Nonlinear programming

About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.

Trust Region Augmented Lagrangian Methods for Sequential Response Surface Approximation and Optimization

Abstract: A common engineering practice is the use of approximation models in place of expensive computer simulations to drive a multidisciplinary design process based on nonlinear programming techniques. The use of approximation strategies is designed to reduce the number of detailed, costly computer simulations required during optimization while maintaining the pertinent features of the design problem. To date the primary focus of most approximate optimization strategies is that application of the method should lead to improved designs. This is a laudable attribute and certainly relevant for practicing designers. However to date few researchers have focused on the development of approximate optimization strategies that are assured of converging to a solution of the original problem. Recent works based on trust region model management strategies have shown promise in managing convergence in unconstrained approximate minimization. In this research we extend these well established notions from the literature on trust-region methods to manage the convergence of the more general approximate optimization problem where equality, inequality and variable bound constraints are present. The primary concern addressed in this study is how to manage the interaction between the optimization and the fidelity of the approximation models to ensure that the process converges to a solution of the original constrained design problem. Using a trust-region model management strategy, coupled with an augmented Lagrangian approach for constrained approximate optimization, one can show that the optimization process converges to a solution of the original problem. In this research an approximate optimization strategy is developed in which a cumulative response surface approximation of the augmented Lagrangian is sequentially optimized subject to a trust region constraint. Results for several test problems are presented in which convergence to a Karush-Kuhn-Tucker (KKT) point is observed.

Energy optimization for the design of corn-based ethanol plants

Abstract: In this work, we address the problem of optimizing corn-based bioethanol plants through the use of heat integration and mathematical programming techniques. The goal is to reduce the operating costs of the plant. Capital cost, energy usage, and yields—all contribute to production cost. Yield and energy usage also influence the viability of corn-based ethanol as a sustainable fuel. We first propose a limited superstructure of alternative designs including the various process units and utility streams involved in ethanol production. Our objective is to determine the connections in the network and the flow in each stream in the network such that we minimize the energy requirement of the overall plant. This is accomplished through the formulation of a mixed-integer nonlinear programming problem involving short-cut models for mass and energy balances for all the units in the system, where the model is solved through two nonlinear programming subproblems. We then perform a heat integration study on the resulting flowsheet; the modified flowsheet includes multieffect distillation columns that further reduces energy consumption. The results indicate that it is possible to reduce the current steam consumption required in the transformation of corn into fuel grade ethanol by more than 40% compared to initial basic design. © 2008 American Institute of Chemical Engineers AIChE J, 2008

Optimal Load Balancing in a Multiple Processor System with Many Job Classes

Abstract: A loosely coupled multiprocessor system contains multiple processors which have their own local memories To balance the load among multiple processors is of fundamental importance in enhancing the performance of such a multiple processor system Probabilistic load balancing in a heterogeneous multiple processor system with many job classes is considered in this study The load balancing scheme is formulated as a nonlinear programming problem with linear constraints An optimal probabilistic load balancing algorithm is proposed to solve this nonlinear programming problem The proposed load balancing method is proven globally optimum in the sense that it results in a minimum overall average job response time on a probabilistic basis

Global optimization methods for the discrete network design problem

Abstract: This paper addresses the discrete network design problem (DNDP) with multiple capacity levels, or multi-capacity DNDP for short, which determines the optimal number of lanes to add to each candidate link in a road network. We formulate the problem as a bi-level programming model, where the upper level aims to minimize the total travel time via adding new lanes to candidate links and the lower level is a traditional Wardrop user equilibrium (UE) problem. We propose two global optimization methods by taking advantage of the relationship between UE and system optimal (SO) traffic assignment principles. The first method, termed as SO-relaxation, exploits the property that an optimal network design solution under SO principle can be a good approximate solution under UE principle, and successively sorts the solutions in the order of increasing total travel time under SO principle. Optimality is guaranteed when the lower bound of the total travel time of the unexplored solutions under UE principle is not less than the total travel time of a known solution under UE principle. The second method, termed as UE-reduction, adds the objective function of the Beckmann-McGuire-Winsten transformation of UE traffic assignment to the constraints of the SO-relaxation formulation of the multi-capacity DNDP. This constraint is convex and strengthens the SO-relaxation formulation. We also develop a dynamic outer-approximation scheme to make use of the state-of-the-art mixed-integer linear programming solvers to solve the SO-relaxation formulation. Numerical experiments based on a two-link network and the Sioux-Falls network are conducted.

Scatter search for chemical and bio-process optimization

Abstract: Scatter search is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in 1960s for combining decision rules and problem constraints such as the surrogate constraint method, scatter search uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we develop a general purpose heuristic for a class of nonlinear optimization problems. The procedure is based on the scatter search methodology and treats the objective function evaluation as a black box, making the search algorithm context-independent. Most optimization problems in the chemical and bio-chemical industries are highly nonlinear in either the objective function or the constraints. Moreover, they usually present differential-algebraic systems of constraints. In this type of problem, the evaluation of a solution or even the feasibility test of a set of values for the decision variables is a time-consuming operation. In this context, the solution method is limited to a reduced number of solution examinations. We have implemented a scatter search procedure in Matlab (Mathworks, 2004) for this special class of difficult optimization problems. Our development goes beyond a simple exercise of applying scatter search to this class of problems, but presents innovative mechanisms to obtain a good balance between intensification and diversification in a short-term search horizon. Computational comparisons with other recent methods over a set of benchmark problems favor the proposed procedure.