Good Approximate Solutions Research Articles

Intrinsic squeezing of mechanical motion of a harmonically trapped atom with spin-orbit coupling

In this paper we investigated one-dimensional harmonically trapped atom with Raman-induced spin-orbit coupling by mapping to quantum-like model. Using displacement Fock states in quantum optics and variational methods we found the odd-parity superposition state of left- and right-displaced oscillator state is a good approximate solution to the ground state, which captures the essential physics of the system. The ground state wave function owes nodes which is remarkably different from the conventional no-node theory in quantum mechanics. The results show the atomic motion of center of mass exhibits intrinsic squeezing properties with relation to the Raman and spin-orbit coupling strength characterized by the variance in position and momentum, information entropy, as well as the Wigner function of the ground state. The dynamics of center of mass are also studied which demonstrates intuitive Zitterbewegung oscillations in momentum space and real space. Our results could be used for observing Zitterbewegung oscillations in neutral atomic gases and engineering nonclassic states.

New Algorithms for Steiner Tree Reoptimization

Reoptimization is a setting in which we are given a good approximate solution of an optimization problem instance and a local modification that slightly changes the instance. The main goal is that of finding a good approximate solution of the modified instance. We investigate one of the most studied scenarios in reoptimization known as Steiner tree reoptimization. Steiner tree reoptimization is a collection of strongly NP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf {NP}$$\\end{document}-hard optimization problems that are defined on top of the classical Steiner tree problem and for which several constant-factor approximation algorithms have been designed in the last decades. In this paper we improve upon all these results by developing a novel technique that allows us to design polynomial-time approximation schemes. Remarkably, prior to this paper, no approximation algorithm better than recomputing a solution from scratch was known for the elusive scenario in which the cost of a single edge decreases. Our results are best possible since none of the problems addressed in this paper admits a fully polynomial-time approximation scheme, unless P=NP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf {P}=\ extsf {NP}$$\\end{document}

A projected-search interior-point method for nonlinearly constrained optimization

AbstractThis paper concerns the formulation and analysis of a new interior-point method for constrained optimization that combines a shifted primal-dual interior-point method with a projected-search method for bound-constrained optimization. The method involves the computation of an approximate Newton direction for a primal-dual penalty-barrier function that incorporates shifts on both the primal and dual variables. Shifts on the dual variables allow the method to be safely “warm started” from a good approximate solution and avoids the possibility of very large solutions of the associated path-following equations. The approximate Newton direction is used in conjunction with a new projected-search line-search algorithm that employs a flexible non-monotone quasi-Armijo line search for the minimization of each penalty-barrier function. Numerical results are presented for a large set of constrained optimization problems. For comparison purposes, results are also given for two primal-dual interior-point methods that do not use projection. The first is a method that shifts both the primal and dual variables. The second is a method that involves shifts on the primal variables only. The results show that the use of both primal and dual shifts in conjunction with projection gives a method that is more robust and requires significantly fewer iterations. In particular, the number of times that the search direction must be computed is substantially reduced. Results from a set of quadratic programming test problems indicate that the method is particularly well-suited to solving the quadratic programming subproblem in a sequential quadratic programming method for nonlinear optimization.

Solving tri-criteria:total completion time, total late work, and maximum earliness by using exact, and heuristic methods on single machine scheduling problem

The presented study investigated the scheduling regarding jobs on a single machine. Each job will be processed with no interruptions and becomes available for the processing at time 0. The aim is finding a processing order with regard to jobs, minimizing total completion time , total late work , and maximal tardiness which is an NP-hard problem. In the theoretical part of the present work, the mathematical formula for the examined problem will be presented, and a sub-problem of the original problem of minimizing the multi-objective functions is introduced. Also, then the importance regarding the dominance rule (DR) that could be applied to the problem to improve good solutions will be shown. While in the practical part, two exact methods are important; a Branch and Bound algorithm (BAB) and a complete enumeration (CEM) method are applied to solve the three proposed MSP criteria by finding a set of efficient solutions. The experimental results showed that CEM can solve problems for up to jobs. Two approaches of the BAB method were applied: the first approach was BAB without dominance rule (DR), and the BAB method used dominance rules to reduce the number of sequences that need to be considered. Also, this method can solve problems for up to , and the second approach BAB with dominance rule (DR), can solve problems for up to jobs in a reasonable time to find efficient solutions to this problem. In addition, to find good approximate solutions, two heuristic methods for solving the problem are proposed, the first heuristic method can solve up to jobs, while the second heuristic method can solve up to jobs. Practical experiments prove the good performance regarding the two suggested approaches for the original problem. While for a sub-problem the experimental results showed that CEM can solve problems for up to jobs, the BAB without dominance rule (DR) can solve problems for up to , and the second approach BAB with dominance rule (DR), can solve problems for up to jobs in a reasonable time to find efficient solutions to this problem. Finally, the heuristic method can solve up to jobs. Arithmetic results are calculated by coding (programming) algorithms using (MATLAB 2019a)

Hybrid ant colony and intelligent water drop algorithm for route planning of unmanned aerial vehicles

Route planning is a crucial element in unmanned aerial vehicle (UAV) systems, particularly in autonomous UAV technology. In the past decades, various algorithms have been proposed for UAV route planning. However, they still have defects, such as stagnation and slow search rates. In this study, a novel hybrid algorithm which integrates ant colony optimization (ACO) and intelligent water drop (IWD) is proposed for UAV route planning. First, the advantages of the IWD and ACO algorithms are combined in an iterative strategy, to ensure mutual cooperation via exchange of information for route optimization. Initially, the water drops optimize the soil and pheromones within the environment simultaneously to generate good approximate solutions and an initial pheromone distribution for the ant colony. Based thereupon, the ant colony roams the solution space to further optimize the routes, thus combining the exploration potential and exploitability of two types of agents. Additionally, a novel node selection strategy is proposed to guide the agents’ route planning along a reasonable direction. Compared with state-of-the-art algorithms, the convergence accuracy, success rate, and stability of the proposed algorithm exhibited significant improvements of approximately 8.25%, 4.20%, and 66.20%, respectively.

Minimizing cost for influencing target groups in social network: A model and algorithmic approach

Stimulated by practical applications arising from economics, viral marketing, and elections, this paper studies the problem of Groups Influence with Minimum cost (GIM), which aims to find a seed set with the smallest cost that can influence all target groups in a social network, where each user is assigned a cost and a score and a group of users is influenced if the total score of influenced users in the group is at least a certain threshold. As the group influence function, defined as the number of influenced groups or users, is neither submodular nor supermodular, theoretical bounds on the quality of solutions returned by the well-known greedy approach may not be guaranteed.In this work, two efficient algorithms with theoretical guarantees for tackling the GIM problem, named Groups Influence Approximation (GIA) and Exact Groups Influence (EGI), are proposed. GIA is a bi-criteria polynomial-time approximation algorithm and EGI is an (almost) exact algorithm; both can return good approximate solutions with high probability. The novelty of our approach lies in two aspects. Firstly, a novel group reachable reverse sample concept is proposed to estimate the group influence function within an error bound. Secondly, a framework algorithmic is designed to find serial candidate solutions with checking theoretical guarantees at the same time. Besides theoretical results, extensive experiments conducted on real social networks show our algorithms’ performance. In particular, both EGI and GIA provide the solution quality several times better, while GIA is up to 800 times faster than the state-of-the-art algorithms.

A new perspective on the dynamic forced 2-DOF system with the non-perturbative approach

An elegant and straightforward method based on the equivalent linearized method is offered for the analysis of nonlinear vibrations of forced 2-DOF dynamical systems, in search of a simple good approximate solution with the non-perturbative approach. In the present approach, the 2-DOF system is transformed into a decoupled linear oscillator with instantaneous frequency identification. In this approach, we avoid the restriction on the periodic force coefficient, which was considered to be well below unity in various perturbation methods. This liberation of the amplitude of the periodic force led to the emergence of new patterns of the formation of periodic solution waves. It is found that the existence of the periodic force has an inhibitory effect on the scattering factors unless their frequency approaches the natural frequency of the dynamic system. The validation of the scheme is shown by comparing the numerical findings with the existing results. The supremacy of the proposed scheme is demonstrated by making numerical comparisons for each pattern of the obtained solution. The analytical solutions show high consistency proving the accuracy of the non-perturbative approach. This motivates us to extend the scheme for solving free and forced nonlinear vibrations of more coupled structures. It is noteworthy as a new technique with significant usefulness.

A universal quantum algorithm for weighted maximum cut and Ising problems

We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted maximum cut or the Ising Hamiltonian. Measuring the expectation of this operator on a variational quantum state yields the variational energy of the quantum system. The system is enforced to evolve toward the ground state of the problem Hamiltonian by optimizing a set of angles using normalized gradient descent. Experimentally, our algorithm outperforms the state-of-the-art quantum approximate optimization algorithm on random fully connected graphs and challenges D-Wave quantum annealers by producing good approximate solutions. Source code and data files are publicly available (https://github.com/nkuetemeli/UQMaxCutAndIsing).

Automated design of multi-stage forging sequences for die forging

Forgings are produced in several process steps, the so-called forging sequence. The design of efficient forging sequences is a very complex and iterative development process. In order to automate this process and to reduce the development time, a method is presented here, which automatically generates multi-stage forging sequences for different forging geometries on the basis of the component geometry (STL file). The method was developed for closed die forging. The individual modules of this forging sequence design method (FSD method) as well as the functioning of the algorithm for the generation of the intermediate forms are presented. The method is applied to different forgings with different geometrical characteristics. The generated forging sequences are checked with FE simulations for the quality criteria form filling and freedom from folds. The simulation results show that the developed FSD method provides good approximate solutions for an initial design of forging sequences for closed die forging in a short time.

A Multiple Objective Resource Scheduling Algorithm for Network Services on the NFV Infrastructure

Capital expenditure (CAPEX) and operating expenses (OPEX) a key practical concerns for telecommunication companies, emphasizing the attraction of Network Function Virtualization (NFV) in recent years. However, the NFV Infrastructure (NFVI) includes a wide variety of resource types and stakeholders. While many attempts have been made to enhance the ability of existing resource scheduling approaches to support the complex and conflicting NFV ecosystem, they are no longer sufficient. In this paper, I propose the Multiple Objective Resource Scheduling Algorithm (MORSA) to optimize the NFVI resource usage. In developing MORSA, I designed a plug-in architecture to satisfy various requirements related to NFVI resources and stakeholder policies. MORSA allows the NFVI Resource Scheduler to optimize, simultaneously, any combination of possibly conflicting objectives with multifaceted constraints in complex real world situations. Evaluation results show that MORSA obtains good approximate solutions by resolving conflicting objectives in reasonable computation times.

An efficient PGM-based algorithm with backtracking strategy for solving quadratic optimization problems with spherical constraint

We utilize projected gradient method (PGM for short) to solve quadratic optimization problem with spherical constraint. Based on the global convergence of simple first order conic method for trust region subproblem, we show that under some conditions, the global convergence of the PGM is guaranteed if the initial point is chosen specially. With only the multiplication of matrix and vector involved, a good approximation solution can be obtained in a low computation cost for large scale applications.

Folding lattice proteins with quantum annealing

Quantum annealing is a promising approach for obtaining good approximate solutions to difficult optimization problems. Folding a protein sequence into its minimum-energy structure represents such a problem. For testing new algorithms and technologies for this task, the minimal lattice-based HP model is well suited, as it represents a considerable challenge despite its simplicity. The HP model has favorable interactions between adjacent, not directly bound hydrophobic residues. Here, we develop a novel spin representation for lattice protein folding tailored for quantum annealing. With a distributed encoding onto the lattice, it differs from earlier attempts to fold lattice proteins on quantum annealers, which were based upon chain growth techniques. With our encoding, the Hamiltonian by design has the quadratic structure required for calculations on an Ising-type annealer, without having to introduce any auxiliary spin variables. This property greatly facilitates the study of long chains. The approach is robust to changes in the parameters required to constrain the spin system to chain-like configurations, and performs very well in terms of solution quality. The results are evaluated against existing exact results for HP chains with up to $N=30$ beads with 100% hit rate, thereby also outperforming classical simulated annealing. In addition, the method allows us to recover the lowest known energies for $N=48$ and $N=64$ HP chains, with similar hit rates. These results are obtained by the commonly used hybrid quantum-classical approach. For pure quantum annealing, our method successfully folds an $N=14$ HP chain. The calculations were performed on a D-Wave Advantage quantum annealer.

Quantum walk in a reinforced free-energy landscape: Quantum annealing with reinforcement

Providing an optimal path to a quantum annealing algorithm is key to finding good approximate solutions to computationally hard optimization problems. Reinforcement is one of the strategies that can be used to circumvent the exponentially small energy gaps of the system in the annealing process. Here a time-dependent reinforcement term is added to the Hamiltonian in order to give lower energies to the most probable states of the evolving system. In this study, we take a local entropy in the configuration space for the reinforcement and apply the algorithm to a number of easy and hard optimization problems. The reinforced algorithm performs better than the standard quantum annealing algorithm in the quantum search problem, where the optimal parameters behave very differently depending on the number of solutions. Moreover, the reinforcements can change the discontinuous phase transitions of the mean-field p-spin model ($p>2$) to a continuous transition. The algorithm's performance in the binary perceptron problem is also superior to that of the standard quantum annealing algorithm, which already works better than a classical simulated annealing algorithm.

A multi-objective evolutionary algorithm based on niche selection in solving irregular Pareto fronts

The key characteristic of multi-objective evolutionary algorithm is that it can find a good approximate multi-objective optimal solution set when solving multi-objective optimization problems(MOPs). However, most multi-objective evolutionary algorithms perform well on regular multi-objective optimization problems, but their performance on irregular fronts deteriorates. In order to remedy this issue, this paper studies the existing algorithms and proposes a multi-objective evolutionary based on niche selection to deal with irregular Pareto fronts. In this paper, the crowding degree is calculated by the niche method in the process of selecting parents when the non-dominated solutions converge to the first front, which improves the the quality of offspring solutions and which is beneficial to local search. In addition, niche selection is adopted into the process of environmental selection through considering the number and the location of the individuals in its niche radius, which improve the diversity of population. Finally, experimental results on 23 benchmark problems including MaF and IMOP show that the proposed algorithm exhibits better performance than the compared MOEAs.

Scalable node-disjoint and edge-disjoint multiwavelength routing.

Probabilistic message-passing algorithms are developed for routing transmissions in multiwavelength optical communication networks, under node- and edge-disjoint routing constraints and for various objective functions. Global routing optimization is a hard computational task on its own but is made much more difficult under the node- and edge-disjoint constraints and in the presence of multiple wavelengths, a problem which dominates routing efficiency in real optical communication networks that carry most of the world's internet traffic. The scalable principled method we have developed is exact on trees but provides good approximate solutions on locally treelike graphs. It accommodates a variety of objective functions that correspond to low latency, load balancing, and consolidation of routes and can be easily extended to include heterogeneous signal-to-noise values on edges and a restriction on the available wavelengths per edge. It can be used for routing and managing transmissions on existing topologies as well as for designing and modifying optical communication networks. Additionally, it provides the tool for settling an open and much-debated question on the merit of wavelength-switching nodes and the added capabilities they provide. The methods have been tested on generated networks such as random-regular, Erdős Rényi, and power-law graphs, as well as on optical communication networks in the United Kingdom and United States. They show excellent performance with respect to existing methodology on small networks and have been scaled up to network sizes that are beyond the reach of most existing algorithms.

Assessment of jeans sewing thread consumption by applying metaheuristic optimization methods

Assessment of jeans sewing thread consumption by applying metaheuristic optimization methods

The quantum dynamics of a mesoscopic driven RLC circuit consisting of a linear inductor, a linear resistor and a nonlinear capacitor

The nonlinear capacitor that obeys of a cubic polynomial voltage–charge relation (usually a power series in charge) is introduced. The quantum theory for a mesoscopic electric circuit with charge discreteness is investigated, and the Hamiltonian of a quantum mesoscopic electrical circuit comprised by a linear inductor, a linear resistor and a nonlinear capacitor under the influence of a time-dependent external source is expressed. Using the numerical solution approaches, a good analytic approximate solution for the quantum cubic Duffing equation is found. Based on this, the persistent current is obtained antically. The energy spectrum of such nonlinear electrical circuit has been found. The dependency of the persistent current and spectral property equations to linear and nonlinear parameters is discussed by the numerical simulations method, and the quantum dynamical behavior of these parameters is studied.

EICIC Configuration of Downlink and Uplink Decoupling With SWIPT in 5G Dense IoT HetNets

Interference management and power transfer can provide a significant improvement over the 5th generation mobile networks (5G) dense Internet of Things (IoT) heterogeneous networks (HetNets). In this paper, we present a novel approach to simultaneously manage inferences at the downlink (DL) and uplink (UL), and to identify opportunities for power transfer and additional UL transmissions integrated with existing protocols and infrastructures for enhanced inter-cell interference coordination (eICIC) protocol in dense IoT HetNets, while considering practical non-linear energy harvesting (EH) model. The design is formulated as the joint optimization of interference aware UL/DL decoupling, airtime resource allocation and energy transfer. The key insight of our algorithm is to translate the original, intractable joint-optimization problem into a problem space where a good approximate solution can be quickly found. We evaluate our scheme through theoretical analysis and simulation. The evaluation shows that our approach improves the system utility by over 20% compared to start-of-the-art in dense IoT HetNets. Compared to alternative schemes, our approach maintains the best user fairness and rate experience and can solve the problem in a fast and scalable way.

Sequential sampling approach to energy‐based multi‐objective design optimization of steel frames with correlated random parameters

AbstractThis work presents a novel sequential sampling approach to the multi‐objective reliability‐based design optimization of moment‐resisting steel frames subjected to earthquake excitation. The optimization problem is formulated with two objective functions, namely, the total mass and the energy dissipated by beam members of the frame, and subject to uncorrelated probabilistic constraints on dynamic responses under the effects of correlated random parameters of floor masses, external loads, and material properties. The dynamic responses for a small number of designs are found by nonlinear response history analysis and further approximated by Gaussian process (GP) models to mitigate the computational burden during the optimization process. Approximate solutions sorted among existing candidate solutions are updated after each optimization iteration using discrete random local and global searches. The GP models are also refined after each optimization iteration by specifying new sampling points that lie on the Pareto front of a bi‐objective deterministic maximization problem formulated for the improvement in the current approximate solutions and the feasibility of the new sampling points. As demonstrated in a test problem, the new sampling points tend to distribute in the neighborhood of the exact solutions, thereby underpinning a quick termination as well as the robustness of the proposed method. Optimization results from the test problem and a design example show that good approximate solutions are always obtained as the solution quality converges.

An optimal variational iteration method for investigating the physical behavior of quasi-steady squeezing flow confined between parallel rigid walls

An efficient numerical method for investigating the physical behavior of an axisymmetric 2D incompressible squeeze flow between two rigid parallel plates is proposed. Due to the low velocity of the moving rigid wall, the flow is considered as a quasi-steady flow. The nonlinear governing equations can be transformed to a single fourth-order nonlinear differential equation. A new efficient iteration method based on coupling of variational iteration method with some auxiliary convergence-control parameters, known as the optimal variational iteration method is proposed to obtain a solution for the generated nonlinear fourth-order differential equation. In the proposed method, the residual function and its error of norm two are implemented to change the problem into an optimization one in order to choose the auxiliary convergence-control parameters optimally. Consequently, a good approximate solution is obtained. The main benefit of the proposed method is the availability of adjusting and controlling the convergence region in an easy way. This property leads to faster convergence, simplicity of wide-range application and efficiency. To show the efficiency and accuracy of the established method, the problem is also solved by various iterative methods, such as perturbation method, homotopy perturbation method and optimal homotopy asymptotic method. As a comparison, the proposed method provides a straightforward way to control the convergence and consequently readily tuning the convergence regions. These properties lead to quick convergence to the exact solution and needing less computational efforts.