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Bound Contraction Strategy Applied to Network Synthesis with Regeneration and Reuse to Minimize Water Consumption

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SSRN

SSRN 2024年

作者： Pedroza, Ivone Cristina Barros da Silva Sá Ravagnani, Mauro Antônio The State University of Bahia Portugal The State University of Maringá Brazil Campus IX Department of Human Sciences Department of Chemical Engineering Universidade Estadual de Maringá Brazil University of Maringá Main Campus Department of Chemical Engineering Brazil

SUMMARY The present work uses the global bound contraction optimization technique to solve problems of synthesis of water networks with regeneration and reuse in industrial processes. The objective is to obtain viable solutions that allow the reduction in the consumption of fresh water and the generation of effluents. The problems addressed have a formulation of mixed integer nonlinear programming (MINLP), containing bilinear terms. The results always presented the solution to the global optimum in all the cases studied. The costs of the analyzed networks were reduced, and the models generated always presented an increasingly smaller distance between the lower and upper limits for the variables studied. It can be concluded that the strategy used can contribute to a reassessment of existing water networks, as well as to the application in the design of new networks. © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

mixed-integer linear Optimization for Cardinality-Constrained Random Forests

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arXiv 2024年

作者： Burgard, Jan Pablo Pinheiro, Maria Eduarda Schmidt, Martin Trier University Department of Economic and Social Statistics Universitätsring 15 Trier54296 Germany Trier University Department of Mathematics Universitätsring 15 Trier54296 Germany

Random forests are among the most famous algorithms for solving classification problems, in particular for large-scale data sets. Considering a set of labeled points and several decision trees, the method takes the majority vote to classify a new given point. In some scenarios, however, labels are only accessible for a proper subset of the given points. Moreover, this subset can be non-representative, e.g., due to collection bias. Semi-supervised learning considers the setting of labeled and unlabeled data and often improves the reliability of the results. In addition, it can be possible to obtain additional information about class sizes from undisclosed sources. We propose a mixed-integer linear optimization model for computing a semi-supervised random forest that covers the setting of labeled and unlabeled data points as well as the overall number of points in each class for a binary classification. Since the solution time rapidly grows as the number of variables increases, we present some problem-tailored preprocessing techniques and an intuitive branching rule. Our numerical results show that our approach leads to better accuracy and a better Matthews correlation coefficient for biased samples compared to random forests by majority vote, even if only a few labeled points are *** Codes 90C11, 90C90, 90-08, 68T99 © 2024, CC BY.

关键词： mixed-integer linear programming

A functional equation for monomial functions

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arXiv 2024年

作者： Gselmann, Eszter Iqbal, Mehak Department of Analysis University of Debrecen P.O. Box 400 DebrecenH-4002 Hungary Doctoral School of Mathematical and Computational Sciences University of Debrecen P.O. Box 400 DebrecenH-4002 Hungary

Let F Ă K be fields with characteristic zero, n be a positive integer and κ ∊ K. In this paper, we determine those monomials f: F Ñ K of degree n for which (Formula presented) holds for all x ∊ F. We show that similar to the classical results, where additive functions were considered, the monomial functions in the equation can be represented with the aid of homomorphisms and higher-order *** Codes Primary 39B55, Secondary 39B72 © 2024, CC BY.

关键词： mixed-integer linear programming

integer programming Approaches for Distributionally Robust Chance Constraints with Adjustable Risks

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arXiv 2023年

作者： Zhang, Yiling Industrial and Systems Engineering University of Minnesota United States

We study distributionally robust chance-constrained programs (DRCCPs) with individual chance constraints under a Wasserstein ambiguity. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints (DRCCs) as decision variables to trade off between the system cost and risk of violations by penalizing the risk tolerances in the objective function. The introduction of adjustable risks, unfortunately, leads to NP-hard optimization problems. We develop integer programming approaches for individual chance constraints with uncertainty either on the right-hand side or on the left-hand side. In particular, we derive mixed integer programming reformulations for the two types of uncertainty to determine the optimal risk tolerance for the chance constraint. Valid inequalities are derived to strengthen the formulations. We test diverse instances of diverse sizes. © 2023, CC BY-NC-ND.

关键词： mixed-integer linear programming

Fair and Accurate Regression: Strong Formulations and Algorithms

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arXiv 2024年

作者： Deza, Anna Gómez, Andrés Atamtürk, Alper Industrial Engineering and Operations Research University of California United States Industrial and System Engineering University of Southern California United States

This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we study the polynomially-solvable single-factor and single-observation subproblems as building blocks and derive their closed convex hull descriptions. Strong formulations obtained for the general fair regression problem in this manner are utilized to solve the problem with a branch-and-bound algorithm exactly or as a relaxation to produce fair and accurate models rapidly. Moreover, to handle large-scale instances, we develop a coordinate descent algorithm motivated by the convex-hull representation of the single-factor fair regression problem to improve a given solution efficiently. Numerical experiments conducted on fair least squares and fair logistic regression problems show competitive statistical performance with state-of-the-art methods while significantly reducing training times. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Cycle-Configuration: A Novel Graph-theoretic Descriptor Set for Molecular Inference

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arXiv 2024年

作者： Song, Bowen Zhu, Jianshen Azam, Naveed Ahmed Haraguchi, Kazuya Zhao, Liang Akutsu, Tatsuya

In this paper, we propose a novel family of descriptors of chemical graphs, named cycle-configuration (CC), that can be used in the standard "two-layered (2L) model" of mol-infer, a molecular inference framework based on mixed integer linear programming (MILP) and machine learning (ML). Proposed descriptors capture the notion of ortho/meta/para patterns that appear in aromatic rings, which has been impossible in the framework so far. Computational experiments show that, when the new descriptors are supplied, we can construct prediction functions of similar or better performance for all of the 27 tested chemical properties. We also provide an MILP formulation that asks for a chemical graph with desired properties under the 2L model with CC descriptors (2L+CC model). We show that a chemical graph with up to 50 non-hydrogen vertices can be inferred in a practical time. © 2024, CC BY.

关键词： mixed-integer linear programming

The Effect of Demand Response in the Minimum Available Reserve of Energy Management

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The Effect of Demand Response in the Minimum Available Reser...

IEEE Power and Energy Society General Meeting

作者： Joao Soares Nuno Borges Ali Fotouhi Zita Vale GECAD - Knowledge Engineering and Decision-Support Research Centre Polytechnic of Porto (ISEP/IPP)

ISBN: (纸本)9781509041695

This paper presents a multi-objective energy scheduling for the daily operation of, a Smart Grid (SG) considering maximization of the minimum available reserve in addition to the cost minimization, to take into account the reliability requirements of critical and vulnerable loads. A Virtual Power Player (VPP) manages the day-ahead energy resource scheduling in the smart grid, considering Distributed Generation (DG) and Vehicle-To-Grid (V2G), while maintaining a highly reliable power for the critical loads. This work considers high penetration of critical loads, e.g. industrial processes that require high power quality, high reliability and few interruptions. A mathematical formulation is described and a deterministic technique based on mixed-integer linear programming (MILP) is used to solve the multi-objective problem. The effect of some customers with DR in this context is analyzed to assess the benefits in the energy scheduling problem. A case study using a 180-bus Portuguese distribution network with 90 load points, several DG units and a large fleet of Electric Vehicles (EVs) with V2G is used to illustrate the performance of the proposed method.

关键词： Electric Vehicles Multi-objective optimization Pareto front mixed-integer linear programming Smart Grid Smart grids Electric vehicles Demand-Responsive recoverable deposits mixed integer linear programming Energy management critical load Energy sources

The mixed integer Trust Region Problem

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arXiv 2024年

作者： Pia, Alberto Del Department of Industrial and Systems Engineering Wisconsin Institute for Discovery University of Wisconsin-Madison MadisonWI United States

In this paper we consider the problem of minimizing a general quadratic function over the mixed integer points in an ellipsoid. This problem is strongly NP-hard, NP-hard to approximate within a constant factor, and optimal solutions can be irrational. In our main result we show that an arbitrarily good solution can be found in polynomial time, if we fix the number of integer variables. This algorithm provides a natural extension to the mixed integer setting, of the polynomial solvability of the trust region problem proven by Ye, Karmarkar, Vavasis, and Zippel. As a result, our findings pave the way for designing efficient trust region methods for mixed integer nonlinear optimization problems. The techniques that we introduce are of independent interest and can be used in other mixed integer nonlinear optimization problems. As an example, we consider the problem of minimizing a general quadratic function over the mixed integer points in a polyhedron. For this problem, we show that a solution satisfying weak bounds with respect to optimality can be computed in polynomial time, provided that the number of integer variables is fixed. It is well known that finding a solution satisfying stronger bounds cannot be done in polynomial time, unless P=NP. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

Finite sample learning of moving targets

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arXiv 2024年

作者： Vertovec, Nikolaus Margellos, Kostas Prandini, Maria Department of Computer Science University of Oxford OX1 3PJ United Kingdom Department of Engineering Science University of Oxford OX1 3PJ United Kingdom Department of Electronics Information and Bioengineering Politecnico di Milano Milano20133 Italy

We consider a moving target that we seek to learn from samples. Our results extend randomized techniques developed in control and optimization for a constant target to the case where the target is changing. We derive a novel bound on the number of samples that are required to construct a probably approximately correct (PAC) estimate of the target. Furthermore, when the moving target is a convex polytope, we provide a constructive method of generating the PAC estimate using a mixed integer linear program (MILP). The proposed method is demonstrated on an application to autonomous emergency braking. © 2024, CC BY.

关键词： mixed-integer linear programming