Maximum Of Objective Function Research Articles

A New Linear Programming Approach for TDGCS Layout Problem

Currently, considering the layout effect, the linear programming method based on column generation is generally proposed to solve the large-scale TDGCS layout problem, but layout scheme which is obtained by this method is the need to get multiple layout, a large number of calculations and a lot of time. However, there must be a balance between the material utilization ratio and computing time in the actual production process. Therefore, in this paper, a new linear programming method, which is based on two aspects of the minimum and maximum of objective function about the layout problem, is proposed. Firstly, a preliminary layout is finished from the aspect of the minimum optimization, then, a precise layout based on the preliminary layout is achieved from the aspect of maximum optimization. Compared with the original algorithm, theoretically speaking, this method can significantly reduce the amount of calculation through the calculation process, guaranteeing the material utilization.

Development of optimization method for plate heat exchanger with undulation

The article deals with optimization of undulated heat transfer surface of plate heat exchanger. The goal of optimization is not only to increase effectiveness of heat transfer but also to reduce the pressure drop. A combined pattern of undulation which combines herringbone pattern and wavy pattern was optimized and best values of four parameters were found; angle of herringbone pattern, number, phase and amplitude of longitudinal waves of wavy pattern. The optimization procedure looked for maximum of objective function which was a linear combination of effectiveness and pressure drop. We used simple Monte Carlo method and the optimum was searched for four values of reference pressure drop. Four different optimization were run and we investigated the effect of various definition of objective function and parameters of undulation. It was found that during optimization of combined pattern, the herringbone pattern is more favoured than wavy pattern. It is caused by the fact that herringbone pattern was described by the only one free parameter, which was the angle of undulation, and therefore it is more likely to be found by a stochastic method. This assumption was confirmed when simple wavy pattern was optimized and higher values of objective function and effectiveness were found.

Practical Optimization Algorithm for Discrete Variables

In order to solve the optimization problems of discrete variable in mechanism design, beginning vertexes to meet all of performance restriction conditions can be given by the technician from upper boundary of design variables by means of man-machine interactive method. Objective function of each beginning vertex is calculated and arranged from small to large, the vertex of maximum and minimum of objective function are found. The difference between the vertex of minimum and maximum of objective function are calculated and new point is made up from the minimum point and the difference. The new point is used in stead of the vertex of the maximum objective function if the objective function of the new point is less than the maximum of beginning vertexes. The new composite figure is made up again and the new point is calculated until all design variables reach to under boundary. Then the vertex of minimum objective function is regarded to as the optimization point. This method is very fit for the optimization of discrete variables of low dimension and is higher calculation efficiency because the hominine brightness is combined with the high speed calculation ability.

Separation of N-alkyl phenothiazine sulfones by HPTLC using an optimum mobile phase

In high performance thin layer chromatography some form of optimization is necessary if complete separation of all components is required. The selection of mobile phase composition is one of the most important components of an optimization strategies. The aim of this paper is the separation of the N-alkyl phenothiazine sulfones by high performance thin layer chromatography using an optimum mobile phase system. The optimum composition of mobile phase (toluene–ethyl ether–chloroform, 30:50:20, v/v) are given by the maximum of objective function ( F obj=10.6110).

Sequential Optimization of Multimodal Discrete Function with Bounded Rate of Change

In this paper a search scheme for finding the maximum of a discrete objective function of several variables is proposed. The scheme is sequential and optimal in the sense that it determines the maximum with minimum number of measurements of the function. Unlike other sequential search techniques with this property the scheme places no condition on the number of possible maxima of the objective function. Instead it requires that some bounds on the rate of change of the function per each variable be known. The points at which measurements of the value of the objective function are to be taken are determined successively by maximization of an auxiliary function updated after each measurement. The algorithm is described in detail, and illustrated by two simple examples.