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Evaluating the performance of various ACOPF formulations using nonlinear interior-point method

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TechRxiv

TechRxiv 2021年

作者： Sadat, Sayed Abdullah Department of Electrical and Computer Engineering University of Utah United States

Alternating current optimal power flow (ACOPF) problem is a non-convex and a nonlinear optimization problem. Similar to most nonlinear optimization problems, ACOPF is an NP-hard problem. On the other hand, Utilities and independent service operators (ISO) require the problem to be solved in almost real-time. The real-world networks are often large in size and developing an efficient and tractable algorithm is critical to many decision-making processes in electricity markets. Interior-point methods (IPMs) for nonlinear programming are considered one of the most powerful algorithms for solving large-scale nonlinear optimization problems. However, the performance of these algorithms is significantly impacted by the optimization structure of the problem. Thus, the choice of the formulation is as important as choosing the algorithm for solving an ACOPF problem. Different ACOPF formulations are evaluated in this paper for computational viability and best performance using the interior-point line search (IPLS) algorithm. Different optimization structures are used in these formulations to model the ACOPF problem representing a range of varying sparsity. The numerical experiments suggest that the least sparse ACOPF formulation with polar voltages yields the best computational results. A wide range of test cases, ranging from 500-bus systems to 9591-bus systems, are used to verify the test results. © 2021, CC BY.

关键词： nonlinear programming

Variable reduction for quadratic unconstrained binary optimization

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arXiv 2021年

作者： Verma, Amit Lewis, Mark Craig School of Business Missouri Western State University Saint JosephMO64507 United States

Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack variables needed for conversion of inequalities. This transformation can lead to a significant increase in the size and density of the problem. Herein, we propose an efficient approach for recasting inequality constraints that reduces the number of linear and quadratic variables. Experimental results illustrate the efficacy. © 2021, CC BY.

关键词： nonlinear programming

Energy-optimal Design and Control of Electric Powertrains under Motor Thermal Constraints

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arXiv 2021年

作者： Konda, Mouleeswar Hofman, Theo Salazar, Mauro Eindhoven5600 MB Netherlands

This paper presents a modeling and optimization framework to minimize the energy consumption of a fully electric powertrain by optimizing its design and control strategies whilst explicitly accounting for the thermal behavior of the Electric Motor (EM). Specifically, we first derive convex models of the powertrain components, including the battery, the EM, the transmission and a Lumped Parameter Thermal Network (LPTN) capturing the thermal dynamics of the EM. Second, we frame the optimal control problem in time domain, and devise a two-step algorithm to accelerate convergence and efficiently solve the resulting convex problem via nonlinear programming. Subsequently, we present a case study for a compact family car, optimize its transmission design and operation jointly with the regenerative braking and EM cooling control strategies for a finite number of motors and transmission technologies. We validate our proposed models using the high-fidelity simulation software Motor-CAD, showing that the LPTN quite accurately captures the thermal dynamics of the EM, and that the permanent magnets’ temperature is the limiting factor during extended driving. Furthermore, our results reveal that powertrains equipped with a continuously variable transmission (CVT) result into a lower energy consumption than with a fixed-gear transmission (FGT), as a CVT can lower the EM losses, resulting in lower EM temperatures. Finally, our results emphasize the significance of considering the thermal behavior when designing an EM and the potential offered by CVTs in terms of downsizing. Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

A sequential approach for speed planning under jerk constraints

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arXiv 2021年

作者： Consolini, Luca Locatelli, Marco Minari, Andrea Dipartimento di Ingegneria e Architettura Università di Parma Parco Area delle Scienze Parma181/A Italy

In this paper we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration and jerk constraints. Such a problem arises in industrial contexts such as automated warehouses, where LGVs need to perform assigned tasks as fast as possible in order to increase productivity. It can be reformulated as an optimization problem with a convex objective function, linear velocity and acceleration constraints, and non-convex jerk constraints, which, thus, represent the main source of difficulty. While existing non-linear programming (NLP) solvers can be employed for the solution of this problem, it turns out that the performance and robustness of such solvers can be enhanced by the sequential line-search algorithm proposed in this paper. At each iteration a feasible direction, with respect to the current feasible solution, is computed, and a step along such direction is taken in order to compute the next iterate. The computation of the feasible direction is based on the solution of a linearized version of the problem, and the solution of the linearized problem, through an approach which strongly exploits its special structure, represents the main contribution of this work. The efficiency of the proposed approach with respect to existing NLP solvers is proved through different computational experiments. © 2021, CC BY-NC-ND.

关键词： nonlinear programming

COBALT: COnstrained Bayesian optimizAtion of computationaLly expensive grey-box models exploiting derivaTive information

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arXiv 2021年

作者： Paulson, Joel A. Lu, Congwen Department of Chemical and Biomolecular Engineering The Ohio State University ColumbusOH United States

Many engineering problems involve the optimization of computationally expensive models for which derivative information is not readily available The Bayesian optimization (BO) framework is a particularly promising approach for solving these problems, which uses Gaussian process (GP) models and an expected utility function to systematically tradeoff between exploitation and exploration of the design space BO, however, is fundamentally limited by the black-box model assumption that does not take into account any underlying problem structure In this paper, we propose a new algorithm, COBALT, for constrained grey-box optimization problems that combines multivariate GP models with a novel constrained expected utility function whose structure can be exploited by state-of-the-art nonlinear programming solvers COBALT is compared to traditional BO on seven test problems including the calibration of a genome-scale bioreactor model to experimental data Overall, COBALT shows very promising performance on both unconstrained and constrained test problems. © 2021, CC BY.

关键词： nonlinear programming

Self-encoding barnacle mating optimizer algorithm for manpower scheduling in flow shop

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arXiv 2021年

作者： Luo, Shuyun Wang, Wushuang Fang, Mengyuan Xu, Weiqiang School of Information Science and Technology Zhejiang Sci-tech University China

Flow Shop Scheduling (FSS) has been widely researched due to its application in many types of fields, while the human participant brings great challenges to this problem. Manpower scheduling captures attention for assigning workers with diverse proficiency to the appropriate stages, which is of great significance to production efficiency. In this paper, we present a novel algorithm called Self-encoding Barnacle Mating Optimizer (SBMO), which solves the FSS problem considering worker proficiency, defined as a new problem, Flow Shop Manpower Scheduling Problem (FSMSP). The highlight of the SBMO algorithm is the combination with the encoding method, crossover and mutation operators. Moreover, in order to solve the local optimum problem, we design a neighborhood search scheme. Finally, the extensive comparison simulations are conducted to demonstrate the superiority of the proposed SBMO. The results indicate the effectiveness of SBMO in approximate ratio, powerful stability, and execution time, compared with the classic and popular counterparts. Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

Finding the sequence of largest small n-polygons by numerical optimization

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arXiv 2021年

作者： Pintér, János D. Kampas, Frank J. Castillo, Ignacio Department of Management Science and Information Systems Rutgers University PiscatawayNJ United States Physicist at Large Consulting LLC Bryn MawrPA United States Lazaridis School of Business and Economics Wilfrid Laurier University WaterlooON Canada

LSP(n), the largest small polygon with n vertices, is the polygon of unit diameter that has maximal area A(n). It is known that for all odd values n ≥ 3, LSP(n) is the regular n-polygon;however, this statement is not valid for even values of n. Finding the polygon LSP(n) and A(n) for even values n ≥ 6 has been a long-standing challenge. In this work, we develop high-precision numerical solution estimates of A(n) for even values n ≥ 4, using the Mathematica model development environment and the IPOPT local nonlinear optimization solver engine. First, we present a revised (tightened) LSP model that greatly assists the efficient solution of the model-class considered. This is followed by numerical results for an illustrative sequence of even values of n, up to n ≤ 1000. Our results are in close agreement with, or surpass, the best results reported in all earlier studies. Most of these earlier works addressed special cases up to n ≤ 20, while others obtained numerical optimization results for a range of values from 6 ≤ n ≤ 100. For completeness, we also calculate numerically optimized results for a selection of odd values of n, up to n ≤ 999: these results can be compared to the corresponding theoretical (exact) values. The results obtained are used to provide regression model-based estimates of the optimal area sequence {A(n)}, for all even and odd values n of interest, thereby essentially solving the entire LSP model-class numerically, with demonstrably high precision. © 2021, CC BY.

关键词： nonlinear programming

Optimal design of a multimodal distribution network for a chemical company

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Optimal design of a multimodal distribution network for a ch...

作者： E. C. M. Van Den Broek Eindhoven University of Technology

学位级别：硕士

Motivated by the current globalization, it is beneficial for companies to have a proper distribution network that can take advantages of multi-modality. Therefore, this thesis presents a methodology to determine the optimal (re)design for a multimodal facility location problem such that the total distribution network costs are minimized. The methodology focuses on consolidating the logistic activities to one centralized distribution center from where goods are transported to the customer, which can be done directly or through a cross docking facility. In order to find the optimal locations for these facilities, two gravity studies are proposed. At first, a single-facility gravity study is presented to investigate the optimal distribution center location by minimizing the total transportation costs. Secondly, a multi-facility gravity study is presented to determine the optimal cross docking facility locations by minimizing the outbound transportation costs (from facility to customer). By using the solutions of the gravity studies, a set of possible facilities with multi-modal connection is defined. In order to determine the optimal (re)design, a multi-modal facility location problem is developed with the aim to minimize the total distribution network costs by deciding on which facilities to open and which transportation modes to use. The solution of this model depends on a given customer service lead-time.

关键词： Network Optimization Distribution network (re-)design Gravity study Multi-modal Facility Location Problem Truck-loading problem nonlinear programming Chemical industry

Resilience-based restoration sequence optimization of disrupted transportation networks: A novel matheuristic approach

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Transportation Research Part D: Transport and Environment 2025年 145卷

作者： Cui, Xinhao Li, Bo Zhang, Siyue Ji, Ziguang Wang, Shitao Luo, Rui Ren, Yi Xiao, Yiyong School of Reliability and Systems Engineering Beihang University Beijing100191 China Guangzhou511453 China

Transportation networks are crucial components of modern infrastructure but are highly vulnerable to disruptions caused by frequent, unpredictable disasters, such as earthquakes and rainstorms, which severely compromise connectivity and mobility. Developing resilient restoration plans is thus essential for minimizing disruption impacts and expediting recovery. However, existing approaches primarily depend on experience-driven or importance-based methods, which struggle to identify critical disrupted links and fail to provide optimal sequences. To tackle these challenges, this study proposes a general sequencing framework featuring multi-stage restoration modes and formulates an optimization problem as a mixed-integer nonlinear programming model. To improve computational tractability, a bipartition-based simplification strategy is introduced. Additionally, a novel matheuristic approach combining heuristic flexibility with mathematical programming precision is developed, enabling effective decision-making across diverse scenarios. The framework is validated through the Tongzhou transportation network, demonstrating its robustness and efficiency under varying disruption scenarios, offering valuable insights into resilience-based restoration. © 2025 Elsevier Ltd

关键词： nonlinear programming