Sophisticated models have progressively been developed to address the challenges related to long-term, open-pit mine planning under conditions of geological uncertainty. Prior research has acknowledged that strategies...
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Sophisticated models have progressively been developed to address the challenges related to long-term, open-pit mine planning under conditions of geological uncertainty. Prior research has acknowledged that strategies for mine planning and the design of mineral concentrators are interdependent;thus, it is highly desirable to optimize them together. However, achieving detailed holistic optimization of the entire mineral value chain remains unresolved because of the inherent limitations associated with mathematical formulations and computational processing capacity. This paper details a method that contributes to bridging these limitations by employing a novel parallelized variable neighborhood descent approach combined with an embedded mass-balance component using linear programming techniques refined through Dantzig-Wolfe decomposition. This approach is exemplified through a case study of a gold deposit, which illustrates the enhanced performance capabilities of the new algorithm. The findings demonstrate significant improvements in the optimization process for mine planning, providing a stronger link between the mine's output and processing plant's capabilities.
Upcoming large satellite constellations and the advent of tighter steerable beams will offer unprecedented flexibility. Consequently, this will require resource management strategies to be operated in high-dimensional...
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Upcoming large satellite constellations and the advent of tighter steerable beams will offer unprecedented flexibility. Consequently, this will require resource management strategies to be operated in high-dimensional and dynamic environments, as existing satellite operators are unaccustomed to operational flexibility and automation. Frequency assignment policies have the potential to drive constellations' performance in this new context, but are no exception to scalability and fast operation requirements. Most of existing frequency assignment methods fail to fulfill these requirements, or are unable to meet them without falling short on efficiency. In this paper we propose a new frequency assignment method that prioritizes operational requirements. We present an algorithm based on Integer linear programming that fully defines a frequency plan while respecting key system constraints such as handovers, interference, and gateway dimensioning. We can encode goals such as bandwidth maximization or power reduction and optimize plans according to such objectives. In our experiments on systems with 20 to 5,000 beams, we find this method allocates at least 100% more bandwidth and reduces power consumption by 40% compared to previous benchmarks. To ensure scalability, we also introduce an iterative approach of the formulation, which achieves substantial gains in runtime with minimal loss of performance.
It is necessary to select appropriate active parameters to ensure both the accuracy and computation efficiency before the global analysis of chemical kinetic model. This paper proposes a new method for selecting the a...
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It is necessary to select appropriate active parameters to ensure both the accuracy and computation efficiency before the global analysis of chemical kinetic model. This paper proposes a new method for selecting the active parameters on the base of the combination of sensitivity analysis and linear programming. Compared with the usual methods for selecting active parameters, such as the local sensitive analysis, the characteristics of the proposed method is preliminary visualization of the possible influence of the selected active parameters on the model outputs in the process of parameter selection, ensuring the reliability of the selected active parameters. Considering the computation efficiency, the number of selected active parameters can be controlled in a suitable size through combining with dichotomy or other screening techniques. In the study, the pre-exponential factors of the Arrhenius equations in the USC-Mech II model were considered as the candidate parameters and the uncertainties of the pre-exponential factors were set. Taking the ignition of ethylene for example, the 10 reactions that can increase the ignition time of ethylene under a wide range of conditions with equivalence ratio of 1, 0.1 similar to 1 MPa and 1000 K similar to 1500 K were successfully selected using the proposed method. Then, the 10 active parameters were tested in each condition. The results showed that the selected active parameters can make the ignition delay time close to the target for each condition, which reflects the reliability of active parameter selection.
Cislunar space domain awareness is of increasing interest to the international community as Earth-Moon traffic is projected to increase, which raises the problem of placing space-based sensors optimally in a constella...
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Cislunar space domain awareness is of increasing interest to the international community as Earth-Moon traffic is projected to increase, which raises the problem of placing space-based sensors optimally in a constellation to satisfy the space domain awareness demand in cislunar space. This demand profile can vary over space and time, making the design optimization problem challenging. This paper tackles the problem of satellite constellation design for spatio-temporally varying coverage demand by leveraging an integer linear programming formulation. The developed optimization formulation assumes the circular restricted 3-body dynamics and attempts to minimize the number of satellites required for the requested demand profile.
Thermal power generation is the main source of carbon emissions. Adopting low-carbon dispatching and developing renewable energy sources (RESs) are effective ways to reduce carbon emissions. This article constructs a ...
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Thermal power generation is the main source of carbon emissions. Adopting low-carbon dispatching and developing renewable energy sources (RESs) are effective ways to reduce carbon emissions. This article constructs a mixed-integer programming (MIP) model of low-carbon full-scenario unit commitment with nonanticipativity. To overcome the curse of dimensionality problem caused by the use of a massive number of scenarios, we employ the adjustable robust optimization approach (AROA) to reformulate the full-scenario unit commitment as a deterministic robust model. In addition, we establish the precise adjustable robust convex hull of generation constraints in a higher dimensional space and generate a relaxed linear programming (LP) formulation of the original MIP model. Then, we design a heuristic method for obtaining a near-optimal feasible solution by converting a large-scale MIP into an LP model that can be solved in polynomial time. The numerical experiments presented in this article demonstrate the effectiveness and efficiency of the proposed method.
In this article, an efficient sequential linear programming algorithm (SLP) for uncertainty analysis-based data-driven computational mechanics (UA-DDCM) is presented. By assuming that the uncertain constitutive relati...
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In this article, an efficient sequential linear programming algorithm (SLP) for uncertainty analysis-based data-driven computational mechanics (UA-DDCM) is presented. By assuming that the uncertain constitutive relationship embedded behind the prescribed data set can be characterized through a convex combination of the local data points, the upper and lower bounds of structural responses pertaining to the given data set, which are more valuable for making decisions in engineering design, can be found by solving a sequential of linear programming problems very efficiently. Numerical examples demonstrate the effectiveness of the proposed approach on sparse data set and its robustness with respect to the existence of noise and outliers in the data set.
Thanks to the applications such as Quantum Key Distribution and Distributed Quantum Computing, the deployment of quantum networks is gaining great momentum. A major component in quantum networks is repeaters, which ar...
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Thanks to the applications such as Quantum Key Distribution and Distributed Quantum Computing, the deployment of quantum networks is gaining great momentum. A major component in quantum networks is repeaters, which are essential for reducing the error rate of qubit transmission for long-distance links. However, repeaters are expensive devices, so minimizing the number of repeaters placed in a quantum network while satisfying performance requirements becomes an important problem. Existing solutions typically solve this problem optimally by formulating an Integer linear Program (ILP). However, the number of variables in their ILPs is O(n(2)), where n is the number of nodes in a network. This incurs infeasible running time when the network scale is large. To overcome this drawback, this paper proposes to solve the repeater placement problem by two steps, with each step using a linear program of a much smaller scale with O(n) variables. Although this solution is not optimal, it dramatically reduces the time complexity, making it practical for large-scale networks. Moreover, it constructs networks that have higher node connectivity than those by existing solutions, since it deploys slightly more number of repeaters into networks. Our extensive experiments on both synthetic and real-world network topologies verified our claims.
We study the problem of detecting infeasibility of large-scale linear programming problems using the primal-dual hybrid gradient (PDHG) method of Chambolle and Pock [J. Math. Imaging Vision, 40 (2011), pp. 120--145]. ...
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We study the problem of detecting infeasibility of large-scale linear programming problems using the primal-dual hybrid gradient (PDHG) method of Chambolle and Pock [J. Math. Imaging Vision, 40 (2011), pp. 120--145]. The literature on PDHG has focused chiefly on problems with at least one optimal solution. We show that when the problem is infeasible or unbounded, the iterates diverge at a controlled rate toward a well-defined ray. In turn, the direction of such a ray recovers infeasibility certificates. Based on this fact, we propose a simple way to extract approximate infeasibility certificates from the iterates of PDHG. We study three sequences that converge to certificates: the difference of iterates, the normalized iterates, and the normalized average. All of them are easy to compute and suitable for large-scale problems. We show that the normalized iterates and normalized averages achieve a convergence rate of O \bigl( k-1\bigr) . This rate is general and applies to any fixed-point iteration of a nonexpansive operator. Thus, it is a result of independent interest that goes well beyond our setting. Finally, we show that, under nondegeneracy assumptions, the iterates of PDHG identify the active set of an auxiliary feasible problem in finite time, which ensures that the difference of iterates exhibits eventual linear convergence. These results provide a theoretical justification for infeasibility detection in the newly developed linear programming solver PDLP.
The energy consumption in water distribution systems (WDSs) is significant. Improving the efficiency of pump operation can significantly reduce energy costs. However, optimal pump operation is a nonconvex mixed-intege...
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The energy consumption in water distribution systems (WDSs) is significant. Improving the efficiency of pump operation can significantly reduce energy costs. However, optimal pump operation is a nonconvex mixed-integer nonlinear programming (MINLP) problem, which can be challenging to solve. A feasible approach is to linearize the problem and convert it into a mixed-integer linear programming (MILP) problem. However, this approach introduces many auxiliary variables, which can lead to inefficiency in finding the optimal solution due to the expanded search space. To address this issue, we propose a novel method for linearization of the original MINLP problem and a strategy that can adaptively adjust the number of piecewise linearization breakpoints. By reducing the number of auxiliary variables, our approach achieved competitive computing efficiency and the ability to save energy costs, as demonstrated in two benchmark instances. Furthermore, in a realistic large-scale WDS, our approach saved 9.83% more energy costs than the genetic algorithm and achieved a gap of only 7.36% from the lower bound.(c) 2023 Elsevier B.V. All rights reserved.
This letter investigates the time-optimal trajectory generation for a six-degrees-of-freedom articulated robot moving along a given parametric path. In the generation procedure, besides the velocity, acceleration, and...
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This letter investigates the time-optimal trajectory generation for a six-degrees-of-freedom articulated robot moving along a given parametric path. In the generation procedure, besides the velocity, acceleration, and joint torque, the jerk is also constrained to enhance the smoothness of the robot's motion. Meanwhile, the trajectory generation is formulated as a convex optimization problem with a nonlinear objective function and constraints. Then, the problem is solved with a typical linear programming (LP) approach by discretizing the continuous path into many sampling points. Specifically, the time-optimal problem is formulated as maximizing the sum of the velocities at all discrete points instead of minimizing time. Moreover, the time-optimal trajectory generation with nonlinear jerk constraints is decoupled into two sub-LP problems, and the solution of the first sub-LP is employed to scale the nonlinear constraints. Finally, the proposed method is verified through robotic experiments. The results indicate that the smoothness of the generated trajectory improves significantly. Also, the trajectory planning accuracy and computational efficiency are increased by 36% and 62%, respectively.
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