Solving mixed-integer nonlinear programming (MINLP) problems to optimality is a NP-hard problem, for which many deterministic global optimization algorithms and solvers have been recently developed. MINLPs can be rela...
详细信息
Solving mixed-integer nonlinear programming (MINLP) problems to optimality is a NP-hard problem, for which many deterministic global optimization algorithms and solvers have been recently developed. MINLPs can be relaxed in various ways, including via mixed-integer linear programming (MIP), nonlinearprogramming, and linear programming. There is a tradeoff between the quality of the bounds and CPU time requirements of these relaxations. Unfortunately, these tradeoffs are problem-dependent and cannot be predicted beforehand. This paper proposes a new dynamic strategy for activating and deactivating MIP relaxations in various stages of a branch-and-bound algorithm. The primary contribution of the proposed strategy is that it does not use meta-parameters, thus avoiding parameter tuning. Additionally, this paper proposes a strategy that capitalizes on the availability of parallel MIP solver technology to exploit multicore computing hardware while solving MINLPs. Computational tests for various benchmark libraries reveal that our MIP activation strategy works efficiently in single-core and multicore environments.
This research addresses the capacitated dynamic lot-sizing problem with returns and hybrid products (CLSPRH). The problem is to identify how many of each product type to produce during each period for a hybrid system ...
详细信息
This research addresses the capacitated dynamic lot-sizing problem with returns and hybrid products (CLSPRH). The problem is to identify how many of each product type to produce during each period for a hybrid system with manufacturing capacity constraints. The objective of CLSPRH is to maximise total profit of the production system that consists of new, remanufactured and hybrid products. CLSPRH is a multi-period CLSP, which is modelled as a mixed-integer nonlinear programming problem. The traditional CLSP is NP-hard, and the nonlinearity of CLSPRH makes the problem even harder to solve. Therefore, a Simulated Annealing (SA) algorithm with a neighbourhood list (SA_NL) is proposed. By using a list of several neighbourhoods, the SA algorithm is improved. SA_NL is compared to SA, three variants of Genetic Algorithm (GA) and a Variable Neighbourhood Search (VNS) algorithm. The variants of GA are GA with one-point crossover (GA(OP)), GA with two-point crossover (GA(TP)) and GA with one-point period-based crossover (GA(OPPB)). Over all instances, the results show that the proposed SA_NL outperforms SA, VNS, GA(OP), GA(TP) and GA(OPPB) by 0.54%, 0.34%, 1.92%, 1.78% and 2.92%, respectively.
In this paper we propose a nonlinear Generalized Disjunctive programming model to optimize the 2-dimensional continuous location and allocation of the potential facilities based on their maximum capacity and the given...
详细信息
In this paper we propose a nonlinear Generalized Disjunctive programming model to optimize the 2-dimensional continuous location and allocation of the potential facilities based on their maximum capacity and the given coordinates of the suppliers and customers. The model belongs to the class of Capacitated Multi-facility Weber Problem. We propose a bilevel decomposition algorithm that iteratively solves a discretized MILP version of the model, and its nonconvex NLP for a fixed selection of discrete variables. Based on the bounding properties of the subproblems, -convergence is proved for this algorithm. We apply the proposed method to random instances varying from 2 suppliers and 2 customers to 40 suppliers and 40 customers, from one type of facility to 3 different types, and from 2 to 32 potential facilities. The results show that the algorithm is more effective at finding global optimal solutions than general purpose global optimization solvers tested.
Multiproduct pipelines are the most effective and important way to transport refined products from refineries to the downstream market. The detailed scheduling of a multiproduct pipeline with the hydraulic constraints...
详细信息
Multiproduct pipelines are the most effective and important way to transport refined products from refineries to the downstream market. The detailed scheduling of a multiproduct pipeline with the hydraulic constraints considered plays a vital role in the pipeline's safe and economic operation. Aiming at this issue, this paper proposes a continuous-time mixed-integer nonlinear programming (MINLP) model taking the sum of the pumps' running and start/stop costs as the objective function. Based on a method proposed in a previous study for the rigorous description of the hydraulic loss changes in multiproduct pipelines, the pipeline hydraulic constraints and pump-related functions are considered directly and rigorously in the model. Other actual field processing constraints, such as the pipeline shutdown and contaminated oil flowrate, are also considered. To deal with the nonlinear relationship between the flowrate and pressure/volume, a piecewise linearization method is adopted, and the pipeline flowrate is graded according to the divided intervals. Finally, the application of the established model is successfully conducted on a real-world multiproduct pipeline through two case studies. A comparison with a previous discrete-time model is also performed to verify this model's applicability, accuracy, and superiority. (C) 2019 Elsevier Ltd. All rights reserved.
This study addresses the problem of locating distribution centers in a single-echelon, capacitated distribution network. Such network consists of several potential distribution centers and various demand points disper...
详细信息
This study addresses the problem of locating distribution centers in a single-echelon, capacitated distribution network. Such network consists of several potential distribution centers and various demand points dispersed in different regional markets. The distribution operations of this network generate massive amounts of data. The problem is how to utilize big data generated to identify the right number of distribution centers to open and the right assignment of customers to opened distribution centers while minimizing the total handling and operation costs of distribution centers, transportation, and penalty. Restrictions on both network capacity and single sourcing strategy are also considered. This study formulates this problem as mixed-integernonlinear program. The effects of different scenarios on distribution-center locations as demand, the operation costs of distribution centers and outbound transportation, and the number of customers are analyzed through simulation on randomly generated big datasets. Empirical results indicate that the model presented is appropriate and robust. The operational value of big data in the distribution network design is revealed through a case study in which several design alternatives are evaluated.
We consider the problem of optimizing an unknown function given as an oracle over a mixed-integer box-constrained set. We assume that the oracle is expensive to evaluate, so that estimating partial derivatives by fini...
详细信息
We consider the problem of optimizing an unknown function given as an oracle over a mixed-integer box-constrained set. We assume that the oracle is expensive to evaluate, so that estimating partial derivatives by finite differences is impractical. In the literature, this is typically called a black-box optimization problem with costly evaluation. This paper describes the solution methodology implemented in the open-source library RBFOpt, available on COIN-OR. The algorithm is based on the Radial Basis Function method originally proposed by Gutmann (J Glob Optim 19:201-227, 2001. https://***/10.1023/A:1011255519438), which builds and iteratively refines a surrogate model of the unknown objective function. The two main methodological contributions of this paper are an approach to exploit a noisy but less expensive oracle to accelerate convergence to the optimum of the exact oracle, and the introduction of an automatic model selection phase during the optimization process. Numerical experiments show that RBFOpt is highly competitive on a test set of continuous and mixed-integernonlinear unconstrained problems taken from the literature: it outperforms the open-source solvers included in our comparison by a large amount, and performs slightly better than a commercial solver. Our empirical evaluation provides insight on which parameterizations of the algorithm are the most effective in practice. The software reviewed as part of this submission was given the Digital Object Identifier (DOI) https://***/10.5281/zenodo.597767.
We propose an optimization-based framework for process synthesis under variability in two frequencies. Low-frequency variability is represented through scenarios and high-frequency variability is modeled using modes. ...
详细信息
We propose an optimization-based framework for process synthesis under variability in two frequencies. Low-frequency variability is represented through scenarios and high-frequency variability is modeled using modes. The proposed framework allows for the selection of different process configurations during different modes, a feature necessary to model systems under wide high frequency variability (e.g., solar-based technologies). The optimization problem is formulated as a two-stage stochastic programming model with mode subproblems nested inside each scenario. The proposed framework is applied to the design of concentrating solar power plants with thermochemical energy storage, leading to the formulation of a computationally efficient model, as well as the identification of a superior design. (c) 2018 American Institute of Chemical Engineers AIChE J, 65: e16458 2019
Sampling and reconstruction is a fundamentally important problem in the field of graph signal processing. Many works have been contributed to reconstructing bandlimited signals from measurements taken on a known subse...
详细信息
ISBN:
(纸本)9781538646588
Sampling and reconstruction is a fundamentally important problem in the field of graph signal processing. Many works have been contributed to reconstructing bandlimited signals from measurements taken on a known subset of vertices. However, in some cases, the vertex defects occur randomly over the graph. In such situation, the existing graph signal reconstruction methods fail to deal with such blind reconstruction problem. In this paper, we formulate the blind reconstruction problem as mixed-integer nonlinear programming, and propose a Joint Detection and Reconstruction (JDR) method to simultaneously detect the vertices' working states and reconstruct the bandlimited signal. The convergence property of the proposed method is analyzed. In the experimental part, both synthetic dataset and real-world dataset are applied to verify the proposed methods.
Delay-Constrained Routing (DCR) problems require to route a new flow in a computer network subject to worst-case end-to-end delay guarantees. The delay of a packet flow has three components, one of which is the “queu...
详细信息
This paper addresses the problem of optimal location and sizing of distributed generators (DGs) in direct current (dc) power grids by using a mixed-integer nonlinear programming (MINLP) formulation. The reduction of t...
详细信息
ISBN:
(纸本)9781538678428
This paper addresses the problem of optimal location and sizing of distributed generators (DGs) in direct current (dc) power grids by using a mixed-integer nonlinear programming (MINLP) formulation. The reduction of the power losses in all branches of the network are considered as the objective function;while the restrictions are the power balance, voltage regulation, maximum penetration and maximum distributed generation units available. The general algebraic modeling system (GAMS) is selected as nonlinear optimizing package to solve this problem;besides, a small numerical example of energy production is introduced to illustrate the usability of using GAMS. Finally, a 21-node dc grid with two ideal generators, and multiple constant power loads, is used as test system.
暂无评论