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 reduct...
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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.
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 dy...
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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.
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, quan...
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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.
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 netwo...
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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 feasib...
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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.
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 inf...
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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.
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 syste...
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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 t...
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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.
Low-rank problems are nonlinear minimization problems in which the objective function, by means of a suitable linear transformation of the variables, depends on very few variables. These problems often arise in quanti...
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Low-rank problems are nonlinear minimization problems in which the objective function, by means of a suitable linear transformation of the variables, depends on very few variables. These problems often arise in quantitative management science applications, for example, in location models, transportation problems, production planning, data envelopment analysis and multiobjective programs. They are usually approached by means of outer approximation, branch and bound, branch and select and optimal level solution methods. The paper studies, from both a theoretical and an algorithmic point of view, a class of large-dimension rank-two nonconvex problems having a polyhedral feasible region and f (x) = phi(c(T) x+c(0), d(T) x+d(0)) as the objective function. The proposed solution algorithm unifies a new partitioning method, an outer approximation approach and a mixed method. The results of a computational test are provided to compare these three approaches with the optimal level solutions method. In particular, the new partitioning method performs very well in solving large problems.
Dynamical environments around small celestial bodies are complex and uncertain, leading to highly perturbed, uncertain orbital motions in their proximity. Under such complexity and uncertainty, mission designers need ...
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Dynamical environments around small celestial bodies are complex and uncertain, leading to highly perturbed, uncertain orbital motions in their proximity. Under such complexity and uncertainty, mission designers need to plan robust guidance and control of the spacecraft orbit to meet some requirements derived from their mission objectives such as precise science observation campaigns. To develop a robust planner for spacecraft guidance under uncertainty, this paper presents a stochastic optimal control approach to design robust guidance policies that minimize the expected control effort while ensuring the requirement satisfaction with a user-defined confidence level, i.e., chance constraints. The solution method is formulated as a two-stage optimization framework that consists of a convex programming stage, followed by a nonlinear programming stage. The developed framework is applied to a small-body global-mapping scenario on a science orbit around asteroid Bennu, demonstrating the robustness of the optimized guidance policies;the stochastic orbital states are controlled to meet science requirements to 99.9% confidence over 31 days with minimum control cost. Although the developed framework is demonstrated in a small-body global-mapping scenario, it is independent from specific equations of motion, and hence applicable to other proximity operation scenarios as well.
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