compared to existing tools.

On Resonant Values of Parameters in the Problem on the Stability of Lagrangian Solutions in the Near-Circular Restricted Three-Body Problem

The restricted problem of three bodies (material points) moving under the action of gravitational attraction according to Newton’s law is considered. The orbits of the main attracting bodies are considered to be ellipses with a small eccentricity, and a passively gravitating body can perform arbitrary spatial motion near the triangular libration point. For the Hamiltonian function corresponding to such a motion, the structure of the normal form is pointed in the cases of third-order resonances. In the planar restricted three-body problem, the equations up to the second degree of eccentricity for resonance curves for all resonances up to the sixth order inclusive are obtained.

Deciphering the dynamics of distorted turbulent flows: Lagrangian particle tracking and chaos prediction through transformer-based deep learning models

Turbulent flow is a complex and vital phenomenon in fluid dynamics, as it is the most common type of flow in both natural and artificial systems. Traditional methods of studying turbulent flow, such as computational fluid dynamics and experiments, have limitations such as high computational costs, experiment costs, and restricted problem scales and sizes. Recently, artificial intelligence has provided a new avenue for examining turbulent flow, which can help improve our understanding of its flow features and physics in various applications. Strained turbulent flow, which occurs in the presence of gravity in situations such as combustion chambers and shear flow, is one such case. This study proposes a novel data-driven transformer model to predict the velocity field of turbulent flow, building on the success of this deep sequential learning technique in areas such as language translation and music. The present study applied this model to experimental work by Hassanian et al., who studied distorted turbulent flow with a specific range of Taylor microscale Reynolds numbers 100<Reλ<120. The flow underwent a vertical mean strain rate of 8 s−1 in the presence of gravity. The Lagrangian particle tracking technique recorded every tracer particle's velocity field and displacement. Using this dataset, the transformer model was trained with different ratios of data and used to predict the velocity of the following period. The model's predictions significantly matched the experimental test data, with a mean absolute error of 0.002–0.003 and an R2 score of 0.98. Furthermore, the model demonstrated its ability to maintain high predictive performance with less training data, showcasing its potential to predict future turbulent flow velocity with fewer computational resources. To assess the model, it has been compared to the long short-term memory and gated recurrent units model. High-performance computing machines, such as JUWELS-DevelBOOSTER at the Juelich Supercomputing Center, were used to train and run the model for inference.

Design and Simulation of a High Gain Boost Converter with Reduced Input Current Ripple

Abstract: This paper proposes a high gain novel DC- DC converter. According to this topology gain of the converter can be improved more than a boost converter without using any transformer. In this topology it is possible to increases the gain of the converter without increasing the current ripple in the input current. This proposed topology is capable to reduce the voltage stress of the switches. Implementation of non-isolated topology eliminates the need of the transformer and reduces the magnetic size. The maximum duty restriction problem can be reduced by the higher gain of this proposed converter. The ripple reduction in the input current increases the life of energy storage system.

Groups of small period growth

AbstractWe construct finitely generated groups of small period growth, i.e. groups where the maximum order of an element of word length n grows very slowly in n. This answers a question of Bradford related to the lawlessness growth of groups and is connected to an approximative version of the restricted Burnside problem.

Maximizing Influence Spread through a Dynamic Social Network (Student Abstract)

Modern social networks are dynamic in their nature; a new connections are appearing and old connections are disappearing all the time. However, in our algorithmic and complexity studies, we usually model social networks as static graphs. In this paper, we propose a new paradigm for the study of the well-known Target Set Selection problem, which is a fundamental problem in viral marketing and the spread of opinion through social networks. In particular, we use temporal graphs to capture the dynamic nature of social networks. We show that the temporal interpretation is, unsurprisingly, NP-complete in general. Then, we study computational complexity of this problem for multiple restrictions of both the threshold function and the underlying graph structure and provide multiple hardness lower-bounds.

Energy analysis of the single impulsive Earth–Moon transfer with the temporary lunar capture

The single impulsive planar Earth–Moon transfer strategy is investigated by analyzing the energy change of the lunar capture. A planar bicircular model of the restricted four-body problem is applied to define the single impulsive trajectory to the Moon from the Earth. Then analytical expressions are derived to describe the energy changes of the lunar capture in the Sun–Earth rotating frame. Accordingly, the eccentricity at the perilune of the single impulsive transfer trajectory can be calculated analytically to explore the lunar escape and capture conditions. The error analysis shows that the theoretical solutions serve as good approximations of the energy changes of the single impulsive transfer. Furthermore, it has been found that the perilune angle and the perilune radius are the critical factors for lunar capture. Finally, the theoretical results are successfully employed to find a series of single impulsive planar Earth–Moon transfers.

Convergence analysis of critical point regularization with non-convex regularizers

One of the key assumptions in the stability and convergence analysis of variational regularization is the ability of finding global minimizers. However, such an assumption is often not feasible when the regularizer is a black box or non-convex making the search for global minimizers of the involved Tikhonov functional a challenging task. This is in particular the case for the emerging class of learned regularizers defined by neural networks. Instead, standard minimization schemes are applied which typically only guarantee that a critical point is found. To address this issue, in this paper we study stability and convergence properties of critical points of Tikhonov functionals with a possible non-convex regularizer. To this end, we introduce the concept of relative sub-differentiability and study its basic properties. Based on this concept, we develop a convergence analysis assuming relative sub-differentiability of the regularizer. The rationale behind the proposed concept is that critical points of the Tikhonov functional are also relative critical points and that for the latter a convergence theory can be developed. For the case where the noise level tends to zero, we derive a limiting problem representing first-order optimality conditions of a related restricted optimization problem. Besides this, we also give a comparison with classical methods and show that the class of ReLU-networks are appropriate choices for the regularization functional. Finally, we provide numerical simulations that support our theoretical findings and the need for the sort of analysis that we provide in this paper.

Revealing the properties of the out-of-plane points of equilibrium of the restricted 3-body problem with non-spherical radiating bodies

Our target is to understand and also reveal the dynamics of the out-of-plane points of equilibrium of the restricted version of the 3-body problem with equally massed radiating bodies that have either prolate or oblate shapes. We use standard root-finding numerical methods of high accuracy for determining the coordinates of the locations of the out-of-plane equilibria and also for computing their linear stability. For obtaining a global view of how the two system’s parameters, that is the prolateness/oblateness coefficient and the radiation pressure factor, affect the equilibria dynamics we perform a systematic and thorough scan of the parameters space. Our analysis suggests that the out-of-plane equilibria are highly affected by these two parameters and play a key role in the overall dynamics of the system.

The Problem of Restrictions when taking into Account the Covid-19 Pandemic

The Covid-19 pandemic has radically changed the way people comprehend the concept of ,,fundamental right”. Without previously planning on this, we have been witnesses to an apparent ,,violation” of some rights we do not only consider to be natural, but also mandatory for any democratic society. Being worried about the effects it might have on health, state institutions have taken the decision to restrict certain liberties, be it totally, or partially. Moreover, people have had their right to circulate limited, while others could not benefit from medical services, due to the overload that has affected sanitary institutions. Given this point of view, it is mandatory to analyze the legal boundaries that have to be taken into consideration, when talking about these decisions, so that legal matters be respected, even though, there have been some limitations put in place at the moment.

Transfer from Lunar Gateway to Sun-Earth Halo Orbits Using Solar Sails

To extend the usability of solar sails in the sun–Earth–moon system, we analyze the transfer trajectories from the 9:2 Earth–moon near-rectilinear halo orbit (NRHO) to halo orbits around the sun–Earth L1 and L2 points under the assumption of a future mission for a solar sail spacecraft equipped with a solar electric propulsion (SEP) system deployed from the Lunar Orbital Platform-Gateway. The dynamics are modeled using the bicircular restricted four-body problem, where the gravitational forces from the sun, Earth, and moon as well as solar radiation pressure (SRP) are considered. We propose a trajectory design method that utilizes both SRP and SEP. The method consists of initial guess generation and optimization steps. The initial guess generation comprises the forward propagation of the escape trajectory from the NRHO, the backward propagation of the stable manifold of the target halo orbits, and their apoapsis patching process. Optimization is conducted to minimize propellant consumption by effectively controlling SRP. We perform optimizations with various parameters, namely, the sail area-to-mass ratio (), specifications of SEP, target sun–Earth halo orbit, and departure direction. The results validate the proposed trajectory design method and verify that solar sail acceleration can reduce the necessary amount of propellant, which indicates that such missions can be realized by small CubeSats.

The restriction problem on the ellipsoid

Following a restriction argument in the Euclidean space, we derive a geometric invariant formula for a possible viscosity operator for an incompressible fluid flow on an ellipsoid embedded in R3. We also give an asymptotic expansion of the formula in terms of the eccentricity associated with the ellipsoid.

Restricted Concave Kite Five-Body Problem

The restricted concave kite five-body problem is a problem in which four positive masses, called the primaries, rotate in the concave kite configuration with a mass at the center of the triangle formed by three of the primaries. The fifth body has negligible mass and does not influence the motion of the four primaries. It is assumed that the fifth mass is in the same plane of the primaries and that the masses of the primaries are m 1 , m 2 , m 3 , and m 4 , respectively. Three different types of concave kite configurations are considered based on the masses of the primaries. In case I, one pair of primaries has equal masses; in case II, two pairs of primaries have equal masses; in case III, three of the primaries have equal masses. For all three cases, the regions of central configuration are obtained using both analytical and numerical techniques. The existence and uniqueness of equilibrium positions of the infinitesimal mass are investigated in the gravitational field of the four primaries. It is numerically confirmed that none of the equilibrium points are linearly stable. The Jacobian constant C is used to investigate the regions of possible motion of the infinitesimal mass.

Satisfaction-Based Multiobjective Optimization of the Design of a 65 GHz Millimeter-Wave Connector

It is difficult to simultaneously ensure the radio frequency (RF) performance and mechanical strength of 65 GHz millimeter-wave connectors. To address this, satisfaction-based multiobjective method for connector design optimization is proposed. An optimization model is developed for the structural dimensions of 65 GHz millimeter-wave connectors to minimize the voltage standing wave ratio, insertion loss, and deflection and maximum stress of the center conductor. The proposed optimization model concurrently satisfies the design requirements in terms of characteristic impedance, transmission frequency, and dielectric withstanding voltage. The model is optimized by innovatively using the multiobjective chaotic optimization algorithm in microwave finite-element simulations. The resulting optimal structure satisfies all performance requirements, thereby proving the rationality and feasibility of the proposed method. Moreover, this study establishes a novel design for other microwave devices to solve the problem of multiple performance index restrictions.

A Class of Symmetric Dziobek Configurations in Restricted Problems for Homogeneous Force Laws

A Class of Symmetric Dziobek Configurations in Restricted Problems for Homogeneous Force Laws

Geometric Analysis of Sun-Assisted Lunar Transfer Trajectories in the Planar Bicircular Four-Body Model

This research presents a geometric analysis of Sun-assisted low-energy lunar transfers and several convenient tools that enable the systematic trajectory design in the framework of the planar bicircular restricted four-body problem. By analogy with the patched conic approximation approach for high-energy transfers, a Sun-assisted low-energy trajectory is divided into three legs. Two interior legs, departing and arriving, are located inside the Earth–Moon region of prevalence and designed in the Earth–Moon circular restricted three-body problem, whereas the exterior leg lies outside the region of prevalence and is calculated in the Earth–Moon–Sun bicircular restricted four-body model. The whole trajectory is obtained by smoothly patching the three legs on the boundary of the region of prevalence. The arrival conditions are met by targeting a specific point in the L2 lunar gateway. The interior legs are easily adjustable to the four-body dynamics. The database of planar lunar transfer trajectories can be used to select an initial guess for the multiple-shooting procedure of designing a three-dimensional Sun-assisted lunar transfer in high-fidelity dynamical models.

Effect of Stokes drag in the restricted four-body problem with variable mass

The aim of this paper is to study the existence, locations and stability of the equilibrium points as well as zero velocity curves (ZVCs) under the effect of dissipative force (Stokes drag) in the restricted four-body problem (R4BP) with a variable mass. We have studied the dynamics of the infinitesimal body whose mass is variable and changing according to Jeans’ law. We have determined the equations of motion of the infinitesimal body by using the space time transformation of Meshcherskii when the change in mass is non-isotropic. We have determined the locations of equilibrium points in the special case of non-isotropic variation of mass under the effect of the dissipative force and found that all the equilibrium points are non-collinear. The effect of parameter k(0<k<1), which controls the dissipative force, on the locations of the libration points and their stability are investigated. It has been observed that the energy integral is time dependent due to the presence of the Stokes drag force. Further, it has been observed that all the equilibrium points are unstable for all values of the parameters used.

Studying and Simulating the Fractional COVID-19 Model Using an Efficient Spectral Collocation Approach

We give a theoretical and numerical analysis of a coronavirus (COVID-19) infection model in this research. A mathematical model of this system is provided, based on a collection of fractional differential equations (in the Caputo sense). Initially, a rough approximation formula was created for the fractional derivative of tp. Here, the third-kind Chebyshev approximations of the spectral collocation method (SCM) were used. To identify the unknown coefficients of the approximate solution, the proposed problem was transformed into a system of algebraic equations, which was then transformed into a restricted optimization problem. To evaluate the effectiveness and accuracy of the suggested scheme, the residual error function was computed. The objective of this research was to halt the global spread of a disease. A susceptible person may be moved immediately into the confined class after being initially quarantined or an exposed person may be transferred to one of the infected classes. The researchers adopted this strategy and considered both asymptomatic and symptomatic infected patients. Results acquired with the achieved results were contrasted with those obtained using the generalized Runge-Kutta method.

Spatial positioning method based on UWB antenna array layout

Aiming at the problem of spatial positioning of dynamic targets in traditional power systems, this paper provides a cost controllable and high precision UWB antenna array layout method for spatial positioning to solve the problems of low precision and multiple restrictions of ultra wideband in spatial environment. First, a base station is set in each area. The base station contains a group of UWB antenna arrays composed of multiple antenna pairs. The distance L from the base station with the location tag is accurately measured through the UWB. Then, the UWB antenna array uses the PDOA phase difference principle to measure the direction of the signal. Finally, the spatial azimuth of the UWB signal from the tag to be located relative to the base station is calculated. The feasibility of the proposed method is verified by an example, which can significantly improve the positioning accuracy. The proposed method can provide strong technical support for intelligent operation and maintenance of power system and safe production.