The aim of this paper is to deepen the study of solution methods for rank-two nonconvex problems with polyhedral feasible region, expressed by means of equality, inequality and box constraints, and objective function ...
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The aim of this paper is to deepen the study of solution methods for rank-two nonconvex problems with polyhedral feasible region, expressed by means of equality, inequality and box constraints, and objective function in the form of phi c T x + c 0 , d T x + d 0 b T x + b 0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi \left( c<^>Tx+c_0,\frac{d<^>Tx+d_0}{b<^>Tx+b_0}\right) $$\end{document} or phi over bar c over bar T y + c over bar 0 a T y + a 0 , d T y + d 0 b T y + b 0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{\phi }\left( \frac{\bar{c}<^>Ty+\bar{c}_0}{a<^>Ty+a_0}, \frac{d<^>Ty+d_0}{b<^>Ty+b_0}\right) $$\end{document} . These problems arise in bicriteria programs, quantitative management science, data envelopment analysis, efficiency analysis and performance measurement. Theoretical results are proved and applied to propose a solution algorithm. Computational results are provided, comparing various splitting criteria.
The advent of Urban Air Mobility (UAM) presents the scope for a transformative shift in the domain of urban transportation. However, its widespread adoption and economic viability depends in part on the ability to opt...
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ISBN:
(数字)9781624107160
ISBN:
(纸本)9781624107160
The advent of Urban Air Mobility (UAM) presents the scope for a transformative shift in the domain of urban transportation. However, its widespread adoption and economic viability depends in part on the ability to optimally schedule the fleet of aircraft across vertiports in a UAM network, under uncertainties attributed to airspace congestion, changing weather conditions, and varying demands. This paper presents a comprehensive optimization formulation of the fleet scheduling problem, while also identifying the need for alternate solution approaches, since directly solving the resulting integer nonlinear programming (INLP) problem is computationally prohibitive for daily fleet scheduling. Previous work has shown the effectiveness of using (graph) reinforcement learning (RL) approaches to train real-time executable policy models for fleet scheduling. However, such policies can often be brittle on out-of-distribution scenarios or edge cases. Moreover, training performance also deteriorates as the complexity (e.g., number of constraints) of the problem increases. To address these issues, this paper presents an imitation learning approach where the RL-based policy exploits expert demonstrations yielded by solving the exact optimization using a Genetic Algorithm. The policy model comprises Graph Neural Network (GNN) based encoders that embed the space of vertiports and aircraft, Transformer networks to encode demand, passenger fare and transport cost profiles, and a Multi-head attention (MHA) based decoder. Expert demonstrations are used through the Generative Adversarial Imitation Learning (GAIL) algorithm. Interfaced with a UAM simulation environment involving 8 vertiports and 40 aircrafts, in terms of the daily profits earned reward, the new imitative approach achieves better mean performance and remarkable improvement in the case of unseen worst-case scenarios, compared to pure RL results.
We guarantee the strong duality and the existence of a saddle point of the hyperbolic augmented Lagrangian function (HALF) in convex optimization. To guarantee these results, we assume a set of convexity hypothesis an...
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We guarantee the strong duality and the existence of a saddle point of the hyperbolic augmented Lagrangian function (HALF) in convex optimization. To guarantee these results, we assume a set of convexity hypothesis and the Slater condition. Finally, we computationally illustrate our theoretical results obtained in this work.
This paper introduces an approach for synthesizing feasible safety indices to derive safe control laws under state-dependent control spaces. The problem, referred to as Safety Index Synthesis (SIS), is challenging bec...
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ISBN:
(纸本)9798350382662;9798350382655
This paper introduces an approach for synthesizing feasible safety indices to derive safe control laws under state-dependent control spaces. The problem, referred to as Safety Index Synthesis (SIS), is challenging because it requires the existence of feasible control input in all states and leads to an infinite number of constraints. The proposed method leverages Positivstellensatz to formulate SIS as a nonlinear programming (NP) problem. We formally prove that the NP solutions yield safe control laws with two imperative guarantees: forward invariance within user-defined safe regions and finite-time convergence to those regions. A numerical study validates the effectiveness of our approach.
The mitigation of the energy crisis necessitates the exploration of alternative sources, including hydrokinetic energy derived from downstream regions of hydroelectric facilities. In this context, harnessing the deflu...
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ISBN:
(纸本)9783031530357;9783031530364
The mitigation of the energy crisis necessitates the exploration of alternative sources, including hydrokinetic energy derived from downstream regions of hydroelectric facilities. In this context, harnessing the defluent flow from hydroelectric plants through hydrokinetic turbines has become increasingly vital. This study aims to develop a comprehensive model that furnishes essential parameters for the design of hydrokinetic turbines positioned downstream of dams. The model comprises two key modules: a module for predicting remaining energy and defluent flow, and a module for optimizing reservoir operation. The first module employs a Multi-Layer Perceptron (MLP) model with Backpropagation (MLP-BP) and integrates Autoregressive Integrated Moving Average (ARIMA) models. The second module leverages non-linear programming optimization techniques and advanced process modeling. This module ensures efficient reservoir operation by optimizing generation and defluent flow in hydroelectric plants. It enables sustainable operational simulations, capable of minimizing conflicts arising from periods of flood, drought, and high-energy demands. The results demonstrate the model's fundamental significance in both the design and operation of hydrokinetic turbines installed downstream of hydroelectric plants. It enables the optimization of generation and defluent flow, even during challenging conditions, while facilitating sustainable operational simulations that mitigate conflicts of use. The developed model thus emerges as a crucial tool in enhancing the efficiency and sustainability of hydroelectric power generation.
The surgical services provided in the operating rooms of the hospital are an essential part of the healthcare system. These services are usually life-threatening and time-sensitive, and require highly trained surgeons...
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ISBN:
(纸本)9798350371635;9798350371628
The surgical services provided in the operating rooms of the hospital are an essential part of the healthcare system. These services are usually life-threatening and time-sensitive, and require highly trained surgeons and staff, as well as the latest medical equipment. Furthermore, because of the high cost of these resources, hospitals can have only a limited number of operating rooms and staff members. Thus, it is crucial to optimize various aspects of operating room functions to maximize overall utilization. This survey summarizes various optimization models proposed in the literature for such problems faced in operating rooms. The goal of this work is to provide researchers with a guide for further research in the field. Methods: This survey includes articles from Pubmed, since 2010. The search queries were related to the terms scheduling operating room, optimization model, and queuing. More than 400 articles were found, and the authors filtered the articles based on their relevance to this survey. The analysis found that a) the studies are usually very specific to optimizing a particular problem related to the operating room, b) datasets are not available in the literature and it is difficult to conduct comparative analysis, similarly c) the source code is not available on publicly available repositories like GitHub, and d) it is difficult to replicate the studies and establish benchmarks.
This paper demonstrates the scalability of open-source GPU-accelerated nonlinear programming (NLP) *** and ***-for solving multiperiod alternating current (AC) optimal power flow (OPF) problems on GPUs with high memor...
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ISBN:
(纸本)9798350384697;9798350384680
This paper demonstrates the scalability of open-source GPU-accelerated nonlinear programming (NLP) *** and ***-for solving multiperiod alternating current (AC) optimal power flow (OPF) problems on GPUs with high memory capacities (e.g., NVIDIA GH200 with 480 GB of unified memory). There has been a growing interest in solving multi-period AC OPF problems, as the increasingly fluctuating electricity market requires operation planning over multiple periods. These problems, formerly deemed intractable, are now becoming technologically feasible to solve thanks to the advent of high-memory GPU hardware and accelerated NLP tools. This study evaluates the capability of these tools to tackle previously unsolvable multi-period AC OPF instances. Our numerical experiments, run on an NVIDIA GH200, demonstrate that we can solve a multi-period OPF instance with more than 10 million variables up to 10(-4) precision in less than 10 minutes. These results demonstrate the efficacy of the GPU-accelerated NLP frameworks for the solution of extreme-scale multi-period OPF. We provide ***, an open-source modeling tool for multi-period AC OPF models for GPUs.
The aim of this paper is to study optimality conditions for differentiable linearly constrained pseudoconvex programs. The stated results are based on new transversality conditions which can be used instead of complem...
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The aim of this paper is to study optimality conditions for differentiable linearly constrained pseudoconvex programs. The stated results are based on new transversality conditions which can be used instead of complementarity ones. Necessary and sufficient optimality conditions are stated under suitable generalized convexity properties. Moreover, two different pairs of dual problems are proposed and weak and strong duality results proved. Finally, it is shown how transversality conditions can be applied to characterize optimality of convex quadratic problems and to efficiently solve a particular class of Max-Min problems
Recently, an increasing demand for low-latency tasks such as VR/AR necessitates stringent latency requirements. Traditionally, low-latency tasks have been offloaded to base stations (BSs) with superior computing capab...
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Recent developments inefficient, large-scale nonlinear optimization strategies have had significants impact on the design and operation of engineering systems with equation-oriented (EO) models. On the other hand, rig...
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Recent developments inefficient, large-scale nonlinear optimization strategies have had significants impact on the design and operation of engineering systems with equation-oriented (EO) models. On the other hand, rigorous first-principle procedural (i.e., black-box 'truth') models maybe difficult to incorporate directly within this optimization framework. Instead, black-box models are often substituted by lower fidelity surrogate models that may compromise the optimal solution. To overcome these challenges, Trust Region Filter (TRF) methods have been developed, which combine surrogate models optimization with intermittent sampling of truth models. The TRF approach combines efficient solution strategies with minimal recourse to truth models, and leads to guaranteed convergence to the truth model optimum. This survey paper provides a perspective on the conceptual development and evolution of the TRF method along with a review of applications that demonstrate the effectiveness of the TRF approach. In particular, three cases studies are presented on flowsheet optimization with embedded CFD models for advanced power plants and CO2 capture processes, as well as synthesis of heat exchanger networks with detailed finite-element equipment models.
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