Application of Sequential Linear Goal Programming Method and Modified Simplex Method for Production Planning Optimization

The nonlinear magnetic properties of an iron core should be considered when topology optimization (TO) is applied to a realistic problem. However, a scheme for introduction of the magnetic nonlinearity to material-density-based TO has not been rigorously established. In this paper, TO by using material density with magnetic nonlinearity is proposed. The numerical instability of the sequential linear programming method is a well-known topic. The stabilized sequential linear programming method, which realizes the stabilized convergence characteristics of an objective function, is proposed and investigated in the 3-D design problem of a magnetic circuit.

This article deals with the optimization of energy resource management of industrial districts, with the aim of minimizing customer energy expenses. A model of the district is employed, whose optimization gives rise to a nonlinear constrained optimization problem. Here the focus is on its numerical solution. Two different methods are considered: a sequential linear programming method and a particle swarm optimization method. Efficient implementations of both approaches are devised and the results of the tests performed on several energetic districts are reported, including a real case study.

Zebrafish serves as a model organism in morphogenesis studies in cell biology. One of the main difficulties of modeling a specific morphogenetic process come from the proper identification of its key features. To study the influence of geometric constraint in morphogenesis, here this article models the notochord as hard spheres assemble in an elliptical cylinder and optimize the packing density. This article implements linear approximation on the hard sphere constraints and find the optimal packing configuration by the sequential linear programming (SLP) method. During the process, this article modifies the SLP scheme into expanding the spheres in a fixed cylindrical confinement. This article finds the staircase and similar structures becomes predominant as increasing the ellipticity of the confinement. Our study deepens the understanding of the notochord morphogenesis, and also provides methodological guidance on related modeling studies involving geometric constraints.

Swarm algorithms have been successfully applied to obtain global optimal solutions for complex problems such as multi-peak problems. However these algorithms have not been applied to complicated structural and mechanical optimization problems since local optimization c apability is still inferior to general numerical optimization methods. This paper discusses new swarm metaphors that incorporate design sensitivities concerning objective and constraint functions and are applicable to structural and mechanical design optim ization problems. Single - and multiobjective optimization techniques using swarm algorithms are combined with a sequential linear programming (SLP) method. In the proposed techniques, swarm optimization algorithms and SLP are conducted simultaneously. Fina lly, truss structure design optimization problems are solved by the proposed hybrid method to verify the optimization efficiency.

This study investigates the optimal power flow (OPF) problem for distribution networks with the integration of distributed generation (DG). By considering the objectives of minimal line loss, minimal voltage deviation and maximum DG active power output, the proposed OPF formulation is a multi‐object optimisation problem. Through normalisation of each objective function, the multi‐objective optimisation is transformed to single‐objective optimisation. To solve such a non‐convex problem, the trust‐region sequential quadratic programming (TRSQP) method is proposed, which iteratively approximates the OPF by a quadratic programming with the trust‐region guidance. The TRSQP utilises the sensitivity analysis to approximate all the constraints with linear ones, which will reduce the optimisation scale. Active set method is utilised in TRSQP to solve quadratic programming sub‐problem. Numerical tests on IEEE 33‐, PG&E 69‐ and actual 292‐, 588‐, 1180‐bus systems show the applicability of the proposed method, and comparisons with the primal–dual interior point method and sequential linear programming method are provided. The initialisation and convergence condition of the proposed method are also discussed. The computational result indicates that the proposed algorithm for DG control optimisation in distribution system is feasible and effective.

世の中には化学プラントや製鉄プラント等のように複数のサブシステムからなる大規模システムが数多く存在する。このようなシステムの最適運用は多くの制約や目標を持つ多変数の問題となるため、一般に数理計画法によって定式化されることが多い。ここでは、複雑な大規模システムの例として閉鎖生態系生命維持システム(CELSS)を取り上げ、今回開発したmオペレータを導入することで、従来の逐次ファジィ線形計画法がより強力な方法となり得ることが判明したので報告する。

Optimal design of machine components using notch correction and plasticity models

In this paper, a method of optimizing the shape and the stiffness distribution of a thin-walled beam structure is presented. The thin-walled beam can be analyzed by a finite element method based on the beam theory considering shear warping deformation. The objective for the optimization of shape and stiffness distribution is to minimize the compliance of the structure under the condition of a volume constraint. The size ratio of each cross-section and thickness of membrane plates are selected as the design variables. The optimum design problem is solved by sequential linear programming method. By a fundamental example of 2D cantilever beam, the validity of present method is shown. For the application of present method, highrise building models are analyzed as a thin-walled beam with equivalent strain energy. And the applicability of present method for the structural design or design planning of highrise building is investigated.

The paper deals with homologous topology optimization of structures undergoing large deformations. The objective function is defined so that the load-displacement curve follows the prescribed trajectry, which shows a typical snap-through buckling. The geometrically non-linear behavior of the structures is modeled using the total-Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson iterative scheme. In order to escape from the singularity at critical points, the displacement control is utilized. The sensitivities of the objective functions are found with the adjoint method and the optimization problem is solved using the sequential linear programming method. Two algorithms are proposed to obtain homologous deformation. Several numerical examples are demonstrated to validate the present optimization method.

The fundamental frequencies of fiber-reinforced laminated curved panels with a given material system are maximized with respect to fiber orientations by using a sequential linear programming method together with a simple move-limit strategy. Significant influence of the panel thickness, curvature, aspect ratio, cutout and end condition on the optimal fundamental frequencies and the associated optimal fiber orientations of laminated curved panels has been shown through this investigation.

Adhesive bonding has been widely used to join or repair metallic and composite structural components to achieve or restore their designated structural stiffness and strengths. However, current analysis methods and empirical databases for composite bonded patch repairs or joints are limited to flat structures, and there exists a very limited knowledge on the effect of curvature on the performance and durability of composite bonded joints and repairs. Recently, a novel finite element formulation was presented for developing adhesive elements for conducting 2.5‐D simplified stress analysis of bonded repairs to curved structures. This paper presents the work on optimal shape design of a bonded curved composite patch using the newly developed adhesive element. The Sequential Linear Programming (SLP) method is employed as the optimization algorithm in conjunction with a fully implemented mesh generation algorithm into which new features have been incorporated. The objective of shape optimization is to minimize the maximum stress in the entire adhesive layer to ensure that the bonded patch effectively works together with the parent structure in service. Several different objective functions, related to possible failure mechanisms of the adhesive layer, are proposed to optimize the shape of a bonded patch. Copyright © 2003 John Wiley & Sons, Ltd.

This paper presents structural topology optimization applied to the coupled magneto-structural problem. The design goals are to minimize mechanical compliance and to maximize total magnetic force. To calculate the compliance and magnetic force, coupled magneto-structural analysis is performed using the finite-element method. From the solution of a magnetostatic analysis, distribution of the magnetic body force is obtained using the virtual air gap scheme. The structural analysis from the calculated force distribution then provides the mechanical compliance. The design sensitivity analysis for the optimization is performed using the adjoint method, and the derived sensitivity is verified by comparing it with the finite difference sensitivity. The optimization problem is formulated and solved using the sequential linear programming (SLP) method. To show the validity of the proposed analysis and optimization approach, design of the solenoid actuator is presented.

Omah Jenang is one of the industries engaged in the production of traditional snacks. Currently Omah Jenang does not yet have guidelines for realizing the formation of the composition of production quantities correctly based on calculations that still use forecasting methods. Therefore Omah Jenang often experiences difficulties in providing raw materials and determining maximum profits. The purpose of this study was to de-termine the optimum yield of profits at Omah Jenang by using the simplex method linear program with the help of Lindo Software. The data used is food production data at the Omah Jenang Home Industry in 2022. The method used in this study is the Linear Pro-gramming simplex method and the Lindo Software application. The results of optimization calculations using the linear programming method and the help of Lindo Software are that the maximum profit in a month is IDR 20,000,000 in producing 800 packages of madumongso. Based on the calculation results it can be concluded that the benefits obtained by using the simplex method with the help of Lindo Software can be obtained maximum results.

<p>CV. Baja Utama Landasan Ulin is a business entity that manufactures various products using the basic ingredients of iron. In the management of raw materials for the production of common regulatory process raw materials into sections for further processing. This setting is often done manually without doing careful planning, so that at the end of each production process there are many remaining pieces of the raw materials that should be used in production. In addition to the determination of the production is necessary to reference how the product should be made for each type of existing products. This is often an important factor that pushed for the optimization of production planning in determining the number of products for each type of product and raw material consumption.Linear Programming is one of the methods used in production planning to regulate the use of raw materials is limited. Simplex method is part of the linear programming method that can be used in the production planning system implementation. Simplex method identifies an initial basic solution and then move systematically to other basic solution that has the potential to improve the value of the objective function.The calculation result of production planning using the simplex method can be used as a reference in the decision making production planning. By building an application using the simplex method can assist in the calculation of production peencanaan more efficiently and effectively. Accuracy testing system constructed show significant results with great value reached 94% level of accuracy.<br />Keywords: simplex, production planning, the maximum gain, linear programming</p>

Move limits definition in structural optimization with sequential linear programming. Part II: Numerical examples