We provide the first meaningful documentation and analysis of the 'Idiot' crash implemented by Forrest in Clp that aims to obtain an approximate solution to linear programming (LP) problems for warm-starting t...
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We provide the first meaningful documentation and analysis of the 'Idiot' crash implemented by Forrest in Clp that aims to obtain an approximate solution to linear programming (LP) problems for warm-starting the primal simplex method. The underlying algorithm is a penalty method with naive approximate minimization in each iteration. During initial iterations an approach similar to augmented Lagrangian is used. Later the technique corresponds closely to a classical quadratic penalty method. We discuss the extent to which it can be used to obtain fast approximate solutions of LP problems, in particular when applied to linearizations of quadratic assignment problems.
In this article, we consider a variant of the bandwidth packing problem, in which some demands need to be scheduled within given time windows. The emergence of cloud services has introduced a new challenge to the band...
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In this article, we consider a variant of the bandwidth packing problem, in which some demands need to be scheduled within given time windows. The emergence of cloud services has introduced a new challenge to the bandwidth packing problem. For example, a typical cloud service network consists of multiple data centres (DCs), and a huge amount of data must be exchanged between DCs to ensure the integrity of the data. This operation is not necessarily real-time, which allows network operators to schedule the demands over time. Motivated by a real-life network service provider in South Korea, we developed a practical heuristic algorithm for the problem. The algorithm utilises an open source linear programming solver. The performance of the proposed algorithm was assessed on the real-life telecommunication network in South Korea. The computational results showed that the proposed approach can provide near-optimal solutions within a short time.
Servo error pre-compensation and feedrate optimization are often performed independently to improve the accuracy and speed of manufacturing machines. However, this independent approach leads to unnecessary trade-offs ...
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Servo error pre-compensation and feedrate optimization are often performed independently to improve the accuracy and speed of manufacturing machines. However, this independent approach leads to unnecessary trade-offs between productivity and quality in manufacturing. This paper proposes a novel linear programming approach for combined servo error pre-compensation and feedrate optimization, subject to contour error (tolerance) and kinematic constraints. The incorporation of servo error pre-compensation into feedrate optimization allows for faster motions without violating tolerance constraints. Experiments carried out on a 3D printer and precision motion stage are respectively used to demonstrate up to 43% and 47% reduction in cycle time without compromising part quality using the proposed approach compared with the independent approach.
It is an NP-complete problem to find several figures from a given set of figures and make their sum equal to a designated figure. In this paper, the linear programming model is used to model it, and its Excel solution...
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In the process of determination of breakpoints for overcurrent relays (OCR), different sets with equal number of OCRs can be selected as minimum breakpoint set (MBPS). Therefore, determination of the most appropriate ...
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In the process of determination of breakpoints for overcurrent relays (OCR), different sets with equal number of OCRs can be selected as minimum breakpoint set (MBPS). Therefore, determination of the most appropriate MBPS is an issue which must be considered. This paper proposes a prioritization between different MBPSs based on the sum of operating times of OCRs. In this case, a set which results the minimum sum of operating times is selected as the appropriate MBPS. For this purpose, the proposed method combines two problems: determination of MBPS and coordination of OCRs, and is expressed in mixed-integer linear programming (MILP) form. Also, a modified depth-first search (DFS) algorithm is applied to determine the OCRs contained loops of studied networks. It is shown that the proposed method has the capability to be combined with previous defined expert rules in this field in order to consider the network conditions in the process of determination of optimal breakpoint set (OBPS). The proposed method has been implemented on various size networks, and the results show the effectiveness of proposed method in determining breakpoint set with the least number in first priority and minimum operating times of relays in second priority.
This paper presents models and optimization algorithms to compute the fuel-optimal energy management strategies for a parallel hybrid electric powertrain on a given driving cycle. Specifically, we first identify a mix...
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This paper presents models and optimization algorithms to compute the fuel-optimal energy management strategies for a parallel hybrid electric powertrain on a given driving cycle. Specifically, we first identify a mixed-integer model of the system, including the engine on/off signal and the gear-shift commands. Thereafter, by carefully relaxing the fuel-optimal control problem to a linear program, we devise an iterative algorithm to rapidly compute the minimum-fuel energy management strategies including the optimal gear-shift trajectory. We validate our approach by comparing its solution with the globally optimal one obtained solving the mixed-integer linear program and with the one resulting from the implementation of the optimal strategies in a high-fidelity nonlinear simulator. We showcase the effectiveness of the presented algorithm by assessing the impact of different powertrain configurations and electric motor size on the achievable fuel consumption. Our numerical results show that the proposed algorithm can assess fuel-optimal control strategies with low computational burden, and that powertrain design choices significantly affect the achievable fuel consumption of the vehicle.
This study focuses on the problem of event-triggered control for positive switched systems without/with input saturation in both continuous-time and discrete-time contexts. First, a 1-norm based event-triggering mecha...
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This study focuses on the problem of event-triggered control for positive switched systems without/with input saturation in both continuous-time and discrete-time contexts. First, a 1-norm based event-triggering mechanism is established for continuous-time positive switched systems. By means of the matrix decomposition technique, an event-triggered controller for the systems is designed by decomposing controller gain matrix into non-positive and non-negative components. Under the designed controller, the resulting closed-loop systems are positive and stable. For the systems with input saturation, the saturation term is transformed into interval form under the event-triggering condition. Then, an event-triggered controller gain matrix and a cone domain of attraction gain matrix are designed for the corresponding interval systems in terms of linear programming, respectively. Furthermore, the presented approaches are extend to discrete-time positive switched systems without/with input saturation. Compared with existing results on positive switched systems, the designed event-triggered controller can reduce sampling frequency and save resources. Finally, two numerical examples are provided to verify the effectiveness of the obtained results.
In this work, we consider adaptive linear programming (ALP) decoding of linear codes over prime fields, i.e., the finite fields F-p of size p where p is a prime, when used over a p-ary input memoryless channel. In par...
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In this work, we consider adaptive linear programming (ALP) decoding of linear codes over prime fields, i.e., the finite fields F-p of size p where p is a prime, when used over a p-ary input memoryless channel. In particular, we provide a general construction of valid inequalities (using no auxiliary variables) for the codeword polytope (or the convex hull) of the so-called constant-weight embedding of a single parity-check (SPC) code over any prime field. The construction is based on sets of vectors, called building block classes, that are assembled to form the left-hand side of an inequality according to several rules. In the case of almost doubly-symmetric valid classes we prove that the resulting inequalities are all facet-defining, while we conjecture this to be true if and only if the class is valid and symmetric. Valid symmetric classes impose certain symmetry conditions on the elements of the vectors from the class, while valid doubly-symmetric classes impose further technical symmetry conditions. For p=3, there is only a single valid symmetric class and we prove that the resulting inequalities together with the so-called simplex constraints give a complete and irredundant description of the codeword polytope of the embedded SPC code. For p>5, we show that there are additional facets beyond those from the proposed construction. As an example, for p=7, we provide additional inequalities that all define facets of the embedded codeword polytope. The resulting overall set of linear (in)equalities is conjectured to be irredundant and complete. Such sets of linear (in)equalities have not appeared in the literature before, have a strong theoretical interest, and we use them to develop an efficient (relaxed) ALP decoder for general (non-SPC) linear codes over prime fields. The key ingredient is an efficient separation algorithm based on the principle of dynamic programming. Furthermore, we construct a decoder for linear codes over arbitrary fields F-q with q=p(m) an
We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavio...
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We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavior of acellular slime mold Physarum polycephalum, and more recently considered as a method to solve LP instances. We study the convergence time of the continuous Physarum dynamics in the context of the linear programming problem, and derive a new time bound to approximate optimality that depends on the relative entropy between projected versions of the optimal point and of the initial point. The bound scales logarithmically with the LP cost coefficients and linearly with the inverse of the relative accuracy, establishing the efficiency of the dynamics for arbitrary LP instances with positive costs.
Sensitivity analysis is applied to the robust linear programming problem in this paper. The coefficients of the linear program are assumed to be perturbed in three perturbation manners within ellipsoidal sets. Our rob...
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Sensitivity analysis is applied to the robust linear programming problem in this paper. The coefficients of the linear program are assumed to be perturbed in three perturbation manners within ellipsoidal sets. Our robust sensitivity analysis is to calculate the maximal radii of the perturbation sets to keep some properties of the robust feasible set. Mathematical models are formulated for the robust sensitivity analysis problems and all models are either reformulated into linear programs or convex quadratic programs except for the bi-convex programs where more than one row of the constraint matrix is perturbed. For the bi-convex programs, we develop a binary search algorithm.
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