Usual Mathematical Programming Research Articles

New heuristics for the vertex coloring problem based on semidefinite programming

The Lovasz theta number Lovasz (IEEE Trans Inf Theory 25:1–7, 1979) is a well-known lower bound on the chromatic number of a graph \(G\), and \(\varPsi _K(G)\) is its impressive strengthening Gvozdenovic and Laurent (SIAM J Optim 19(2):592–615, 2008). The bound \(\varPsi _K(G)\) was introduced in very specific and abstract setting which is tough to translate into usual mathematical programming framework. In the first part of this paper we unify the motivations and approaches to both bounds and rewrite them in a very similar settings which are easy to understand and straightforward to implement. In the second part of the paper we provide explanations how to solve efficiently the resulting semidefinite programs and how to use optimal solutions to get good coloring heuristics. We propose two vertex coloring heuristics based on \(\varPsi _K(G)\) and present numerical results on medium sized graphs.

Optimization of the crushing characteristics of triangulated aluminum beverage cans

In this study, a cylindrical shell body of the aluminum cans is triangulated and optimized for being folded down easily and safely for recycling. The triangulated cylindrical shell is constructed by a family of triangular surfaces based on one set of helical strips and circles lying on a cylindrical side surface. The intersections of helical strips and circles are used as the vertexes of the triangular surfaces. By changing the helical angle of the strips, the number of the strips, and the number of the circles, various triangulated cylindrical shells with different crushing characteristics can be developed. On the basis of the numerical simulation, the minimization problem of the crushing force of the triangulated cylindrical shells is solved using the crashworthiness maximization technique for tubular structures that combines the techniques of design of experiment, response surface approximation as well as usual mathematical programming.

Crashworthiness optimisation of S-shape square tubes

During a car frontal crash, the front side member is expected to be folded progressively, so as to absorb more energy and to ensure enough passenger space. As the front member of a vehicle body, the crushing characteristics of an S-shape thin-walled box beam under an axial load has received crucial attention both experimentally and numerically. In this paper, the axial impact crushing behaviour of the S-shape square tube is studied by the finite element method, and effectiveness of stiffening at the curved parts and shape perturbation at two straight parts of tubes are discussed. Based on the numerical analyses, maximisation problem of the dynamic crushing energy absorption of S-shape square tubes is solved by using the crashworthiness maximisation technique for tubular structure which combines the techniques of the response surface approximation design-of-experiment as well as the usual mathematical programming.

Maximization Of The Impact Energy Absorption Of Stiffened And Unstiffened Square Tubes

The axial impact crushing behaviors of square tubes with and without stiffeners are studied by Finite Element method. Comparisons of mean axial crushing force between numerical estimations and theoretical predications as well as qualitative comparisons of folding patterns between numerical simulations and experimental observations are made and discussed. Based on the numerical analyses. maximization problems of dynamic crushing energy absorption of square tubes with and without stiffeners are solved respectively by using the crashworthiness maximization technique for tubular structures which combined the techniques of design-of-experiment, response surface approximation as well as usual mathematical programming. In addition, the capacities of crushing energy absorption of cylindrical tubes and square tubes with and without stiffeners are also compared.

A Study On The Crashworthiness Of S-shape Square Tubes

The axial impact crushing behavior of a S-shape square tube is studied by the finite element method, and effectiveness of stiffening at the curved parts and shape perturbation at two straight parts of tubes are discussed. Based on the numerical analyses, maximization problem of the dynamic crushing energy absorption of Sshape square tubes is solved by using the crashworthiness maximization technique for tubular structures which combines the techniques of response surface approximation, design-of-experiment as well as the usual mathematical programming.

Optimization of the Crushing Characteristic of Triangulated Cans.

The axial crushing behavior of a triangulated cylindrical shell constructed by one set of helical strips and circles lying on the surface, is simulated by the finite element method. This paper also discusses the affection to the crushing characteristic of the angle and the number of the helix as well as the number of the circles along the axial direction of the cylinder. Based on the numerical analyses, minimizing problems of the axial crushing force of triangulated cylindrical shells are solved by using the crashworthiness maximization technique for tubular structures which combined the techniques of design-of-experiment, response surface approximation as well as usual mathematical programming. Moreover, the behavior of the triangulated cylinders when subjected simultaneously to axial crushing and twisting forces is optimized.

Maximization of the crushing energy absorption of cylindrical shells

This paper concerns with the development of the crashworthiness maximization technique for tubular structures, and the application to the axial crushing problems of cylindrical tubes. In the program system presented in this study, an explicit finite element code, DYNA3D is adopted for simulating complicated crushing behavior of tubular structures. A series of aluminum cylindrical tubes are tested under axial impact condition for the experimental validation of the numerical solutions. Moreover, the response surface approximation technique is applied to construct an approximated design subproblem for optimization in the pre-assigned design space by using the technique of design-of-experiment. The approximated subproblem is then solved by the usual mathematical programming technique. These optimization processes are repeated until the given convergence conditions are satisfied.

Maximization of the Absorbing Energy for Dynamic Crushing of Thin-Walled Curved Beam.

The axial impact crushing behavior of a curved tube is studied by the finite element simulation, and effectiveness of stiffening at the curved parts and shape perturbation at two straight parts of tube are discussed. Based on the numerical analyses, maximization problem of dynamic crushing energy absorption of curved square tubes is solved by using the crashworthiness maximization technique for tubular structures which combined the techniques of design-of-experiment, response surface approximation as well as usual mathematical programming.

127 三角形平面化した空缶の圧潰特性の最適化

The axial crushing behavior of a triangulated cylindrical shell constructed by one set of helical strips and circles lying on the surface, is simulated by the finite element method. This paper also discusses the affection to the crushing characteristic of the angle and the number of the helix as well as the division along the axis direction of the cylinder. Based on the numerical analyses, minimum problem of the axial crushing force of triangulated cylindrical shells are solved by using the crashworthiness maximization technique for tubular structures which combined the techniques of design-of-experiment, response surface approximation as well as usual mathematical programming. Moreover, the behavior of the triangulated cylinders when subjected simultaneously to crushing and twisting forces is studied.

A Study on Maximization of Dynamic Crushing Energy Absorption of Square Tubes with and without Stiffener.

The axial impact crushing behavior of square tubes with and without stiffeners are studied by Finite Element method, and comparisons of mean axial crushing force between numerical solutions and theoretical prediction as well as qualitative comparisons of folding patterns between numerical simulations and experimental observations are made and discussed. Based on the numerical analyses, maximization problems of dynamic crushing energy absorption of square tubes with and without stiffeners, respectively, are solved using the crashworthiness maximization technique for tubular structures which combined the techniques of design-of-experiment, response surface approximation as well as usual mathematical programming. In addition, the energy absorbing capability of cylindrical tubes and square tubes with and without stiffeners are also compared.

A Study on Maximization of Dynamic Crushing Energy Absorption of Square Tubes with and without Stiffener.

The axial impact crushing behavior of square tubes with and without stiffeners are studied by Finite Element method, and comparisons of mean axial crushing force between numerical solutions and theoretical predications as well as qualitative comparisons of folding patterns between numerical simulations and experimental observations are made and discussed. Based on the numerical analyses, dynamic crushing energy absorption maximization problems of square tubes with and without stiffeners are respectively solved using the crashworthiness maximization technique for tubular structures which combined the techniques of design of experiment, response surface approximation as well as usual mathematical programming. In addition, the capacities of crushing energy absorbing of cylindrical tubes and square tubes with and without stiffeners are also compared.

Maximization of the crushing energy absorption of tubes

This paper concerns the development of crashworthiness maximization techniques for tubular structures, and the application to the axial crushing problem of cylindrical tubes as well as square tubes. In the program system presented in this study, an explicit finite element code, DYNA3D is adopted for simulating complicated crushing behaviour of tubular structures. The response surface approximation technique is applied to construct an approximated design subproblem in the preassigned design space by using the technique of design-of-experiment. The approximated subproblem is solved by the usual mathematical programming technique. These optimization processes are repeated until the given convergence conditions are satisfied. Moreover, a comparison of the crushing energy absorption between cylindrical tubes and square tubes is discussed.

A Study on Maximization of Dynamic Crushing Energy Absorption of Cylindrical Shell Structures.

The crushing behavior of cylindrical shells subjected to an axial impact force is studied by FEM, and a comparison between numerical results and theoretical predictions as well as a qualitative comparison between numerical estimates and experimental results are made and discussed. Moreover, a crashworthiness maximization technique for shell structures is developed and applied to the axial crushing problem of cylindrical shell. In the program system presented in this study, an explicit finite element code, DYNA3D is adopted for simulating complicate crushing behavior of shell structures. The response surface approximation technique is applied to construct an approximated design sub-problem in the preassigned design space by using the technique of design-of-experiment. The approximated sub-problem is solved by the usual mathematical programming technique. These optimization processes is repeated until the given convergence conditions will be satisfied.

A possibilistic linear program is equivalent to a stochastic linear program in a special case

In this paper, we discuss an equivalent condition between a possibilistic linear programming problem with a quadratic membership function and a stochastic linear programming problem with a multivariate normal distribution. First, the possibilistic linear programming problem is formulated as a usual mathematical programming problem based on maximizing the necessity measure. Next, the stochastic linear programming problem is formulated as a usual mathematical programming problem by introducing the flexible programming approach. Since these two formulated programming problems are similar in their forms, an equivalent condition between these problems is given. Lastly, the equivalence is examined from a geometric viewpoint.

On formalization of a general fuzzy mathematical problem

The problem considered in this paper concerns decision-making on the basis of information presented in a fuzzy form. It differs from the usual mathematical programming problems of maximizing a given function over a given set of alternatives mainly in that the values of such function are fuzzy and are represented by fuzzy sets. The question is how to choose alternatives from the given set which give in some sense “the best” fuzzy value of this function. The fuzzy-valued function in question may be thought of as a fuzzy utility function specifying fuzzy utility estimates to the alternatives, or as a performance function of a system with reaction to choices of alternatives (controls) allowing only fuzzy description. The values of this function have the form of fuzzy subsets of some universal set of estimates (or reactions) and a binary preference relation (generally fuzzy) is assumed to be specified in this set. In the paper this relation is extended from the elements of the universal set onto fuzzy subsets of this set. Some properties of this induced relation are studied. This relation is used to extract a fuzzy subset of nondominated alternatives and maximal elements of this subset are suggested as rational choices. It is shown that under some assumptions alternatives exist which are in fact unfuzzily dominated thus serving as unfuzzy solutions to a fuzzily formulated problem.

Maximization Of Crushing Energy Of CylindricalShells

This paper concerns about the development of crashworthiness maximization technique for shell structures, and the application to the axial crushing problem of cylinder. In the program system presented here, an implicit finite element code, DYNA3D, is adopted for simulating complicate crushing behavior of shell structures, and the response surface approximation technique is used to construct an approximated design subproblem in the preassigned design space based upon the technique of design-of-experiment. The approximated subproblem has been solved by the usual mathematical programming technique.