On the effectiveness of sequential linear programming for the pooling problem

The use of optimization in a simulation-based design of automotive, aerospace and consumer products has become a common trend today. Designers are faced with the continuous challenge of reducing manufacturing costs and design cycle times while improving the systems performance and reliability. In practical design, sequential linear programming (SLP) is very popular because of its inherent simplicity and easy availability. However, the inherent conceptual simplicity makes the SLP techniques not globally convergent. This research presents a new algorithm that uses a linearization error and an interior point trust-region method in SLP to truss structures that is both considered sizing and configuration problems. The algorithm may be suitable for large optimization problems where time is a constraint and the optimization may be stopped before convergence is achieved. Results of application studies are presented, illustrating the applicability of the proposed algorithm.

Numerical implementations of optimization algorithms often use parameters whose values are not strictly determined by the derivation of the algorithm, but must fall in some appropriate range of values. This work describes how fuzzy logic can be used to “control” such parameters to improve algorithm performance. This concept is shown with the use of sequential linear programming (SLP) due to its simplicity in implementation. The algorithm presented in this paper implements heuristics to improve the behavior of SLP based on current iterate values of design constraints and changes in search direction. Fuzzy logic is used to implement the heuristics in a form similar to what a human observer would do. An efficient algorithm, known as the infeasible primal-dual path-following interior-point method, is used for solving the sequence of LP problems. Four numerical examples are presented to show that the proposed SLP algorithm consistently performs better than the standard SLP algorithm.

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

This paper presents a sequential linear programming approach for the determination of time-optimal controller for nonlinear systems. The sequential linear programming solution is used to update the control profile so as to satisfy the terminal conditions for an assumed maneuver time. A univariant minimization approach which brackets the optimal value of the maneuver time, such as the bisection algorithm is used in an outer loop to converge to the minimum time. The proposed technique is illustrated on two benchmark problems: the attitude control of a spacecraft and the minimum time control of a robot.

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.

We investigate the problem of clock network sizing subject to general skew constraints. A novel approach based on sequential linear programming is presented. The original nonlinear programming problem is transformed into a sequence of linear programs by taking the first-order Taylor's expansion of clock path delay with respect to buffer and/or wire widths. For each linear program, the sensitivities of clock path delay, with respect to buffer and/or wire widths, are efficiently updated by applying time-domain analysis to the clock network in a divide-and-conquer fashion. Our technique can take into account power supply and process variations. We demonstrate experimentally that the proposed technique is not only capable of optimizing effectively the skew and area of clock network, but also of providing more accurate delay and skew results compared to the traditional approaches.

A diaphragm spring is an important component of a clutch assembly, characteristics of which depends largely on that of a diaphragm spring. A diaphragm spring is subject to high stress concentration in driving condition, which frequently causes cracks and fracture around finger area. In this paper, behavior of a diaphragm spring is analysed by finite element method to calculate sensitivity of design parameters, which is used to perform optimal design of diaphragm spring shape. As an object function, hoop stresses are taken and minimized to improve durability. Characteristics of the diaphragm is used as equality constraint to maintain the original design purpose and sequential linear programming(SLP) is utilized as an optimization tool. With optimized design, it is verified that concentrated stress is decreased maintaining release load characteristic.

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.

Analytical target cascading (ATC) is a multidisciplinary design optimization method for multilevel hierarchical systems. To improve computational efficiency, especially for problems under uncertainty or with strong monotonicity, a sequential linear programming (SLP) algorithm was previously employed as an alternate coordination strategy to solve ATC and probabilistic ATC problems. The SLP implementation utilizes L∞ norms to maintain the linearity of SLP subsequences. This note offers a proof that there exists a set of weights such that the ATC algorithm converges when L∞ norms are used. Examples are also provided to illustrate the effectiveness of using L∞ norms as a penalty function to maintain the formulation linear and differentiable. The examples show that the proposed method provides more robust results for linearized ATC problems due to the robustness of the linear programming solver.

Upper bound sequential linear programming mesh adaptation scheme for collapse analysis of masonry vaults

A discontinuous quasi-upper bound limit analysis approach with sequential linear programming mesh adaptation

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.

Production planning is an important thing in company management. Every company aims to seek maximum profit in its business activities, so it must be able to utilize its resources as optimally as possible. This study was conducted to determine whether or not any production planning that has been implemented at Istana Roti Hilyah Bakery is optimal. This research aimed to maximize revenue and profit, minimize production costs and raw material usage and optimize production quantities using the sequential linear goal programming method and the simplex modification method with the assistance of LINGO software. Based on the study's results, the revenue increased by IDR 60,000, and the profit increased by IDR 66,679. The minimization value of production costs decreased by IDR 6,679, with the production amount of White Bread as many as 60 pcs, Almond Crumble Bread as many as 45 pcs, Chocolate Crumble Bread as many as 50 pcs, Wheat Bran Bread as many as 55 pcs, Sweet Comb Bread as many as 82 pcs and Jam Comb Bread as many as 84 pcs.

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.

An optimization process can be viewed as a closed-loop control system. Traditional “controllers”, the numerical optimization algorithms, are usually “crisply” designed for well defined mathematical models. However, when applied to engineering design optimization problems in which function evaluations can be expensive and imprecise, very often the crisp algorithms will become impractical or will not converge. A common strategy for designers is to monitor the optimization process and keep “tuning” the process in an interactive manner, using their judgment on the information obtained from previous iterations, and their knowledge of the problem. This paper presents how the heuristics of this human supervision can be modeled into the optimization algorithms using fuzzy set theory. A fuzzy version of sequential linear programming is used to demonstrate this idea. Fuzzy rules, which describe the human supervision during the optimization process, are combined with the numerical rules of the original algorithm to refine the output of each iteration. Several design optimization problems are used to show the feasibility and practicality of this approach.