Global Minimum Value Research Articles

Efficiently embedding QUBO problems on adiabatic quantum computers

Adiabatic quantum computers like the D-Wave 2000Q can approximately solve the QUBO problem, which is an NP-hard problem, and have been shown to outperform classical computers on several instances. Solving the QUBO problem literally means solving virtually any NP-hard problem like the traveling salesman problem, airline scheduling problem, protein folding problem, genotype imputation problem, thereby enabling significant scientific progress, and potentially saving millions/billions of dollars in logistics, airlines, healthcare and many other industries. However, before QUBO problems are solved on quantum computers, they must be embedded (or compiled) onto the hardware of quantum computers, which in itself is a very hard problem. In this work, we propose an efficient embedding algorithm, that lets us embed QUBO problems fast, uses less qubits and gets the objective function value close to the global minimum value. We then compare the performance of our embedding algorithm to that of D-Wave’s embedding algorithm, which is the current state of the art, and show that our embedding algorithm convincingly outperforms D-Wave’s embedding algorithm. Our embedding approach works with perfect Chimera graphs, i.e., Chimera graphs with no missing qubits.

Research on Rosenbrock Function Optimization Problem Based on Improved Differential Evolution Algorithm

The Rosenbrock function optimization belongs to unconstrained optimization problems, and its global minimum value is located at the bottom of a smooth and narrow valley of the parabolic shape. It is very difficult to find the global minimum value of the function because of the little information provided for the optimization algorithm. According to the characteristics of the Rosenbrock function, this paper specifically proposed an improved differential evolution algorithm that adopts the self-adaptive scaling factor F and crossover rate CR with elimination mechanism, which can effectively avoid premature convergence of the algorithm and local optimum. This algorithm can also expand the search range at an early stage to find the global minimum of the Rosenbrock function. Many experimental results show that the algorithm has good performance of function optimization and provides a new idea for optimization problems similar to the Rosenbrock function for some problems of special fields.

Unimodal Model-Based Inter Mode Decision for High Efficiency Video Coding

In this paper, a fast inter mode decision algorithm, called the unimodal model-based inter mode decision (UMIMD), is proposed for the latest video coding standard, the high-efficiency video coding. Through extensive simulations, it has been observed that a unimodal model (i.e., with only one global minimum value) can be established among the size of different prediction unit (PU) modes and their resulted rate-distortion (RD) costs for each quad-tree partitioned coding tree unit (CTU). To guarantee the unimodality and further search the optimal operating point over this function for each CTU, all the PU modes need to be first classified into 11 mode classes according to their sizes. These classes are then properly ordered and sequentially checked according to the class index, from small to large so that the optimal mode can be early identified by checking when the RD cost starts to arise. In addition, an effective instant SKIP mode termination scheme is developed by simply checking the SKIP mode against a pre-determined threshold to further reduce the computational complexity. The extensive simulation results have shown that the proposed UMIMD algorithm is able to individually achieve a significant reduction on computational complexity at the encoder by 61.9% and 64.2% on average while incurring only 1.7% and 2.1% increment on the total Bjontegaard delta bit rate (BDBR) for the low delay and random access test conditions, compared with the exhaustive mode decision in the HEVC. Moreover, the experimental results have further demonstrated that the proposed UMIMD algorithm outperforms multiple state-of-the-art methods.

Ultrasonic Computerized Tomography Imaging Method With Combinatorial Optimization Algorithm for Concrete Pile Foundation

Concrete pile foundations are the main load-carrying and aseismic structures for many large-scale building structures. Their structural quality will have a great impact on the safety of building structures. However, the imaging results still cannot easily meet practical demands in current ultrasonic Computerized Tomography (CT) imaging tests of concrete structures. In view of the current difficulties, a combinatorial optimization tomographic imaging method is proposed. First, a quadric broadening objective function with a clear physical meaning is established according to the characteristics of ultrasonic propagation in concrete. Then, a new CT imaging method of concrete pile foundation is formed by combining fast adaptive optimization search ability of Genetic Algorithm (GA) with the global search control ability of Simulated Annealing Algorithm (SAA). The numerical simulation experiments have shown that the usage of the correct priori information and the excellent characteristic of the Simulated Annealing Genetic Algorithm (SAGA) in searching for the global minimum value of the function have produced accurate and effective results with stable numerical values. Finally, the imaging method is verified by experiment, where results show that SAGA requires fewer iterations, has faster computation speed and gives more accurate imaging results compared with the single GA.

A robust MoF method applicable to severely deformed polygonal mesh

The MoF (Moment of Fluid) method is an accurate approach for interface reconstruction in numerical simulation of multi-material fluid flow. So far, most works focus on improving its accuracy and efficiency, such as developing analytic reconstruction method and deducing the iteration schemes based on high order derivatives of the objective function. In this paper, we mainly concern on improving its robustness, especially for severely deformed polygonal meshes, in which case the objective function has multiple minimum value points. By using an efficient method for solving multiple roots of the nonlinear equation in large scope, a new algorithm is developed to enhance robustness of the MoF method. The main idea of this algorithm is as follows. The first derivative of the objective function is continuous, so the minimum value points of the objective function must be the zero points of the first derivative. Instead of finding the zero points of the first derivative directly, we turn to calculating the minimum value points (also zero points) of the square of the first derivative, which is a convex function on a neighborhood of each zero point. Applying the properties of convex function, the neighbor of each extreme minimum point of it can be obtained efficiently. Then each zero point of the square of the first derivative can be obtained using the iterative formula in its neighbor. Finally, by comparing the values of the objective function at these zero points of the first derivative, the global minimum value point of the objective function can be found and is the desired solution. The new algorithm only uses the first derivative of the objective function. It doesn't need an initial guess for the solution, which has to be carefully chosen in previous works. Numerical results are presented to demonstrate the accuracy and robustness of this new algorithm. The results show that it is applicable to severely deformed polygonal mesh, even with concave cells.

Fuzzy Supervised Clustering Algorithm with the Particle Swarm Optimization

In GK-algorithm, fuzzy clustering algorithm with preserved volume was used. However, the added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. A Fuzzy C-Means algorithm based on Mahalanobis distance (FCM-HM) was proposed to improve those limitations of GG and GK algorithms, but it is not stable enough when some of its covariance matrices are not equal. The singular problem and the selecting initial values problem are improved. We pointed out that the initial memberships of fuzzy c-mean algorithm which was based on Mahalanobis distance algorithm and the traditional Fuzzy c-means algorithm (FCM) Algorithm can’t be all equal. The other important issue is how to approach the global minimum value that can improve the cluster accuracy. The methods to detect the local extreme value were developed by this paper. Focusing attention to these two faults, an improved new algorithm, “Fuzzy C-Means based on Particle Swarm Optimization with Mahalanobis distance (PSO-FCM-HM)”, is proposed. We have two aims and goals of our research summary. One is to compare the classification accuracies of fuzzy clustering algorithms based on Mahalanobis distances and Euclidean distances. The other is to choose the initial membership to promote the classification accuracies.

Grey wolf algorithm for multidimensional engine optimization of converted plug-in hybrid electric vehicle

The paper presents the application of grey wolf algorithm for multidimensional engine optimization of converted parallel operated diesel plug-in hybrid electric vehicle to optimize specific fuel consumption (FC) and emissions. All emissions hydrocarbon (HC), carbon monoxide (CO), nitrogen oxide (NOx) and particulate matter (PM) are considered as optimization parameters. Offline engine maps of FC, HC, CO, NOx and PM are generated for 70 hp engine by data obtained from Oak Ridge National Laboratory for study. MATLAB program is used for simulation. A grey wolf coding is developed and tested extensively for various values of speed and torque. The optimization results obtained are verified by available engine maps. The optimization performance and its environmental impact are discussed in detail. It is observed that grey wolf optimizer (GWO) gives the global minimum value with slight deviation, although least computation time and simplicity makes this algorithm a potential candidate for real-time implementation.

Numerical analysis of transverse reciprocating velocity effects in EHL point contacts

Abstract Experimental results by Fryza et al. [1] on the effect of transverse harmonic vibrations over the film thickness in EHL point contacts are directly compared here with numerical simulations assuming isothermal conditions and either Newtonian or Non-Newtonian fluid rheology. The simulations agree well with the experiments at the highest reciprocating speed frequency applied. It is then apparent from the comparison that with the oils and contact conditions analyzed, phenomena such as shear and thermal thinning, starvation and rig inertia have a minimal impact if not entirely absent. The simulated time-dependent film thickness fluctuations also show that, whereas the mean central film thickness decreases as reported by Fryza et al., both the global minimum and average film values increase as a result of adding a transverse reciprocating speed. Possible explanations for the obtained results are provided, highlighting the need for a broader analysis to better understand this type of problems.

Potential energy surface and cold collision dynamics of Xe-NH(X3∑-) system

Sympathetic cooling is one of the most promising techniques for producing ultracold molecules from precooled molecules. Previous researches have shown that it is inadequate to use the ultracold alkali-metal atoms as coolant for sympathetic cooling. To explore the possibility of ultracold alkali-earth-metal atoms as coolant, in this paper a theoretical investigation is performed of the cold collision dynamics for Xe-NH(X3∑-) system in magnetic fields. The interaction potential energies of Xe-NH complex are calculated respectively by using the single and double excitation coupled-cluster theory with the noniterative treatment of triple excitations[CCSD(T)] method and complete basis set limit extrapolated method. An analytic express of potential energy surface (PES) is given for the first time. A single global minimum value occurs at R=7.14a0, θ=102.76° with an energy of-153.54 cm-1, and the PES has a weak anisotropy. Combine the ab initio PES with quantum scattering theory, then the cold collisional dynamics of Xe-NH system in a magnetic field will be studied. The elastic and inelastic transition cross sections and their ratios of NH molecules in the lowest low-field following state (n=0, mj=1) under different magnetic fields and collisional energies are calculated. The results show that the elastic cross section is independent of magnetic field, and the inelastic cross section changes with magnetic field, especially at an ultracold temperature. A common rule of thumb is that to successfully implement cooling, the ratio of elastic cross section to inelastic cross section needs to reach 100 at least. The results suggest that it is likely to be a challenging work to perform sympathetic cooling of NH molecule by ultracold Xe atom.

Comparative Performance Analysis of Optimal PID Parameters Tuning Based on the Optics Inspired Optimization Methods for Automatic Generation Control

The Optics Inspired Optimization (OIO) algorithm is a new metaheuristic optimization method. In this paper, the OIO algorithm was proposed for automatic production control parameters in electrical power systems. The performance of the proposed algorithm was realized on two power systems that have different structures. The first structure is a two-area interconnected thermal reheat power system and the other one is a two-area interconnected multi-unit hydro-thermal power system. The results obtained with the proposed algorithm were compared with an artificial bee colony and particle swarm optimization, initial values are randomly defined that are commonly used in literature. The results were examined using four different cost functions based on area control error. Considering the obtained results, the proposed algorithm reached to the global minimum value with less number of iterations and is more suitable for online optimization. According to the results obtained with this novel method, it has a better performance for maximum overshoot and settling time values when the test systems are implemented.

A Stochastic Level-Value Estimation Method for Global Optimization

In this paper, we propose a stochastic level-value estimation method to solve a kind of box-constrained global optimization problem. For this purpose, we first derive a generalized variance function associated with the considered problem and prove that the largest root of the function is the global minimal value. Then, Newton’s method is applied to find the root. The convergence of the proposed method is established under some suitable conditions. Based on the main idea of the cross-entropy method to update the sampling density function, an important sampling technique is proposed in the implementation. Preliminary numerical experiments indicate the validity of the proposed method.

ACS algorithm tuned ANFIS-based controller for LFC in deregulated environment

Abstract In this paper, an artificial cooperative search (ACS) algorithm tuned adaptive network-based fuzzy inference system (ANFIS) controller for optimal gain tuning of load frequency control (LFC) operation in deregulated scenario has been offered. The conventional controllers for load frequency control operation are having fixed gain values intended for nominal operating conditions of the power system and they do not afford effective and efficient performance over a large range of operating scenarios in the deregulated environment. To progress the system performance to its near optimum for all probable operating circumstances of the power system, the controller gains have to be computed for the equivalent operating conditions by using the restructured parameters. For this intention, a controller based on an adaptive network-based fuzzy inference system seems to be the most excellent and valuable preference. The ANFIS is trained by off-line data obtained using a new optimization technique, artificial cooperative search optimization algorithm and the corresponding gains are updated in real-time as per the changing operating conditions. ACS is a swarm intelligence algorithm developed for solving numerical optimization problems. The swarm intelligence philosophy behind ACS algorithm is based on the migration of two artificial superorganisms as they biologically interact to achieve the global minimum value pertaining to the problem. To exhibit the competence and robustness of the projected ACS algorithm tuned ANFIS controller, the controller has been implemented on a two-area two-unit interconnected deregulated power system having one reheat unit and one non-reheat unit in each area. The simulation results exhibit the ability of the designed ACS algorithm tuned ANFIS controller for online LFC operation in deregulated environment.

The Particle Swarm Optimization Based on Mahalanobis Distance

An improved new fuzzy clustering algorithm is developed to obtain better quality of fuzzy clustering results. The objective function includes the regulating terms about the covariance matrices. The cluster centers and the covariance matrices are directly derived from the Lagrange’s method. The fuzzy c-mean algorithm is different from the GK and GG algorithms. The singular problem and the selecting initial values problem are improved by the Eigenvalue method and the Ratio method. We proposed a proposition which pointed out that the initial memberships of fuzzy c-mean algorithm which was based on Mahalanobis distance Algorithm and the traditional FCM Algorithm can not be all equal. The other important issue is how to approach the global minimum value that can improve the cluster accuracy. The methods to detect the local extreme value were developed by this paper. Focusing attention to these two faults, an improved new algorithm, “Fuzzy C-Means based on Particle Swarm Optimization with Mahalanobis distance (PSO-FCM-M)”, is proposed. We have two aims and goals of our research summary. One is to compare the classification accuracies of fuzzy clustering algorithms based on mahalanobis distances and euclidean distances. The other is to choose the initial membership to promote the classification accuracies.

A variational approach for restoring images corrupted by noisy blur kernels and additive noise

SummaryIn this paper, we study a deblurring algorithm for distorted images by random impulse response. We propose and develop a convex optimization model to recover the underlying image and the blurring function simultaneously. The objective function is composed of 3 terms: the data‐fitting term between the observed image and the product of the estimated blurring function and the estimated image, the squared difference between the estimated blurring function and its mean, and the total variation regularization term for the estimated image. We theoretically show that under some mild conditions, the resulting objective function can be convex in which the global minimum value is unique. The numerical results confirm that the peak‐to‐signal‐noise‐ratio and structural similarity of the restored images by the proposed algorithm are the best when the proposed objective function is convex. We also present a proximal alternating minimization scheme to solve the resulting minimization problem. Numerical examples are presented to demonstrate the effectiveness of the proposed model and the efficiency of the numerical scheme.

Measurement of Common Risk Factors: A Panel Quantile Regression Model for Returns

This paper investigates how to measure common market risk factors using newly proposed Panel Quantile Regression Model for Returns. By exploring the fact that volatility crosses all quantiles of the return distribution and using penalized fixed effects estimator we are able to control for otherwise unobserved heterogeneity among financial assets. Direct benefits of the proposed approach are revealed in the portfolio Value–at–Risk forecasting application, where our modeling strategy performs significantly better than several benchmark models according to both statistical and economic comparison. In particular Panel Quantile Regression Model for Returns consistently outperforms all the competitors in the 5% and 10% quantiles. Sound statistical performance translates directly into economic gains which is demonstrated in the Global Minimum Value–at–Risk Portfolio and Markowitz-like comparison. Overall results of our research are important for correct identification of the sources of systemic risk, and are particularly attractive for high dimensional applications.

Composition Dependence of the Na(+) Ion Conductivity in 0.5Na2S + 0.5[xGeS2 + (1 - x)PS5/2] Mixed Glass Former Glasses: A Structural Interpretation of a Negative Mixed Glass Former Effect.

A negative mixed glass former effect (MGFE) in the Na(+) ion conductivity of glass has been found in 0.5Na2S + 0.5[xGeS2 + (1 - x)PS5/2] glasses where the Na(+) ion conductivity is significantly smaller for all of the ternary glasses than either of the binary end-member glasses. The minimum conductivity of ∼0.4 × 10(-6) (Ω cm)(-1) at 25 °C occurs for the x = 0.7 glass. Prior to this observation, the alkali ion conductivity of sulfide glasses at constant alkali concentration, but variable ratio of one glass former for another (x) ternary mixed glass former (MGF) glasses, has always produced a positive MGFE in the alkali ion conductivity; that is, the ternary glasses have always had higher ion conductivities that either of the end-member binary glasses. While the Na(+) ion conductivity exhibits a single global minimum value, the conductivity activation energy exhibits a bimodal double maximum at x ≈ 0.4 and x ≈ 0.7. The modified Christensen-Martin-Anderson-Stuart (CMAS) model of the activation energies reveals the origin of the negative MGFE to be due to an increase in the dielectric stiffness (a decrease in relative dielectric permittivity) of these glasses. When coupled with an increase in the average Na(+) ion jump distance and a slight increase in the mechanical stiffness of the glass, this causes the activation energy to go through maximum values and thereby produce the negative MGFE. The double maximum in the conductivity activation energy is coincident with double maximums in CMAS calculated strain, ΔES, and Coulombic, ΔEC, activation energies. In these ternary glasses, the increase in the dielectric stiffness of the glass arises from a negative deviation of the limiting high frequency dielectric permittivity as compared to the binary end-member glasses. While the CMAS calculated total activation energies ΔEact = ΔES + ΔEC are found to reproduce the overall shape of the composition dependence of the measured ΔEact values, they are consistently smaller than the measured values for all compositions x. The new concept of an effective Madelung constant for the Na(+) ions in glass is introduced, MD(Na(+)), to account for the difference. Calculated MD(Na(+)) values necessary to bring the CMAS and experimental ΔEact values into agreement are in excellent agreement with nominal values for typical oxide crystals containing Na(+). New MD simulations of oxide glasses were performed and were used to calculate MD(Na(+)) values for Na2O + SiO2 glasses for the first time and were found to agree quite well with the values for the sulfide glasses studied here. Insights from the current study have been used to predict and design new MGF systems that may lead to a positive MGFE in the ionic conductivity.

On the global minimum in a balanced circular packing problem

The paper considers balanced packing problem of a given family of circles into a larger circle of the minimal radius as a multiextremal nonlinear programming problem. We reduce the problem to unconstrained minimization problem of a nonsmooth function by means of nonsmooth penalty functions. We propose an efficient algorithm to search for local extrema and an algorithm for improvement of the lower bound of the global minimum value of the objective function. The algorithms employ nonsmooth optimization methods based on Shor’s r-algorithm. Computational results are given.

Intelligent PID Controller Tuning for Higher Order Process System

This paper demonstrates the implementation of PID controller tuning using evolutionary technique which is Genetic Algorithm (GA). The optimal PID control scheme is applied to higher order system. The execution of this evolutionary strategy is evaluated by setting the objective function as mean square error (MSE), Integral time absolute error (ITAE) and Integral absolute error (IAE) one at a time. This technique will determine the global minimum value of its objective function and hence gives the optimal value of the gain parameters. The PID controller performance analysis using Ziegler-Nichols Tuning methodology and Genetic Algorithm is also demonstrated in this paper.

A parametric linear relaxation algorithm for globally solving nonconvex quadratic programming

In this article, we present a parametric linear relaxation algorithm for globally solving the nonconvex quadratic programming (NQP). In this algorithm, a new parametric linearized technique is proposed for generating parametric linear relaxation programming (PLRP) of the NQP, which can be used to determine the lower bound of global minimum value of the NQP. To improve the convergent speed of the proposed algorithm, a pruning operation is employed to compress the investigated region. By subdividing subsequently the initial domain and solving subsequently a series of parametric linear relaxation programming problems over the subdivided domain, the proposed algorithm is convergent to the global minimum of the NQP. Finally, an engineering problem for the design of heat exchanger network and some test examples are used to verify the effectiveness of the proposed algorithm.

Solving the undirected feedback vertex set problem by local search

An undirected graph consists of a set of vertices and a set of undirected edges between vertices. Such a graph may contain an abundant number of cycles, in which case a feedback vertex set (FVS) is a set of vertices intersecting with each of these cycles. Constructing a FVS of cardinality approaching the global minimum value is an optimization problem in the nondeterministic polynomial-complete complexity class, and therefore it might be extremely difficult for some large graph instances. In this paper we develop a simulated annealing local search algorithm for the undirected FVS problem by adapting the heuristic procedure of Galinier et al. [P. Galinier, E. Lemamou, M.W. Bouzidi, J. Heuristics 19, 797 (2013)], which worked for the directed FVS problem. By defining an order for the vertices outside the FVS, we replace the global cycle constraints by a set of local vertex constraints on this order. Under these local constraints the cardinality of the focal FVS is then gradually reduced by the simulated annealing dynamical process. We test this heuristic algorithm on large instances of Erdös-Rényi random graph and regular random graph, and find that this algorithm is comparable in performance to the belief propagation-guided decimation algorithm.