求线性二层规划∈-全局最优解的一种方法

本文研究了线性二层规划问题.利用下层问题的KKT最优性条件将其转化为一个具有互补约束的数学规划问题,提出了一种新的求解方法.该方法仅仅需要求解若干个双线性规划问题,便可以获得原问题的-全局最优解.最后,通过一个算例说明了所提出方法的可行性.

ε-最优解与相应的ε-有效解的关系

考虑多目标优化问题中ε-有效解存在的必要条件.主要讨论了多目标优化问题的三种纯量化方法,并确定了多目标优化问题的ε-有效解和三种纯量优化问题的ε-最优解的相应关系.

Research on a Class of Non-linear Programming Problems

A detailed study of some simple forms which have a given special structure have been solved, in this paper, we research the extension of this kind of special structure problems.

Layout problem of multi-component systems arising for improving maintainability

To improve the mainlainability design efficiency and quality, a layout optimization method for maintainability of multi-component systems was proposed. The impact of the component layout design on system maintainability was analyzed, and the layout problem for maintainability was presented. It was formulated as an optimization problem, where maintainability, layout space and distance requirement were formulated as objective functions. A multi-objective particle swarm optimization algorithm, in which the constrained-domination relationship and the update strategy of the global best were simply modified, was then used to obtain Pareto optimal solutions for the maintainability layout design problem. Finally, application in oxygen generation system of a spacecraft was studied in detail to illustrate the effectiveness and usefulness of the proposed method. The results show that the concurrent maintainability design can be carried out during the layout design process by solving the layout optimization problem for maintainability.

Improvement of Lagrangian relaxation performance for open pit mines constrained long-term production scheduling problem

Constrained long-term production scheduling problem(CLTPSP) of open pit mines has been extensively studied in the past few decades due to its wide application in mining projects and the computational challenges it poses become an NP-hard problem.This problem has major practical significance because the effectiveness of the schedules obtained has strong economical impact for any mining project.Despite of the rapid theoretical and technical advances in this field,heuristics is still the only viable approach for large scale industrial applications.This work presents an approach combining genetic algorithms(GAs) and Lagrangian relaxation(LR) to optimally determine the CLTPSP of open pit mines.GAs are stochastic,parallel search algorithms based on the natural selection and the process of evolution.LR method is known for handling large-scale separable problems; however,the convergence to the optimal solution can be slow.The proposed Lagrangian relaxation and genetic algorithms(LR-GAs) combines genetic algorithms into Lagrangian relaxation method to update the Lagrangian multipliers.This approach leads to improve the performance of Lagrangian relaxation method in solving CLTPSP.Numerical results demonstrate that the LR method using GAs to improve its performance speeding up the convergence.Subsequently,highly near-optimal solution to the CLTPSP can be achieved by the LR-GAs.

Multi-objective optimization for draft scheduling of hot strip mill

A multi-objective optimization model for draft scheduling of hot strip mill was presented, rolling power minimizing, rolling force ratio distribution and good strip shape as the objective functions. A multi-objective differential evolution algorithm based on decomposition （MODE/D）. The two-objective and three-objective optimization experiments were performed respectively to demonstrate the optimal solutions of trade-off. The simulation results show that MODE/D can obtain a good Pareto-optimal front, which suggests a series of alternative solutions to draft scheduling. The extreme Pareto solutions are found feasible and the centres of the Pareto fronts give a good compromise. The conflict exists between each two ones of three objectives. The final optimal solution is selected from the Pareto-optimal front by the importance of objectives, and it can achieve a better performance in all objective dimensions than the empirical solutions. Finally, the practical application cases confirm the feasibility of the multi-objective approach, and the optimal solutions can gain a better rolling stability than the empirical solutions, and strip flatness decreases from （0± 63） IU to （0±45） IU in industrial production.

Hierarchical multicast with inter-layer random network coding

To maximize the aggregate throughput achieved in heterogeneous networks, this paper investigates inter-session network coding for the distribution of layered source data. We define inter-layer hierarchical random linear network codes （IHRLNC）, which not only take the flexibility of intersession network coding for layer mixing but also consider the strict priority inherent in the layered source data. Furthermore, we propose the inter-layer hierarchical multicast （IHM）, which performs IHRLNC in the network such that each sink can recover some source layers according to its individu- al capacity. To determine the optimal type of IHRLNC that should be performed on each edge in IHM, we formulate an optimization problem based on 0-1 integer linear programming, and propose a heuristic approach to approximate the optimal solution in polynomial time. Simulation results show that the proposed IHM can achieve throughput gains over the layered muhicast schemes.

Symmetry Breaking for Black-Scholes Equations

Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a. result, symmetry reductions and corresponding solutions for the resulting equations are obtained.

Study on Hydrocracking of VGO Derived from Kazakhstan-Russian Mixed Crude

This article investigates the influence of the property of VGO derived from the Kazakhstan- Russian mixed crude on the hydrocracking catalyst. The influence of reaction temperature, reaction pressure, space velocity and hydrogen/oil ratio on the distribution and quality of products was analyzed with the optimal process regime determined, when the VGO was hydrocracked in the presence of the FC-16 catalyst.

Multi-Period Model of Portfolio Investment and Adjustment Based on Hybrid Genetic Algorithm

This paper proposes a multi-period portfolio investment model with class constraints, transaction cost, and indivisible securities. When an investor joins the securities market for the first time, he should decide on portfolio investment based on the practical conditions of securities market. In addition, investors should adjust the portfolio according to market changes, changing or not changing the category of risky securities. Markowitz meanvariance approach is applied to the multi-period portfolio selection problems. Because the sub-models are optimal mixed integer program, whose objective function is not unimodal and feasible set is with a particular structure, traditional optimization method usually fails to find a globally optimal solution. So this paper employs the hybrid genetic algorithm to solve the problem. Investment policies that accord with finance market and are easy to operate for investors are put forward with an illustration of application.

Optimization of Enzyme-assisted Extraction Technology for Tartary Buckwheat Shell Procyanidins with Response Surface Methodology

This study was conducted to investigate the effects of cellulase dosage, enzymolysis time, pH and enzymolysis temperature on procyanidin extraction rate by single factor experiment, with tartary buckwheat shell as an experimental material.Main process parameters were optimized to obtain a regression model by response surface methodology. The results of variance analysis indicated that the regression model reflected the relationship between buckwheat shell procyanidin extraction rate with enzyme dosage, enzymolysis time, pH and enzymolysis temperature; and the optimal process parameters were enzyme dosage of 6.5 mg/g, enzymolysis time of 1.5 h, pH at 4.7 and enzymolysis temperature at 46 ℃. Three parallel experiments were conducted under these process parameters. In practice, the highest procyanidin extraction rate was 6.78 g/100 g. The relative error between the predicted value of regression model and the actual value was 1.3%. The regression equation fitted the real situation better.

Signal pre-processing method and application design of edge nodes for distributed electromechanical system

A signal pre-processing method based on optimal variational mode decomposition(OVMD)is proposed to improve the efficiency and accuracy of local data filtering and analysis of edge nodes in distributed electromechanical systems.Firstly,the singular points of original signals are eliminated effectively by using the first-order difference method.Then the OVMD method is applied for signal modal decomposition.Furthermore,correlation analysis is conducted to determine the degree of correlation between each mode and the original signal,so as to accurately separate the real operating signal from noise signal.On the basis of theoretical analysis and simulation,an edge node pre-processing system for distributed electromechanical system is designed.Finally,by virtue of the signal-to-noise ratio(SNR)and root-mean-square error(RMSE)indicators,the signal pre-processing effect is evaluated.The experimental results show that the OVMD-based edge node pre-processing system can extract signals with different characteristics and improve the SNR of reconstructed signals.Due to its high fidelity and reliability,this system can also provide data quality assurance for subsequent system health monitoring and fault diagnosis.

On ε-Constraint Based Methods for the Generation of Pareto Frontiers

Over the years, a number of methods have been proposed for the generation of uniform and globally optimal Pareto frontiers in multi-objective optimization problems. This has been the case irrespective of the problem definition. The most commonly applied methods are the normal constraint method and the normal boundary intersection method. The former suffers from the deficiency of an uneven Pareto set distribution in the case of vertical （or horizontal） sections in the Pareto frontier, whereas the latter suffers from a sparsely populated Pareto frontier when the optimization problem is numerically demanding （ill-conditioned）. The method proposed in this paper, coupled with a simple Pareto filter, addresses these two deficiencies to generate a uniform, globally optimal, well-populated Pareto frontier for any feasible bi-objective optimization problem. A number of examples are provided to demonstrate the performance of the algorithm.

L1 norm optimal solution match processing in the wavelet domain

Greater attention has been paid to vintage-merge processing of seismic data and extracting more valuable information by the geophysicist. A match filter is used within many important areas such as splicing seismic data, matching seismic data with different ages and sources, 4-D seismic monitoring, and so on. The traditional match filtering method is subject to many restrictions and is usually difficult to overcome the impact of noise. Based on the traditional match filter, we propose the wavelet domain L1 norm optimal matching filter. In this paper, two different types of seismic data are decomposed to the wavelet domain, different detailed effective information is extracted for Ll-norm optimal matching, and ideal results are achieved. Based on the model test, we find that the L1 norm optimal matching filter attenuates the noise and the waveform, amplitude, and phase coherence of result signals are better than the conventional method. The field data test shows that, with our method, the seismic events in the filter results have better continuity which achieves the high precision seismic match requirements.

A Modified Algorithm for Nonliear Integer Programming

Based on the analysis to the random sear ch algorithm of LUUS, a modified random directed integer search algorithm (MRDI SA) is given for first time. And a practical example is given to show that the adva ntage of this kind of algorithm is the reliability can’t be infuenced by the ini tial value X (0) and the start search domain R (0) . Besides, i t can be applied to solve the higher dimensional constrained nonlinear integer p rogramming problem.

A Fuzzy Satisfactory Method for Decentralized Bi Level Linear Programming

Based on the theory of fuzzy decision making, a two phrase approach is proposed for the decentralized bi level linear programming problem(DBLPP). The approach considers the conflicts between the upper and lower levels decision makers (DMs), and among the lower level DMs themselves, a satisfactory solution is got with the non conflict matrix and decision power distribution. Compared with the other methods that have ever been proposed, the solution process is more fit to a kind of real decision making processes.

The optimal fractional Gabor transform based on the adaptive window function and its application

We designed the window function of the optimal Gabor transform based on the time-frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time-frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time-frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.

A Hybrid Improved Genetic Algorithm and Its Application in Dynamic Optimization Problems of Chemical Processes

The solutions of dynamic optimization problems are usually very difficult due to their highly nonlinear and multidimensional nature. 13enetic algorithm （GA） has been proved to be a teasibte method when the gradient is difficult to calculate. Its advantage is that the control profiles at all time stages are optimized simultaneously, but its convergence is very slow in the later period of evolution and it is easily trapped in the local optimum. In this study, a hybrid improved genetic algorithm （HIGA） for solving dynamic optimization problems is proposed to overcome these defects. Simplex method （SM） is used to perform the local search in the neighborhood of the optimal solution. By using SM, the ideal searching direction of global optimal solution could be found as soon as possible and the convergence speed of the algorithm is improved. The hybrid algorithm presents some improvements, such as protecting the best individual, accepting immigrations, as well as employing adaptive crossover and Ganssian mutation operators. The efficiency of the proposed algorithm is demonstrated by solving several dynamic optimization problems. At last, HIGA is applied to the optimal production of secreted protein in a fed batch reactor and the optimal feed-rate found by HIGA is effective and relatively stable.

Optimization of air quantity regulation in mine ventilation networks using the improved differential evolution algorithm and critical path method

In mine ventilation networks, the reasonable airflow distribution is very important for the production safety and economy. Three basic problems of the natural, full-controlled and semi-controlled splitting were reviewed in the paper. Aiming at the high difficulty semi-controlled splitting problem, the general nonlinear multi-objectives optimization mathematical model with constraints was established based on the theory of mine ventilation networks. A new algorithm, which combined the improved differential evaluation and the critical path method （CPM） based on the multivariable separate solution strategy, was put forward to search for the global optimal solution more efficiently. In each step of evolution, the feasible solutions of air quantity distribution are firstly produced by the improved differential evolu- tion algorithm, and then the optimal solutions of regulator pressure drop are obtained by the CPM. Through finite steps iterations, the optimal solution can be given. In this new algorithm, the population of feasible solutions were sorted and grouped for enhancing the global search ability and the individuals in general group were randomly initialized for keeping diversity. Meanwhile, the individual neighbor- hood in the fine group which may be closely to the optimal solutions were searched locally and slightly for achieving a balance between global searching and local searching, thus improving the convergence rate. The computer program was developed based on this method. Finally, the two ventilation networks with single-fan and multi-fans were solved. The results show that this algorithm has advantages of high effectiveness, fast convergence, good robustness and flexibility. This computer program could be used to solve lar^e-scale ~eneralized ventilation networks o^timization problem in the future.

Design of Underwater Robot Lines Based on a Hybrid Automatic Optimization Strategy

In this paper, a hybrid automatic optimization strategy is proposed for the design of underwater robot lines. Isight is introduced as an integration platform. The construction of this platform is based on the user programming and several commercial software including UG6.0, GAMBIT2.4.6 and FLUENT12.0. An intelligent parameter optimization method, the particle swarm optimization, is incorporated into the platform. To verify the strategy proposed, a simulation is conducted on the underwater robot model 5470, which originates from the DTRC SUBOFF project. With the automatic optimization platform, the minimal resistance is taken as the optimization goal;the wet surface area as the constraint condition; the length of the fore-body, maximum body radius and after-body＇s minimum radius as the design variables. With the CFD calculation, the RANS equations and the standard turbulence model are used for direct numerical simulation. By analyses of the simulation results, it is concluded that the platform is of high efficiency and feasibility. Through the platform, a variety of schemes for the design of the lines are generated and the optimal solution is achieved. The combination of the intelligent optimization algorithm and the numerical simulation ensures a global optimal solution and improves the efficiency of the searching solutions.