An interactive method for multiple-objective mathematical programming problems

An interactive method is developed for solving the general nonlinear multiple objective mathematical programming problems. The method asks the decision maker to provide partial information (local tradeoff ratios) about his utility (preference) function at each iteration. Using the information, the method generates an efficient solution and presents it to the decision maker. In so doing, the best compromise solution is sought in a finite number of iterations. This method differs from the existing feasible direction methods in that (i) it allows the decision maker to consider only efficient solutions throughout, (ii) the requirement of line search is optional, and (iii) it solves the problems with linear objective functions and linear utility function in one iteration. Using various problems selected from the literature, five line search variations of the method are tested and compared to one another. The nonexisting decision maker is simulated using three different recognition levels, and their impact on the method is also investigated.     

Quantum cutting in Gd2SiO5: Eu3+ by VUV excitation

The emission and excitation spectra of Gd2SiO5: Eu3+ were investigated using the VUVbeam line of the Beijing Synchrotron Radiation Facility (BSRF). The experimental results werediscussed in the frame of visible quantum cutting process involved in Gd3+-Eu3+ system. Upon di-rect excitation into the 6GJ states of Gd3+, two visible photon emissions from Eu3+ were observed.Cursory evaluation proved that Gd2SiO5: Eu3+ is an efficient visible quantum cutter.     

Accelerating column generation for variable sized bin-packing problems

In this paper, we study different strategies to stabilize and accelerate the column generation method, when it is applied specifically to the variable sized bin-packing problem, or to its cutting stock counterpart, the multiple length cutting stock problem. Many of the algorithms for these problems discussed in the literature rely on column generation, processes that are known to converge slowly due to primal degeneracy and the excessive oscillations of the dual variables. In the sequel, we introduce new dual-optimal inequalities, and explore the principle of model aggregation as an alternative way of controlling the progress of the dual variables. Two algorithms based on aggregation are proposed. The first one relies on a row aggregated LP, while the second one solves iteratively sequences of doubly aggregated models. Working with these approximations, in the various stages of an iterative solution process, has proven to be an effective way of achieving faster convergence.     

Laser cutting of thick ceramic tile

This paper details developments in the CO₂ laser cutting of thick ceramic tiles, that is thicknesses of 8.5 mm and 9.2 mm. These tiles were cut at a combination of different cutting speeds to determine the necessary cutting parameters for various tile geometries. Different cutting modes were used in conjunction with different cutting speeds to investigate cut quality after laser processing. The work also looked into the effects on cutting through using various shield gases. Multipass cutting and underwater cutting were performed to examine their effects on thermal load during processing.     

Processing of concretes with a high power CO2 laser

Laser material processing, being a non-contact process, minimizes many of the complexities involved in the decontamination and decommissioning of nuclear facilities. A high power laser beam incident on a concrete surface can produce spalling, glazing or vaporization, depending upon the laser power density and scan speed. This paper presents effect of various laser processing parameters on the efficiency of material removal by surface spalling and glazing. The size of laser beam at constant fluence or energy density had significantly different effect on the spalling process. In thick concrete block cutting the flow or removal of molten material limits the cutting depth. By employing repeated laser glazing followed by mechanical scrubbing process cutting of 150 mm thick concrete block was carried out. Gravitation force was utilized for molten materials to flow out while drilling holes on vertical concrete walls. The dependence of the incident laser beam angle on drilling time was experimentally studied.     

截断切割问题的参数规划模型

对一个截断切割问题,本文给出了一个参数网络规划模型,总结了[3]中的解法,并给出了一个实例.     

On Poljak's improved subgradient method

Poljak has suggested an improved subgradient method and provided a lower bound on the improvement of the Euclidean distance to an optimal solution. In this paper, we provide a stronger lower bound and show that the direction of movement in this method forms a more acute angle with the direction toward the set of optimal solutions than that in the subgradient method.Most of this research has been performed while the first author was visiting the Decision and Information Systems Department, College of Business, Arizona State University, Tempe, Arizona.     

Mixed-integer bilinear programming problems

This paper addresses a class of problems called mixed-integer bilinear programming problems. These problems are identical to the well known bilinear programming problems with the exception that one set of variables is restricted to be binary valued, and they arise in various production, location—allocation, and distribution application contexts. We first identify some special cases of this problem which are relatively more readily solvable, even though their continuous relaxations are still nonconvex. For the more general case, we employ a linearization technique and design a composite Lagrangian relaxation-implicit enumeration-cutting plane algorithm. Extensive computational experience is provided to test the efficacy of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm.     

Cutting by a high power laser at a long distance without an assist gas for dismantling

As the applications of laser processing progress, new fields of use are being investigated, including dismantling with power lasers. To fulfil our dismantling requirements we propose a new laser method that we have called the laser dismantling (LD) process. This cutting method uses a high-power laser at a long distance, without an assist gas, and with a focal length of the system of 1 m to 10 m. Precision and accuracy in the process are not the same as for laser cutting for production and assembly. The first application of the laser dismantling process, on which we demonstrate our method, is the dismantling of obsolete nuclear plants with remote controlled, or automatic, robots in irradiated environments. For our demonstrator, the beam from a Nd:YAG laser was focused by a multimode optical fibre. The objectives of this paper are: to discuss the criteria for determining the theoretical feasibility of LD; to discuss issues related to future industrial implementation by introducing the process's basic principles; and to compare LD with classical laser processing, which differs not only in the consideration of cutting quality and speed, but also in the cutting irregularities that could be accepted.     

Lp-based combinatorial problem solving

A tutorial outline of the polyhedral theory that underlies linear programming (LP)-based combinatorial problem solving is given. Design aspects of a combinatorial problem solver are discussed in general terms. Three computational studies in combinatorial problem solving using the polyhedral theory developed in the past fifteen years are surveyed: one addresses the symmetric traveling salesman problem, another the optimal triangulation of input/output matrices, and the third the optimization of large-scale zero-one linear programming problems.