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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.


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Journal ArticleDOI
TL;DR: In this article, the authors proposed a new constraint handling approach for general constraints that is applicable to a widely used class of constrained derivative-free optimization methods, such as lower triangular mesh adaptive direct search (LTMads) methods.
Abstract: We propose a new constraint-handling approach for general constraints that is applicable to a widely used class of constrained derivative-free optimization methods. As in many methods that allow infeasible iterates, constraint violations are aggregated into a single constraint violation function. As in filter methods, a threshold, or barrier, is imposed on the constraint violation function, and any trial point whose constraint violation function value exceeds this threshold is discarded from consideration. In the new algorithm, unlike the filter method, the amount of constraint violation subject to the barrier is progressively decreased adaptively as the iteration evolves. We test this progressive barrier (PB) approach versus the extreme barrier (EB) with the generalized pattern search (Gps) and the lower triangular mesh adaptive direct search (LTMads) methods for nonlinear derivative-free optimization. Tests are also conducted using the Gps-filter, which uses a version of the Fletcher-Leyffer filter approach. We know that Gps cannot be shown to yield kkt points with this strategy or the filter, but we use the Clarke nonsmooth calculus to prove Clarke stationarity of the sequences of feasible and infeasible trial points for LTMads-PB. Numerical experiments are conducted on three academic test problems with up to 50 variables and on a chemical engineering problem. The new LTMads-PB method generally outperforms our LTMads-EB in the case where no feasible initial points are known, and it does as well when feasible points are known. which leads us to recommend LTMads-PB. Thus the LTMads-PB is a useful practical extension of our earlier LTMads-EB algorithm, particularly in the common case for real problems where no feasible point is known. The same conclusions hold for Gps-PB versus Gps-EB.

167 citations

Journal ArticleDOI
TL;DR: In this paper, a dynamic dispatch procedure is proposed which is capable of taking into account the integral nature of the emission constraints and the management of multifuel plants are taken into account with the purpose of obtaining a cost-effective operation for all thermal plants in compliance with emission limitations.

166 citations

Journal ArticleDOI
TL;DR: In this article, a mixed-integer nonlinear programming (MINLP) model for performing structural and parameter optimization of utility plants that satisfy given electrical, mechanical and heating demands of industrial processes is presented.
Abstract: This paper presents a mixed-integer nonlinear programming (MINLP) model for performing structural and parameter optimization of utility plants that satisfy given electrical, mechanical and heating demands of industrial processes. In this model, nonlinear equations are extensively used for the cost of equipment and for the plant performance in terms of enthalpies, entropies and efficiencies. The proposed approach allows for the simultaneous optimization of the configuration, and selection of flowrates, enthalpies and steam turbine efficiencies. All major conventional utility plant equipment are included in the superstructure for the MINLP model. The proposed approach is not only useful for synthesis, but also for analysing different design alternatives. The model has been implemented in the computer package STEAM, and several applications are reported to illustrate the program capabilities, including a comparison with a simplified MILP model.

166 citations

Journal ArticleDOI
TL;DR: Application of the proposed algorithm on some benchmark functions demonstrated its good capability in comparison with Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) and the results of the experiments showed the good performance of FOA in some data sets from the UCI repository.
Abstract: In this article, a new evolutionary algorithm, Forest Optimization Algorithm (FOA), suitable for continuous nonlinear optimization problems has been proposed. It is inspired by few trees in the forests which can survive for several decades, while other trees could live for a limited period. In FOA, seeding procedure of the trees is simulated so that, some seeds fall just under the trees, while others are distributed in wide areas by natural procedures and the animals that feed on the seeds or fruits. Application of the proposed algorithm on some benchmark functions demonstrated its good capability in comparison with Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). Also we tested the performance of FOA on feature weighting as a real optimization problem and the results of the experiments showed the good performance of FOA in some data sets from the UCI repository.

166 citations

Journal ArticleDOI
TL;DR: An overview for deriving MINLP formulations through generalized disjunctive programming (GDP), which is an alternative higher-level representation of MINLP problems, is presented and a review of solution methods for GDP problems is provided.
Abstract: This work presents a review of the main deterministic mixed-integer nonlinear programming (MINLP) solution methods for problems with convex and nonconvex functions. An overview for deriving MINLP formulations through generalized disjunctive programming (GDP), which is an alternative higher-level representation of MINLP problems, is also presented. A review of solution methods for GDP problems is provided. Some relevant applications of MINLP and GDP in process systems engineering are described in this work.

166 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023113
2022259
2021615
2020650
2019640
2018630