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The Shortest Path Interdiction Problem with Randomized Interdiction Strategies: Complexity and Algorithms

OPERATIONS RESEARCH 2021年第1期69卷 82-99页

作者： Holzmann, Tim Smith, J. Cole US Air Force Dept Operat Sci Inst Technol Dayton OH 45433 USA Syracuse Univ Dept Elect Engn & Comp Sci Syracuse NY 13244 USA

Shortest-path interdiction problems involve a leader and a follower playing a zero-sum game over a directed network. The leader interdicts a set of arcs, and arc costs increase as a function of the number of times they are interdicted. The follower observes the leader's actions and selects a shortest path in response. The leader's optimal interdiction strategy maximizes the follower's minimum-cost path. In classic formulations of these problems, the leader's interdiction actions are deterministic. In this paper the leader selects a policy of randomized interdiction actions, and the follower only knows the probability of where interdictions are deployed on the network. The follower identifies a path having the minimum expected cost, whereas the leader seeks to maximize the follower's objective. When the arc costs are affine functions of the number of times they are interdicted, this problem is solvable by linear programming. However, when the cost functions are convex or when they are concave, we show that the expected costs are Schur concave or convex, respectively. This property allows us to prove that the problem becomes strongly NP-hard in the nonaffine case. We also propose several algorithms for this problem. Some are for special cases, and one is a general algorithm. We examine the efficacy of our algorithms on a test bed of randomly generated instances by comparing our algorithms to a standard solver.

关键词： networks/graphs nonlinear programming military Schur convexity

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Real-Time Guidance for Low-Thrust Transfers Using Deep Neural Networks

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2021年第2期44卷 315-327页

作者： Izzo, Dario Ozturk, Ekin ESA European Space Res & Technol Ctr Adv Concepts Team NL-2201 AZ Noordwijk Netherlands

We consider the Earth-Venus mass-optimal interplanetary transfer of a low-thrust spacecraft and show that the optimal guidance can be represented by deep networks in a large portion of the state space. This opens up the possibility to compute the guidance profile continuously on board the spacecraft, circumventing all convergence issues associated to optimal solvers, and thus constituting a valid alternative to solutions based on the convexification of the underlying optimal control problem. A new general methodology called "backward generation of optimal examples" is proposed to create the data necessary to train the artificial neural networks. With respect to previous works, our databases contain orders of magnitude more optimal trajectories. Several schemes to train representations of either the optimal policy (thrust profile) or the value function (optimal mass) are proposed and tested. We find that they accurately approximate the optimal thrust and that a spacecraft employing these networks would be able to reach the target conditions using only 2% more propellant than in the corresponding mathematically optimal transfer. All networks trained are tested during simulations of interplanetary transfers with respect to their ability to reach optimally the target conditions starting from nominal and off-nominal conditions.

关键词： Artificial Neural Network Thrust Hamilton Jacobi Bellman Equation Propellant Earth Powered Descent Guidance Astronomical Unit nonlinear programming International Celestial Reference Frame Stochastic Gradient Descent

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Spacing Optimization of Distributed MIMO-SAR Satellites Based on Improved Genetic Algorithm

Spacing Optimization of Distributed MIMO-SAR Satellites Base...

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2022 International Conference on Computer, Artificial Intelligence, and Control Engineering, CAICE 2022

作者： Zhaoke, Wang Feng, He Zaoyu, Sun College of Electronic Science and Technology National University of Defense Technology Changsha410073 China

ISBN: (纸本)9781510655942

In the design of distributed MIMO-SAR systems, the optimization of the satellite spacing along track is an important prerequisite for achieving the task of high resolution and wide swath. From the perspective of system performance optimization， this paper takes the along-track distance between adjacent satellites and PRF is used as an optimization variable, while considering the change of the vertical track baseline, combining genetic algorithm and nonlinear programming to obtain a global optimal solution. A method of optimizing the satellite spacing along track based on improved genetic algorithm is proposed and verified by simulation the correctness of the optimization method. The indicators and methods given in this article are of great significance for guiding the structural design of formation satellite systems and improving the performance of high resolution and wide swath measurement of SAR along track. © 2022 SPIE.

关键词： nonlinear programming

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Obstacle Avoidance for Unmanned Aerial Vehicle Trajectory Planning Using Virtual Convex Projection Technique

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2021年第3期45卷 558-569页

作者： Zhao, Zichen Shang, Haibin Dong, Yue Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China Beijing Inst Technol Key Lab Dynam & Control Flight Vehicle Beijing 100081 Peoples R China

A study demonstrates the development of a convex-optimization-based method that can ensure a solution without relying on successive iterations and initialization. This is achieved by a three-step solution space reduction technique that reformulates the original problem as a convex optimization problem and ensures that its solution is feasible for the original problem. The first step is similar to the standard way to initialize s sequential convex programming (SCP) in many studies, where the trajectory planning problem without considering avoidance-related constraints is constructed and solved to obtain the optimal trajectory in an obstacle-free environment, called the virtual trajectory. A series of virtual directions of control are generated to describe desirable controlling directions to drive the UAV to move away from the obstacles according to the geometric relationship between the obstacles and time-varying positional information of the UAV.

关键词： UAV Obstacle Avoidance nonlinear programming Multirotor Fuel Consumption Search Algorithm Computing Attitude Stabilization Numerical Simulation Damage Assessment

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Optimization for Multitarget, Multispacecraft Impulsive Rendezvous Considering J2 Perturbation

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2021年第10期44卷 1811-1822页

作者： Chen, Shiyu Jiang, Fanghua Li, Haiyang Baoyin, Hexi Tsinghua Univ Sch Aerosp Engn Beijing 100084 Peoples R China

Optimization for active debris removal using multiple spacecraft is investigated. The main challenge is to determine the rendezvous sequences of the targets considering the J(2) perturbation, which is a large-scale dynamic combinatorial optimization problem. A framework to solve this problem is presented. First, a semi-analytical method of fast estimation for characteristic velocity is proposed to help construct the sequences. The K-medoid method is applied to distribute all the targets to multiple spacecraft so that each spacecraft can remove as many targets as possible with limited propellant. Given a distribution of targets, the sequences for each spacecraft are searched separately;thus the original combinatorial optimization problem is split into multiple small-scale ones that can be efficiently solved by tree search algorithms. An evolutionary algorithm nested with a tree search algorithm is proposed to improve the distribution of the targets, so that the spacecraft can remove all the targets with a low cost. Then optimal sequences are further searched using an ant colony optimization algorithm, and the rendezvous epochs are refined by a nonlinear programming algorithm. The efficiency of these methods is demonstrated by two scenarios of active debris removal.

关键词： Propellant Characteristic Velocity nonlinear programming Particle Swarm Optimization Search Algorithm Ant Colony Optimization Algorithms Trajectory Optimization Earth Orbital Elements Orbital Period

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A mixed integer nonlinear multiperiod model for supply chain management of a company in the retail sector

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RAIRO-OPERATIONS RESEARCH 2021年第2期55卷 997-1013页

作者： Teixeira, Ana Costa e Silva, Eliana Lopes, Cristina Politecn Porto ESTG CIICESI Felgueiras Portugal Polytech Porto ISCAP CEOS PP Sao Mamede De Infesta Portugal

The fluctuations in the business environment and seasonal variations characteristic of food supply chains contribute greatly to the increasing complexity of the entire Supply Chain planning. In the present paper, quantitative models are applied to support the decision-making purchasing management department of a retail company. Specifically, a multiperiod mathematical model was developed with the aim of optimizing decision-making of the purchasing managers. The developed model consists of a multiperiod Mixed Integer nonlinear programming model, with the objective to minimize the ratio between how much is costing the company to move the products along the Supply Chain and the products' costs. It is discussed how to order the product, what is the most advantageous storage mode and whether it is preferable to order once or twice a week. Real instances, provided by a Portuguese retail company, regarding the demand for one year are tested for two scenarii, which are used currently by the company. The results show that the proposed model can reduce, on both scenarios, the ratio between operational costs and merchandise costs, for almost all products, and therefore it can be an important tool for supporting decision-making of the purchasing manager.

关键词： Supply chain management nonlinear programming purchasing distribution logistics

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Cooperative Resource Allocation for NOMA-MEC Multi-Cell Network

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IEEE Transactions on Vehicular Technology 2025年

作者： Cai, Yujin Zhang, Zaichen Huang, Yongming Yu, Wenwu Nie, Xiaokai Liu, Hongzhe Southeast University School of Mathematics Jiangsu Nanjing211189 China Southeast University National Mobile Communications Research Laboratory Nanjing211189 China Purple Mountain Laboratories Nanjing211111 China Southeast University School of Automation Key Laboratory of Measurement and Control of Complex Systems of Engineering Ministry of Education Nanjing210096 China Southeast University Shenzhen Research Institute Shenzhen518057 China

Integrating non-orthogonal multiple access (NOMA) and mobile edge computing (MEC) enables IoT nodes to offload their complicated tasks to MEC servers. Most of the existing resource allocation schemes in NOMA-MEC networks are based on the centralized optimization framework, which may increase the communicational and computational burden on the central unit. In this paper, the NOMA-MEC multi-cell network without the central unit is considered. To minimize the task completion time and offloading cost, a joint optimization problem including sub-channel allocation, transmit power, offloaded proportions, computing frequencies of IoT nodes and MEC servers, and price of MEC resources is investigated. In order to tackle the formulated mixed integer nonlinear programming problem, a two-stage low-complexity distributed algorithm based on the cooperation of all base stations (BSs) is proposed. Specifically, in Stage 1, a distributed heuristic sub-channel allocation algorithm is designed based on the sub-channel gains. In Stage 2, with the obtained sub-channel allocation result, a cooperative distributed continuous variable optimization algorithm is devised based on the distributed optimization and alternating optimization methods. Numerical results demonstrate the convergence of the proposed two-stage algorithm for three interference cases. Besides, the impacts of system parameters and schemes on the network performance are analyzed. More importantly, the resource allocation time can be significantly shortened by employing the cooperation of BSs compared with the centralized algorithm © 1967-2012 IEEE.

关键词： nonlinear programming

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A SOCP Relaxation for Cycle Constraints in the Optimal Power Flow Problem

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IEEE TRANSACTIONS ON SMART GRID 2021年第2期12卷 1663-1673页

作者： Soofi, Arash Farokhi Manshadi, Saeed D. Liu, Guangyi Dai, Renchang San Diego State Univ Dept Elect & Comp Engn San Diego CA 92182 USA Global Energy Interconnect Res Inst North Amer Graph Comp & Grid Modernizat San Jose CA 95134 USA

This article presented a convex relaxation approach for the optimal power flow problem. The proposed approach leveraged the second-order cone programming (SOCP) relaxation to tackle the non-convexity within the feasible region of the power flow problem. Recovering an optimal solution that is feasible for the original non-convex problem is challenging for networks with cycles. The main challenge is the lack of convex constraints to present the voltage angles within a cycle. This article aims to fill this gap by presenting a convex constraint enforcing the sum of voltage angles over a cycle to be zero. To this end, the higher-order moment relaxation matrix associated with each maximal clique of the network is formed. The elements of this matrix are utilized to form a convex constraint enforcing the voltage angle summation over each cycle. To keep the computation burden of leveraging the higher-order moment relaxation low, a set of second-order cone constraints are applied to relate the elements of the higher-order moment relaxation matrix. The case study presented the merit of this work by comparing the solution procured by the introduced approach with other relaxation schemes.

关键词： Reactive power programming Relaxation methods Sparse matrices Three-dimensional displays Electronic mail Optimization Optimal power flow convex relaxation angle recovery second-order cone programming nonlinear programming

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Bi-level programming for Stackelberg Game with Intuitionistic Fuzzy Number: a Ranking Approach

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Journal of the Operations Research Society of China 2021年第1期9卷 131-149页

作者： Sumit Kumar Maiti Sankar Kumar Roy School of Applied Sciences and Humanities Haldia Institute of TechnologyPurba MidnaporeWB 721657India Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeWB 721102India

This paper introduces a ranking function procedure on a bi-level programming for Stackelberg game involving intuitionistic fuzzy *** fuzzy num-ber is considered in many real-life situations,so it makes perfect sense to address decision-making problem by using some specified intuitionistic fuzzy *** this paper,intuitionistic fuzziness is characterized by a normal generalized triangular intuitionistic fuzzy number.A defuzzification method is introduced based on the pro-portional probability density function associated with the corresponding membership function,as well as the complement of non-membership *** the proposed ranking technique,a methodology is presented for solving bi-level programming for Stackelberg *** application example is provided to demonstrate the applica-bility of the proposed methodology,and the achieved results are compared with the existing methods.

关键词： Bi-levelprogramming Triangular intuitionistic fuzz ynumber Ranking function nonlinear programming Optimal solution

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A conjecture on a continuous optimization model for the Golomb Ruler Problem

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RAIRO-OPERATIONS RESEARCH 2021年第4期55卷 2241-2246页

作者： Duxbury, Phil Lavor, Carlile de Salles-Neto, Luiz Leduino Michigan State Univ Nat Sci Bldg288 Farm Lane E Lansing MI 48824 USA Univ Campinas IMECC Unicamp Campinas Brazil Univ Fed Sao Paulo Sci & Technol Inst Sao Jose Dos Campos Brazil

A Golomb Ruler (GR) is a set of integer marks along an imaginary ruler such that all the distances of the marks are different. Computing a GR of minimum length is associated to many applications (from astronomy to information theory). Although not yet demonstrated to be NP-hard, the problem is computationally very challenging. This brief note proposes a new continuous optimization model for the problem and, based on a given theoretical result and some computational experiments, we conjecture that an optimal solution of this model is also a solution to an associated GR of minimum length.

关键词： nonlinear programming Golomb Ruler Problem continuous models

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