This research introduces a novel approach to optimize the distribution of relief items in post-disaster scenarios. Unlike traditional approaches, the model integrates dynamic demand and supply considerations, accounti...
详细信息
This research introduces a novel approach to optimize the distribution of relief items in post-disaster scenarios. Unlike traditional approaches, the model integrates dynamic demand and supply considerations, accounting for fluctuations in population movement within relief camps. The model uniquely incorporates the impact of disaster severity and risk on transportation costs, enabling a more realistic assessment of logistical challenges. By minimizing total costs, including transportation, inventory, and disposal of damaged items, our approach ensures cost-efficient distribution without compromising service delivery levels. A numerical example with a post-disaster relief distribution scenario demonstrates the model's practical application. Sensitivity analysis with multiple parameters confirms the model's robustness and potential to guide efficient and effective humanitarian relief operations. This study contributes to the field of relief chain optimization by offering a comprehensive framework that accounts for several factors influencing disaster logistics. The research highlights the model's potential as a valuable tool for improving the efficiency and effectiveness of humanitarian relief efforts.
Optimization plays a critical role in fields such as economics, engineering, and computational sciences, where finding the optimal values of decision variables is essential for the design of a product, production syst...
详细信息
Optimization plays a critical role in fields such as economics, engineering, and computational sciences, where finding the optimal values of decision variables is essential for the design of a product, production system, or service system. However, many optimization problems remain challenging even with advanced solvers. This study integrates machine learning into optimization by employing a regression tree algorithm that is trained on sampled solutions of the problem to improve the efficiency of derivative-free nonlinear programming solvers. The approach is tested on 24 single-objective functions to reduce the domain of decision variables. The results demonstrate better accuracy and consistency in the solver performance. Incorporating a machine learning technique into an optimization method can be extended to solve black-box optimization problems and paves the way for innovative solutions in engineering design and other domains.
This article presents a nonlinear programming algorithm for finite element limit analysis (FELA) based on feasible arc searching technique (FAST). The proposed algorithm has the potential to significantly reduce the i...
详细信息
This article presents a nonlinear programming algorithm for finite element limit analysis (FELA) based on feasible arc searching technique (FAST). The proposed algorithm has the potential to significantly reduce the iteration numbers required for convergence, making it a valuable tool for solving complex optimization problems from FELA. The algorithm also introduces several new features to the existing methods, including: (i) a novel method for determining a reasonable updating step length;(ii) the avoidance of solving an additional "phase one problem" for finding an initial feasible point;and (iii) the proposition of an empirical criterion for detecting infeasibility problems. The effectiveness of the proposed approach has been demonstrated through several classic examples derived from geotechnical engineering. The initial two examples show the superior convergence speed of the novel approach compared to existing methods. Additionally, the third example highlights the efficacy of the feasibility detection criterion for problems involving both prescribed and unknown external forces.
CNC lathes often use hydraulic systems or motors to lock the turret, which causes the turret to have a high temperature rise and a large thermal deformation. The traditional measuring method couples the thermal distor...
详细信息
CNC lathes often use hydraulic systems or motors to lock the turret, which causes the turret to have a high temperature rise and a large thermal deformation. The traditional measuring method couples the thermal distortions of the spindle and the turret together, which is not conducive to establishing the thermal error model. To solve this problem, a new measuring method was used in this research to decouple the thermal linear and angular distortions of the spindle and the turret. In addition, constraints on the model coefficients were proposed by studying the effects of long-term and short-term variations in ambient temperature on the thermal deformation of machine tools, thus transforming the thermal deformation modeling of the spindle and turret into nonlinear programming problems. After building the thermal deformation models of the spindle and the turret, the thermal distortion model of the whole machine tool was obtained by combining them. Finally, three experiments were designed to verify the validity of the established models, and the models were compared with those established using conventional methods. The experimental results showed that the models built based on thermal distortion decoupling and nonlinear programming had higher accuracy and robustness.
We consider solving high-order and tight semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the S...
详细信息
We consider solving high-order and tight semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new algorithmic framework that blends local search using the nonconvex POP into global descent using the convex SDP. In particular, we first design a globally convergent inexact projected gradient method (iPGM) for solving the SDP that serves as the backbone of our framework. We then accelerate iPGM by taking long, but safeguarded, rank-one steps generated by fast nonlinear programming algorithms. We prove that the new framework is still globally convergent for solving the SDP. To solve the iPGM subproblem of projecting a given point onto the feasible set of the SDP, we design a two-phase algorithm with phase one using a symmetric Gauss-Seidel based accelerated proximal gradient method (sGS-APG) to generate a good initial point, and phase two using a modified limited-memory BFGS (L-BFGS) method to obtain an accurate solution. We analyze the convergence for both phases and establish a novel global convergence result for the modified L-BFGS that does not require the objective function to be twice continuously differentiable. We conduct numerical experiments for solving second-order SDP relaxations arising from a diverse set of POPs. Our framework demonstrates state-of-the-art efficiency, scalability, and robustness in solving degenerate SDPs to high accuracy, even in the presence of millions of equality constraints.
In this paper, we construct a new spline smoothing homotopy method for solving general nonlinear programming problems with a large number of complicated constraints. We transform the equality constraints into the ineq...
详细信息
In this paper, we construct a new spline smoothing homotopy method for solving general nonlinear programming problems with a large number of complicated constraints. We transform the equality constraints into the inequality constraints by introducing two parameters. Subsequently, we use smooth spline functions to approximate the inequality constraints. The smooth spline functions involve only few inequality constraints. In other words, the method introduces an active set technique. Under some weaker conditions, we obtain the global convergence of the new spline smoothing homotopy method. We perform numerical tests to compare the new method to other methods, and the numerical results show that the new spline smoothing homotopy method is highly efficient.
The volume of data is increasing rapidly, which poses a great challenge for resource-constrained users to process and analyze. A promising approach for solving computation-intensive tasks over big data is to outsource...
详细信息
The volume of data is increasing rapidly, which poses a great challenge for resource-constrained users to process and analyze. A promising approach for solving computation-intensive tasks over big data is to outsource them to the cloud to take advantage of the cloud's powerful computing capability. However, it also brings privacy and security issues since the data uploaded to the cloud may contain sensitive and private information which should be protected. In this article, we address this problem and focus on the privacy-preserving and secure outsourcing of large-scale nonlinear programming problems (NLPs) subject to both linear constraints and nonlinear constraints. Large-scale NLPs play an important role in the field of data analytics but have not received enough attention in the context of cloud computing. In our outsourcing protocol, we first apply a secure and efficient transformation scheme at the client side to encrypt the private information of the considered NLP. Then, we use the reduced gradient method and generalized gradient method at the server side to solve the transformed large-scale NLPs under linear constraints and nonlinear constraints, respectively. We provide security analysis of the proposed protocol, and evaluate its performance via a series of experiments. The experimental results show that our protocol can efficiently solve large-scale NLPs and save much time for the client, providing a great potential for real applications.
In this article, we present generalizations of the cone-preinvexity functions and study a pair of second-order symmetric solutions for multiple objective nonlinear programming problems under these generalizations of t...
详细信息
In this article, we present generalizations of the cone-preinvexity functions and study a pair of second-order symmetric solutions for multiple objective nonlinear programming problems under these generalizations of the cone-preinvexity functions. In addition, we establish and prove the theorems of weak duality, strong duality, strict converse duality, and self-duality by assuming the skew-symmetric functions under these generalizations of the cone-preinvexity functions. Finally, we provide four nontrivial numerical examples to demonstrate that the results of the weak and strong duality theorems are true.
The polyester fiber spinning process is extensive, and the involved dynamic models are complex and difficult to solve analytically. This paper presents the optimal control strategy of polyester fiber production. Based...
详细信息
ISBN:
(纸本)9781665478960
The polyester fiber spinning process is extensive, and the involved dynamic models are complex and difficult to solve analytically. This paper presents the optimal control strategy of polyester fiber production. Based on a dynamic model of the spinning process, optimal objectives are determined to minimize production costs and meet production goals. We employ Radau collocation on finite elements to discretize the continuous dynamic model, which is transformed into finite-dimensional nonlinear programming (NLP) model. The developed strategy combines a multiple shot algorithm and half-score method to solve the obtained NLP model. We find the best initial values quickly and achieve the control objective under the constraints of the spinning process's mechanism equations. The objective function measures the difference between the actual production and the desired value, and the merit of the objective function directly affects the control variables. In this paper, single-objective and multi-objective control strategies are designed according to different production requirements. To make the objective function effectively reflect the product quality, its setting is inseparable from each state variable, and we explore the control effect for different objective functions. Finally, simulation results verify the feasibility and superiority of the orthogonal collocation on finite element and multiple shooting algorithms.
Direct optimal control techniques, relying on numerical methods for constrained optimization, are typically used in trajectory planning tasks in high-dimensional spaces. However, general-purpose solvers often fail to ...
详细信息
Direct optimal control techniques, relying on numerical methods for constrained optimization, are typically used in trajectory planning tasks in high-dimensional spaces. However, general-purpose solvers often fail to find a feasible solution when facing cluttered environments. Sampling- or graph-based methods, instead, can explore complex configuration spaces but struggle with dynamic constraints. Here, we propose to combine dynamic programming (DP) and derivative-based methods to reliably solve trajectory planning problems. Specifically, we exploit DP to generate a sequence of waypoints in a low-dimensional space, which are then encoded as pointwise path constraints for a high-dimensional trajectory, whose constraint violations are then represented as a penalty within the Bellman equation to recompute the waypoints. This iterative approach, alternating path and trajectory optimization, avoids both the curse of dimensionality for DP and problematic nonconvexities (such as obstacles) for motion planning. We demonstrate our strategy using numerical experiments on a six-degree-of-freedom robotic manipulator moving in a confined space.
暂无评论