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Optimal design of a small size trigeneration plant in civil users: A MINLP (mixed integer non linear programming Model)

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ENERGY 2015年 80卷 628-641页

作者： Arcuri, P. Beraldi, P. Florio, G. Fragiacomo, P. Univ Calabria Dept Mech Energy & Management Engn I-87030 Cosenza Italy

An optimization procedure for the optimal design of a trigenerative system to satisfy the energy needs of civil users is proposed. For the formulation of the mathematical model, it was necessary to refer to the class of MINLP (mixed integer non linear programming Models), whose complexity is related to the presence of binary decision variables and to the non linear nature of the constraints. These constraints are required to model the variation of the nominal efficiency and of the plant unitary cost in relation to the size of the cogeneration plant, and to model the decrease of the nominal efficiency of the cogeneration plant in relation to load variation. Different plant alternatives (Simple Cycle Gas Turbine, Gas Micro-Turbine, Gas Internal Combustion Engine, Fuel Cells) in the optimization procedure are taken into account with the aim of determining the optimal typology, size and operative strategy of the trigeneration system. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： mixed integer non linear programming Model Cogeneration plant Trigeneration system

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Robust optimal classification trees under noisy labels (Oct, 10.1007/s11634-021-00467-2, 2021)

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2022年第4期16卷 1095-1095页

作者： Blanco, Victor Japon, Alberto Puerto, Justo Univ Seville Inst Math IMUS Seville Spain Univ Granada Inst Math IMAG Granada Spain

In this paper we propose a novel methodology to construct Optimal Classification Trees that takes into account that noisy labels may occur in the training sample. The motivation of this new methodology is based on the superaditive effect of combining together margin based classifiers and outlier detection techniques. Our approach rests on two main elements: (1) the splitting rules for the classification trees are designed to maximize the separation margin between classes applying the paradigm of SVM; and (2) some of the labels of the training sample are allowed to be changed during the construction of the tree trying to detect the label noise. Both features are considered and integrated together to design the resulting Optimal Classification Tree. We present a mixed integer non linear programming formulation for the problem, suitable to be solved using any of the available off-the-shelf solvers. The model is analyzed and tested on a battery of standard datasets taken from UCI Machine Learning repository, showing the effectiveness of our approach. Our computational results show that in most cases the new methodology outperforms both in accuracy and AUC the results of the benchmarks provided by OCT and OCT-H.

关键词： Multiclass classification Optimal classification trees Support vector machines mixed integer non linear programming Classification Hyperplanes

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Usage of the net present value-at-risk to design ground-coupled heat pump systems under uncertain scenarios

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RENEWABLE ENERGY 2021年 173卷 953-971页

作者： Dusseault, Bernard Pasquier, Philippe Polytech Montreal Civil Geol & Min Dept CP 6079 Succ Ctr Ville Montreal PQ H3C 3A7 Canada

Hybrid ground-coupled heat pump systems can efficiently heat and cool buildings by exchanging heat with geological materials. Their sizing is, however, complex and their financial profitability is hard to establish during the design phase due to uncertainties that taint important design parameters. Historically, impacts of uncertainties are assessed after sizing completion using sensitivity analyses. Unfortunately, these analyses cannot mitigate design risks, should the consequences of uncertainties be significant. Here, we show how the net present value-at-risk, a stochastic financial indicator inspired by a metric used in the financial sector, can weave the impacts of uncertainties throughout the design phase. The net present value-at-risk is compared to the net present value in a case study that considers uncertainty of construction costs, building's heat load, energy tariffs and ground thermal conductivity. Results show that this financial indicator, although it comes at a higher computational price than traditional net present value indicator, leads to shorter payback periods, greatly reduces the risks of unforeseen financial losses and does not require further sensitivity analysis. By describing uncertain parameters with statistical distributions during sizing, the proposed designs are more conservative, still efficient and financially viable while being shielded from worst case scenarios. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： Stochastic optimization Net present value-at-risk Design under uncertainty Hybrid ground-coupled heat pump system mixed integer non linear programming

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Fairness in maximal covering location problems

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COMPUTERS & OPERATIONS RESEARCH 2023年第1期157卷

作者： Blanco, Victor Gazquez, Ricardo Univ Granada Inst Math IMAG Granada Spain Univ Granada Dept Quant Methods Econ & Business Granada Spain Univ Malaga OASYS Res Grp Ada Byron Malaga Spain

This paper provides a mathematical optimization framework to incorporate fairness measures from the facilities' perspective to discrete and continuous maximal covering location problems. The main ingredients to construct a function measuring fairness in this problem are the use of (1) ordered weighted averaging operators, a popular family of aggregation criteria for solving multiobjective combinatorial optimization problems;and (2) ⠋-fairness operators which allow generalizing most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are first formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained from an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach.

关键词： Facility location Fair resource allocation Ordered weighted averaging problem mixed integer non linear programming

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An automatic method for generating multiple alignment alternatives for a railway bypass

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COMPUTERS & OPERATIONS RESEARCH 2023年 154卷

作者： Vazquez-Mendez, Miguel E. Casal, Gerardo Castro, Alberte Santamarina, Duarte CITMAga Santiago De Compostela 15782 Spain Univ Santiago Compostela Dept Matemat Aplicada Escola Politecn Super Enxenaria Lugo 27002 Spain Univ Santiago Compostela Dept Enxenaria Agroforestal Escola Politecn Super Enxenaria Lugo 27002 Spain

This paper deals with the problem of designing a bypass on a railway line. Based on a geometrical model capable of determining automatically the need of major structures (bridges, tunnels, overpasses and underpasses), the optimal design of a railway bypass is formulated in the framework of mixed integer non linear programming (MINLP), and it is solved with a numerical algorithm which provides different layout alternatives that are optimal solutions (local minima) from the economic point of view. The proposed method is tested on a case study with the aim of showing its practical usefulness as a support tool for engineers in order to accomplish the complex and time-consuming task to generate a set of initial alternatives for the design of a railway bypass.

关键词： Railway bypass mixed integer non linear programming Railway alignment optimization Obtaining local minima

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A mathematical programming approach to SVM-based classification with label noise

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COMPUTERS & INDUSTRIAL ENGINEERING 2022年第PartA期172卷

作者： Blanco, Victor Japon, Alberto Puerto, Justo Univ Granada Inst Math IMAG Granada Spain Univ Granada Dept Quantitat Methods Econ & Business Granada Spain Univ Seville Inst Math IMUS Seville Spain Univ Seville Dept Stats & OR Seville Spain

In this paper we propose novel methodologies to optimally construct Support Vector Machine-based classifiers that take into account that label noise occur in the training sample. We propose different alternatives based on solving mixed integer linear and non linear models by incorporating decisions on relabeling some of the observations in the training dataset. The first method incorporates relabeling directly in the SVM model while a second family of methods combines clustering with classification at the same time, giving rise to a model that applies simultaneously similarity measures and SVM. Extensive computational experiments are reported based on a battery of standard datasets taken from UCI Machine Learning repository, showing the effectiveness of the proposed approaches.

关键词： Supervised classification SVM mixed integer non linear programming Label noise

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Optimal arrangements of hyperplanes for SVM-based multiclass classification

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ADVANCES IN DATA ANALYSIS AND CLASSIFICATION 2020年第1期14卷 175-199页

作者： Blanco, Victor Japon, Alberto Puerto, Justo Univ Granada IEMath GR E-18001 Granada Spain Univ Seville IMUS E-41012 Seville Spain

In this paper, we present a novel SVM-based approach to construct multiclass classifiers by means of arrangements of hyperplanes. We propose different mixed integer (linear and non linear) programming formulations for the problem using extensions of widely used measures for misclassifying observations where the kernel trick can be adapted to be applicable. Some dimensionality reductions and variable fixing strategies are also developed for these models. An extensive battery of experiments has been run which reveal the powerfulness of our proposal as compared with other previously proposed methodologies.

关键词： Multiclass support vector machines mixed integer non linear programming Classification hyperplanes

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Continuous maximal covering location problems with interconnected facilities

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COMPUTERS & OPERATIONS RESEARCH 2021年 132卷 105310-105310页

作者： Blanco, Victor Gazquez, Ricardo Univ Granada Inst Math Granada Spain Univ Granada Dept Quantitat Methods Econ & Business Granada Spain

In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be linked by means of a given graph structure (provided that two facilities are allowed to be linked if a given distance is not exceed). We propose a mathematical programming framework for the problem and different resolution strategies. First, we provide a mixed integer non linear programming formulation for the problem and derive some geometrical properties that allow us to reformulate it as an equivalent pure integer linear programming problem. We propose two branch-&-cut approaches by relaxing some sets of constraints of the former formulation. We also develop a math-heuristic algorithm for the problem capable to solve instances of larger sizes. We report the results of an extensive battery of computational experiments comparing the performance of the different approaches.

关键词： Maximal covering location Continuous location mixed integer non linear programming integer linear programming Branch-& -cut approaches

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On the multisource hyperplanes location problem to fitting set of points

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COMPUTERS & OPERATIONS RESEARCH 2021年 128卷 105124-105124页

作者： Blanco, Victor Japon, Alberto Ponce, Diego Puerto, Justo Univ Granada IEMath GR Granada Spain Univ Seville IMUS Seville Spain Univ Zaragoza Dept Metodos Estadist Zaragoza Spain

In this paper we study the problem of locating a given number of hyperplanes minimizing an objective function of the closest distances from a set of points. We propose a general framework for the problem in which norm-based distances between points and hyperplanes are aggregated by means of ordered median functions. A compact mixed integer linear (or non linear) programming formulation is presented for the problem and also an extended set partitioning formulation with a huge number of variables is derived. We develop a column generation procedure embedded within a branch-and-price algorithm for solving the problem by adequately performing its preprocessing, pricing and branching. We also analyze geometrically the optimal solutions of the problem, deriving properties which are exploited to generate initial solutions for the proposed algorithms. Finally, the results of an extensive computational experience are reported. The issue of scalability is also addressed showing theoretical upper bounds on the errors assumed by replacing the original datasets by aggregated versions. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Hyperplanes location mixed integer non linear programming Column generation

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integer constraints for enhancing interpretability in linear regression

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SORT-STATISTICS AND OPERATIONS RESEARCH TRANSACTIONS 2020年第1期44卷 67-98页

作者： Carrizosa, Emilio Olivares-Nadal, Alba, V Ramirez-Cobo, Pepa Univ Seville IMUS Inst Math Seville Spain Univ Chicago Booth Sch Business 5751 S Woodlawn Ave Chicago IL 60637 USA Univ Cadiz Dept Stat & Operat Res Cadiz Spain

One of the main challenges researchers face is to identify the most relevant features in a prediction model. As a consequence, many regularized methods seeking sparsity have flourished. Although sparse, their solutions may not be interpretable in the presence of spurious coefficients and correlated features. In this paper we aim to enhance interpretability in linear regression in presence of multicollinearity by: (i) forcing the sign of the estimated coefficients to be consistent with the sign of the correlations between predictors, and (ii) avoiding spurious coefficients so that only significant features are represented in the model. This will be addressed by modelling constraints and adding them to an optimization problem expressing some estimation procedure such as ordinary least squares or the lasso. The so-obtained constrained regression models will become mixed integer Quadratic Problems. The numerical experiments carried out on real and simulated datasets show that tightening the search space of some standard linear regression models by adding the constraints modelling (i) and/or (ii) help to improve the sparsity and interpretability of the solutions with competitive predictive quality.

关键词： linear regression Multicollinearity Sparsity Cardinality constraint mixed integer non linear programming

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