Machine learning predictive models rely on data to make predictions for new input data. However, accurate predictions are not always the end goal;practitioners often aim to make informed decisions through optimization...
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Machine learning predictive models rely on data to make predictions for new input data. However, accurate predictions are not always the end goal;practitioners often aim to make informed decisions through optimization problems (OPs) based on these predictions. While the idea that better predictions lead to better decisions was widely accepted, the latest literature highlights that even small inaccuracies in predictions can lead to poor decisions depending on the structure of the OP. Therefore, recent research has been focused on end-to-end learning approaches that directly improve decision quality without considering prediction accuracy when solving data-driven OPs. Some of these end-to-end learning approaches are mainly called "predict-and-optimize" (PaO), and they aim to learn a predictor based on the quality of the downstream task decisions by incorporating mathematical programming into the learning process. This literature review discusses the variations of and approaches to PaO problems by proposing a unified notation and a taxonomy for them. Throughout the paper, we aim to provide a valuable roadmap for researchers and practitioners in the field, guiding them to choose data-driven methods to solve their decision problems effectively.
The Grey Wolf Optimizer (GWO) algorithm is a very famous algorithm in the field of swarm intelligence for solving global optimization problems and real-life engineering design problems. The GWO algorithm is unique amo...
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The Grey Wolf Optimizer (GWO) algorithm is a very famous algorithm in the field of swarm intelligence for solving global optimization problems and real-life engineering design problems. The GWO algorithm is unique among swarm-based algorithms in that it depends on leadership hierarchy. In this paper, a Modified Grey Wolf optimization Algorithm (MGWO) is proposed by modifying the position update equation of the original GWO algorithm. The leadership hierarchy is simulated using four different types of grey wolves: lambda (lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document}), mu (mu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}), nu (nu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nu$$\end{document}), and xi (xi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi$$\end{document}). The effectiveness of the proposed MGWO is tested using CEC 2005 benchmark functions, with sensitivity analysis and convergence analysis, and the statistical results are compared with six other meta-heuristic algorithms. According to the results and discussion, MGWO is a competitive algorithm for solving global optimization problems. In addition, the MGWO algorithm is applied to three real-life optimization design problems, such a
We introduce a generalized Spiking Locally Competitive Algorithm (LCA) that is biologically plausible and exhibits adaptability to a large variety of neuron models and network connectivity structures. In addition, we ...
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We introduce a generalized Spiking Locally Competitive Algorithm (LCA) that is biologically plausible and exhibits adaptability to a large variety of neuron models and network connectivity structures. In addition, we provide theoretical evidence demonstrating the algorithm's convergence in optimization problems of signal recovery. Furthermore, our algorithm demonstrates superior performance over traditional optimization methods, such as FISTA, particularly by achieving faster early convergence in practical scenarios including signal denoising, seismic wave detection, and computed tomography reconstruction. Notably, our algorithm is compatible with neuromorphic chips, such as Loihi, facilitating efficient multitasking within the same chip architecture-a capability not present in existing algorithms. These advancements make our generalized Spiking LCA a promising solution for real-world applications, offering significant improvements in execution speed and flexibility for neuromorphic computing systems.
The line search methods for optimization problems have garnered widespread adoption across various domains and applications, primarily due to their effectiveness in addressing intricate problems. An important componen...
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This paper is concerned with maximization and minimization problems of the energy integral associated to p-Laplace equations depending on functions that belong to a class of rearrangements. We prove existence and uniq...
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This paper is concerned with maximization and minimization problems of the energy integral associated to p-Laplace equations depending on functions that belong to a class of rearrangements. We prove existence and uniqueness results, and present some features of optimal solutions. The radial case is discussed in detail. We also prove a result of uniqueness for a class of p-Laplace equations under non-standard assumptions. (C) 2011 Elsevier Ltd. All rights reserved.
A consecutive-k-out-of-n:G system consists of n components which are arranged in a line and the system works if and only if at least k consecutive components work. This paper discusses the optimization problems for a ...
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A consecutive-k-out-of-n:G system consists of n components which are arranged in a line and the system works if and only if at least k consecutive components work. This paper discusses the optimization problems for a consecutive-k-out-of-n:G system. We first focus on the optimal number of components at the system design phase. Then, we focus on the optimal replacement time at the system operation phase by considering a preventive replacement, which the system is replaced at the planned time or the time of system failure which occurs first. The expected cost rates of two optimization problems are considered as objective functions to be minimized. Finally, we give study cases for the proposed optimization problems and evaluate the feasibility of the policies.
We consider a mathematical model which describes the contact between a viscoelastic body and a rigid-deformable foundation with memory effects. We derive a variational formulation of the model which is in the form of ...
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We consider a mathematical model which describes the contact between a viscoelastic body and a rigid-deformable foundation with memory effects. We derive a variational formulation of the model which is in the form of a history-dependent variational inequality for the displacement field. Then we prove the existence of a unique weak solution to the problem. We also study the continuous dependence of the solution with respect to the data and prove two convergence results, under different assumptions on the data. The proofs are based on arguments of lower semicontinuity, pseudomonotonicity, and compactness. Finally, we use our convergence results in the study of several optimization problems associated to the viscoelastic contact model. (C) 2019 Elsevier Ltd. All rights reserved.
We study minimization and maximization problems for the principal eigenvalue of a p-Laplace equation in a bounded domain Omega, with weight chi(D), where D subset of Omega is a variable subset with a fixed measure alp...
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We study minimization and maximization problems for the principal eigenvalue of a p-Laplace equation in a bounded domain Omega, with weight chi(D), where D subset of Omega is a variable subset with a fixed measure alpha. We investigate monotonicity, continuity and differentiability with respect to alpha of the optimizing eigenvalues. (C) 2012 Elsevier Inc. All rights reserved.
In this paper, a class of optimization problems with cone constraints in groups and semigroups is investigated by exploiting the image space analysis. Optimality is proved by means of separation arguments in the image...
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In this paper, a class of optimization problems with cone constraints in groups and semigroups is investigated by exploiting the image space analysis. Optimality is proved by means of separation arguments in the image space associated with the given problem, which turns out to be equivalent to the existence of saddle points of generalized Lagrangian functions under suitable assumptions. In particular, Lagrangian-type sufficient or necessary optimality conditions are obtained by introducing convex-like functions and using separation theorems between convex sets in groups and semigroups obtained by Li and Mastroeni.
We study the optimal solutions of optimization problems and well-posedness for locally convex cone-valued functions. Using the non-linear scalarization functions, we prove some existence results and obtain characteriz...
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We study the optimal solutions of optimization problems and well-posedness for locally convex cone-valued functions. Using the non-linear scalarization functions, we prove some existence results and obtain characterizations of the optimal solutions. Then, we consider the well-posedness in Tykhonov sense and discuss the scalar optimization problems.
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