In this paper a fast computational method for a class of nonlinear bilevel programming problems is proposed. In these problems, the lower-level problem can be decomposed into some paratactic and independent sub-proble...
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ISBN:
(纸本)9781424406043
In this paper a fast computational method for a class of nonlinear bilevel programming problems is proposed. In these problems, the lower-level problem can be decomposed into some paratactic and independent sub-problems. First, by Karush-Kuhn-Tucker optimality, the stationary-points of these sub-problems corresponding to the upper-level variables can be determined. As a result, this kind of nonlinear bilevel programming is transformed into a single level optimization problem. The hybrid genetic algorithm is then adopted to solve this single optimization problem. Simulation results on 18 benchmark problems show that the proposed method is able to solve effectively the bilevel programming problems such that their global optima can be found, with high convergent speed and less computational cost compared to other existing algorithms.
Filter methods, introduced by Fletcher and Leyffer for nonlinear programming are characterized by the use of the dominance concept of multi-objective optimization, instead of a penalty parameter whose adjustment can b...
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ISBN:
(数字)9783642161674
ISBN:
(纸本)9783642161667
Filter methods, introduced by Fletcher and Leyffer for nonlinear programming are characterized by the use of the dominance concept of multi-objective optimization, instead of a penalty parameter whose adjustment can be problematic. This paper presents a way to implement a filter based approach to solve a nonlinear bilevel programming problem in a linear approximations framework. The approach presented is based on the trust region idea from nonlinear programming, combined with filter-SQP algorithm, smooth and active sets techniques. The restoration procedure introduced in our algorithm consists in computing a rational solution.
The primary focus of the dissertation is to develop distributionally robust optimization (DRO) models and related solution approaches for decision making in energy and healthcare service systems with uncertainties, wh...
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The primary focus of the dissertation is to develop distributionally robust optimization (DRO) models and related solution approaches for decision making in energy and healthcare service systems with uncertainties, which often involves nonlinear constraints and discrete decision variables. Without assuming specific distributions, DRO techniques solve for solutions against the worst-case distribution of system uncertainties. In the DRO framework, we consider both risk-neutral (e.g., expectation) and risk-averse (e.g., chance constraint and Conditional Value-at-Risk (CVaR)) measures. The aim is twofold: i) developing efficient solution algorithms for DRO models with integer and/or binary variables, sometimes nonlinear structures and ii) revealing managerial insights of DRO models for specific applications. We mainly focus on DRO models of power system operations, appointment scheduling, and resource allocation in healthcare. Specifically, we first study stochastic optimal power flow (OPF), where (uncertain) renewable integration and load control are implemented to balance supply and (uncertain) demand in power grids. We propose a chance-constrained OPF (CC-OPF) model and investigate its DRO variant which is reformulated as a semidefinite programming (SDP) problem. We compare the DRO model with two benchmark models, in the IEEE 9-bus, 39-bus, and 118-bus systems with different flow congestion levels. The DRO approach yields a higher probability of satisfying the chance constraints and shorter solution time. It also better utilizes reserves at both generators and loads when the system has congested flows. Then we consider appointment scheduling under random service durations with given (fixed) appointment arrival order. We propose a DRO formulation and derive a conservative SDP reformulation. Furthermore, we study a scheduling variant under random no-shows of appointments and derive tractable reformulations for certain beliefs of no-show patterns. One preceding problem
Particle swarm optimization (PSO) algorithm has been developing rapidly and has been applied widely since it was introduced, as it is easily understand and realized For nonlinear bilevel programming whose leader is a ...
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ISBN:
(纸本)9780780397361
Particle swarm optimization (PSO) algorithm has been developing rapidly and has been applied widely since it was introduced, as it is easily understand and realized For nonlinear bilevel programming whose leader is a nonlinear function, a hybrid PSO algorithm with a simplex algorithm is presented. So far using PSO to solve the nonlinear bilevel programming problem has not been found in the literature Some numerical examples are given to verify the effectiveness of proposed approach.
The class of stochastic nonlinear programming (SNIP) problems is important in optimization due to the presence of nonlinearity and uncertainty in many applications including those in the field of process systems engin...
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The class of stochastic nonlinear programming (SNIP) problems is important in optimization due to the presence of nonlinearity and uncertainty in many applications including those in the field of process systems engineering. But despite the apparent importance of such problems, solution algorithms for these problems have found few applications due to severe computational and structural restrictions. To that effect, this work proposes a new algorithm for computationally efficient solution of the SNLP problems. Starting with the basic structure of traditional L-shaped method, the new algorithm called L-shaped BONUS incorporates reweighting scheme to ease computational load in the second stage recourse function calculation. The reweighting idea has been previously used successfully in optimization in BONUS, also an algorithm to solve SNLP problems. The proposed algorithm is analyzed using different case study problems including a blending problem relevant to process industry and a large scale novel sensor placement problem for water security networks. All problem results show considerable savings in computational time without compromising accuracy, the performance being better for Hammersley sequence sampling technique as compared to Monte Carlo sampling technique.
Optimization calculation is one of the important application fields in Neural Network. This paper proposes a Neural Network computational method of nonlinear programming problems based on precise F-function for the pr...
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Optimization calculation is one of the important application fields in Neural Network. This paper proposes a Neural Network computational method of nonlinear programming problems based on precise F-function for the problems of not catering to network size, computational efficiency and accuracy when solving the constraint nonlinear programming problems in current Neural Network. A low order precise F-function of constraint nonlinear programming problems is served as energy function of Neural Network. The dynamics equation of Neural Network is constructed and the clarification of its stability is given by the most rapid decreasing principle of the energy function. Theoretical analysis and computational example emulation show that the proposed Neural Network dynamics equation globally and precisely constringes a local optimization solution of the original programming problems. In particular, the neural network dynamics equation is easy to be mapped as dynamic circuit, which is a Real-time calculation method for engineering optimization problems.
We propose a methodology for generating nonlinear goal programs that are suitable for the testing of algorithms. We restrict attention to the most common variant of the class, the preemptive or lexicographic goal prog...
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We propose a methodology for generating nonlinear goal programs that are suitable for the testing of algorithms. We restrict attention to the most common variant of the class, the preemptive or lexicographic goal program. Our methodology produces test instances that are accompanied by information on how close any optimal solution would come to satisfying each of the goals. Our technique for constructing each test instance is similar in form to sequential optimization procedures for solving goal programs. The method can incorporate varying degrees of randomization.
We examine the impact of parallel computing on the field of nonlinear network programming. A general framework for the vectorization of optimization software is presented and applied in the context of two codes. Exper...
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We consider the solution of nonlinear programs with nonlinear semidefiniteness constraints. The need for an efficient exploitation of the cone of positive semidefinite matrices makes the solution of such nonlinear sem...
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