Extended cutting plane method for a class of nonsmooth nonconvex MINLP problems

Eronen, Ville-Pekka; Mäkelä, Marko M.; Westerlund, Tapio

doi:10.1080/02331934.2013.796473

Cited by 13 publications

(21 citation statements)

References 14 publications

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“…Su et al (2015) have presented strategies such as multiple-generation cuts, hybrid methods and partial surrogate cuts for improving the e ciencies of the Outer Approximation and Generalized Benders Decomposition methods and Su et al (2016) have applied one of these techniques in a cracking production process. Other developments such as cutting plane methods (Eronen et al, 2015) and supporting hyperplane techniques (Westerlund et al, 2018) claim to produce easier convergence in nonsmooth, generalised convex formulations and demonstrate applicability to production and scheduling problems. Other methodologies for facilitating solutions in MINLP formulations of planning and scheduling problems include Lagrangian decomposition techniques (e.g.…”

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confidence: 99%

An optimal control approach to scheduling and production in a process using decaying catalysts

Adloor

Pons

Vassiliadis

2020

Computers & Chemical Engineering

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This article presents a novel approach to optimise scheduling and production planning to meet seasonal demand in an industrial process using decaying catalysts, based on its formulation as a multistage mixed-integer optimal control problem (MSMIOCP). Unlike existing methodologies, the MSMIOCP formulation allows to solve this problem as a standard nonlinear optimisation problem without combinatorial optimisation methods, which can be advantageous in providing reliable, robust and e cient solutions. Using this formulation, four case studies of this problem, di↵ering in reaction or deactivation kinetics, are investigated. Two di↵erent solution implementations are used, each having their own relative advantages. The first implementation demonstrates a bang-bang behaviour for the linear scheduling controls, consistent with a theoretical analysis, but faces integration problems and does not always produce high quality solutions. The second implementation, while not demonstrating the bang-bang property, always produces high quality solutions and shows the advantages of the MSMIOCP formulation over existing methodologies.

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confidence: 99%

An optimal control approach to scheduling and production in a process using decaying catalysts

Adloor

Pons

Vassiliadis

2020

Computers & Chemical Engineering

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“…Moreover, we develop an efficient gradient descentbased method to update the predictive model parameter. This method is more efficient than the most popular optimization algorithm used in structured output prediction methods, cutting plane algorithm [6,8,7,1], because it avoids the time-consuming quadratic programming problem of cutting plane algorithm.…”

Section: Our Contributionsmentioning

confidence: 99%

Manifold regularization in structured output space for semi-supervised structured output prediction

Jiang

Jia

Sheng

et al. 2015

Neural Comput & Applic

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Structured output prediction aims to learn a predictor to predict a structured output from a input data vector. The structured outputs include vector, tree, sequence, etc. We usually assume that we have a training set of input-output pairs to train the predictor. However, in many real-world applications, it is difficult to obtain the output for a input, thus for many training input data points, the structured outputs are missing. In this paper, we discuss how to learn from a training set composed of some input-output pairs, and some input data points without outputs. This problem is called semisupervised structured output prediction. We propose a novel method for this problem by constructing a nearest neighbor graph from the input space to present the manifold structure, and using it to regularize the structured output space directly. We define a slack structured output for each training data point, and proposed to predict it by learning a structured output predictor. The learning of both slack structured outputs and the predictor are unified within one single minimization problem. In this problem, we propose to minimize the structured loss between the slack structured outputs of neighboring data points, and the prediction error measured by the structured loss. The problem is optimized by an iterative algorithm. Experiment results over three benchmark data sets show its advantage.

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“…This method can easily solve the continuous optimization problem; however, this has low precision in the process of converting continuous variables into integer variables, and perhaps may not find the optimal solution for some problems. (2) The deterministic method, which uses the branch boundary method [13] and the cutting-plane approach [14] to solve MIP problems. These methods are effective and efficient for solving small-scale problems but, when the scale of the problem increases and the degree of nonlinearity becomes higher, the deterministic method is usually incapable of solving the problem.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Modified Particle Swarm Optimization Algorithm for Solving Mixed-Integer Nonlinear Programming Problems

Sun¹,

Gao²

2019

IJCIS

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This paper presents an efficient modified particle swarm optimization (EMPSO) algorithm for solving mixed-integer nonlinear programming problems. In the proposed algorithm, a new evolutionary strategies for the discrete variables is introduced, which can solve the problem that the evolutionary strategy of the classical particle swarm optimization algorithm is invalid for the discrete variables. An update strategy under the constraints is proposed to update the optimal position, which effectively utilizes the available information on infeasible solutions to guide particle search. In order to evaluate and analyze the performance of EMPSO, two hybrid particle swarm optimization algorithms with different strategies are also given. The simulation results indicate that, in terms of robustness and convergence speed, EMPSO is better than the other algorithms in solving 14 test problems. A new performance index (NPI) is introduced to fairly compare the other two algorithms, and in most cases the values of the NPI obtained by EMPSO were superior to the other algorithms.

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Extended cutting plane method for a class of nonsmooth nonconvex MINLP problems

Cited by 13 publications

References 14 publications

An optimal control approach to scheduling and production in a process using decaying catalysts

An optimal control approach to scheduling and production in a process using decaying catalysts

Manifold regularization in structured output space for semi-supervised structured output prediction

An Efficient Modified Particle Swarm Optimization Algorithm for Solving Mixed-Integer Nonlinear Programming Problems

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