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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

A systematic route to subcritical dynamo branches

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arXiv 2021年

作者： Mannix, Paul M. Ponty, Yannick Marcotte, Florence Université Côte d'Azur Inria CNRS LJAD France Université Côte d'Azur CNRS Observatoire de la Côte d'Azur Laboratoire Lagrange France

We demonstrate that the nonlinear optimisation of a finite-amplitude disturbance over a freely evolving and possibly even turbulent flow, can successfully identify subcritical dynamo branches as well as the structure and amplitude of their critical perturbations. As this approach does not require prior knowledge of the magnetic field amplification mechanisms, it opens a new avenue for systematically probing subcritical dynamo flows. Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

Equivalent circuit programming for power flow analysis and optimization

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arXiv 2021年

作者： Jereminov, Marko Pileggi, Larry Pearl Street Technologies PittsburghPA15206 United States Dept. of Elect. and Comp. Eng. Carnegie Mellon University PittsburghPA15213 United States

The utility of domain-specific knowledge for modeling, simulation, and optimization has been demonstrated for various research problem domains, including power systems. The concept of Equivalent Circuit programming was previously developed and facilitated for robust, efficient, and scalable solution of network simulation and optimization problems. This paper extends the theoretical foundation of Equivalent Circuit programming to enable the fusion of optimization theory and algorithms with the numerical methods that utilize the domainspecific knowledge of power flow models. The generality, scalability, and numerical robustness of the resulting framework are demonstrated on realistic AC power flow (ACPF) models of up to 70k buses with proper enforcement of industry-required operational and security constraints. Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

The direct shooting method is a complete method

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arXiv 2021年

作者： Zhang, Sheng Huang, Jiang-Tao The Computational Aerodynamics Institution China Aerodynamics Research and Development Center Mianyang621000 China

The direct shooting method is a classic approach for the solution of Optimal Control Problems (OCPs). It parameterizes the control variables and transforms the OCP to the nonlinear programming (NLP) problem to solve. This method is easy to use and it often introduces less parameters compared with all-variable parameterization method like the Pseudo-spectral (PS) method. However, it is long believed that its solution is not guaranteed to satisfy the optimality conditions of the OCP and the costates are not available in using this method. In this paper, we show that the direct shooting method may also provide the costate information, and it is proved that both the state and the costate solutions converge to the optimal as long as the control variable tends to the optimal, while the parameterized control may approach the optimal control with reasonable parameterization. This gives us the credit for the optimal control computation when employing the direct shooting method. © 2021, CC BY.

关键词： nonlinear programming

NichtnegativstellensÄtze for definable functions in o-minimal structures

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arXiv 2021年

作者： Dinh, Si-Tiêp Pham, Tiêén-Son Institute of Mathematics VAST 18 Hoang Quoc Viet Road Cau Giay District Hanoi10307 Viet Nam Department of Mathematics Dalat University 1 Phu Dong Thien Vuong Dalat Viet Nam

This paper addresses to Nichtnegativstellensätze for definable functions in o-minimal structures on (R, +, ·). Namely, let f, g1, . . ., gl: Rn → R be definable Cp-functions (p ≥ 2) and assume that f is non-negative on S:= {x ∈ Rn | g1(x) ≥ 0, . . ., gl(x) ≥ 0}. Under some natural hypotheses on zeros of f in S, we show that f is expressible in the form f = φ0 + Pli=1 φigi, where each φi is a sum of squares of definable Cp-2-functions. As a consequence, we derive global optimality conditions which generalize the Karush–Kuhn–Tucker optimality conditions for nonlinear optimization. Copyright © 2021, The Authors. All rights reserved.

关键词： nonlinear programming

Interference identification for time-varying polyhedra

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TechRxiv

TechRxiv 2021年

作者： Bienkowski, Adam Sidoti, David Pattipati, Krishna R. Department of Electrical and Computer Engineering University of Connecticut StorrsCT United States Naval Research Laboratory MontereyCA United States

Identification of when and where moving areas intersect is an important problem in maritime operations and air traffic control. This problem can become particularly complicated when considering large numbers of objects, and when taking into account the curvature of the earth. In this paper, we present an approach to conflict identification as a series of stages where the earlier stages are fast, but may result in a false detection of a conflict. These early stages are used to reduce the number of potential conflict pairs for the later stages, which are slower, but more precise. Our approach is generally applicable to objects moving in piece-wise straight lines on a 2D plane, and we present a specific case where the Mercator Projection is used to transform objects moving along rhumb lines on the earth into straight lines to fit in our approach. We present several examples to demonstrate our methods, as well as to quantify the empirical time complexity by using randomly generated areas. © 2021, CC BY-NC-SA.

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

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

Numerical performance of different formulations for alternating current optimal power flow

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TechRxiv

TechRxiv 2021年

作者： Sadat, Sayed Abdullah Kim, Kibaek Mathematics and Computer Science Division Argonne National Laboratory The U.S. Department of Energy LemontIL60439 United States

Alternating current optimal power flow (ACOPF) problems are nonconvex and nonlinear optimization problems. Utilities and independent service operators (ISO) require ACOPF to be solved in almost real time. Interior point methods (IPMs) are one of the powerful methods for solving large-scale nonlinear optimization problems and are a suitable approach for solving ACOPF with large-scale real-world transmission networks. Moreover, the choice of the formulation is as important as choosing the algorithm for solving an ACOPF problem. In this paper, different ACOPF formulations with various linear solvers and the impact of employing box constraints are evaluated for computational viability and best performance when using IPMs. Different optimization structures are used in these formulations to model the ACOPF problem representing a range of sparsity. The numerical experiments suggest that the least sparse ACOPF formulations with polar voltages yield the best computational results. Additionally, nodal injected models and current-based branch flow models are improved by enforcing box constraints. 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