We consider the problem of learning discounted-cost optimal control policies for unknown deterministic discrete-time systems with continuous state and action spaces. We show that a policy evaluation step of the well-k...
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ISBN:
(数字)9781728113982
ISBN:
(纸本)9781728113999
We consider the problem of learning discounted-cost optimal control policies for unknown deterministic discrete-time systems with continuous state and action spaces. We show that a policy evaluation step of the well-known policy iteration (PI) algorithm can be characterized as a solution to an infinite dimensional linear program (LP). However, when approximating such an LP with a finite dimensional program, the PI algorithm loses its nominal properties. We propose a data-driven PI scheme that ensures a certain monotonic behavior and allows for incorporation of expert knowledge on the system. A numerical example illustrates effectiveness of the proposed algorithm.
The calculation of earthwork volume and the rational formulation of earthwork allocation plan are the key links of large-scale engineering construction projects, which are of great significance for reducing the cost o...
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The calculation of earthwork volume and the rational formulation of earthwork allocation plan are the key links of large-scale engineering construction projects, which are of great significance for reducing the cost of engineering construction projects and saving cost. The traditional earthwork calculation requires not only a large amount of human resources and time, but also a large calculation error between the calculated earthwork volume and the actual. This paper mainly introduces the basic ideas based on Civil 3 D earthwork calculation method and how to solve the problem of earthwork quantity allocation by means of operational planning linear programming mathematical model, and verify the feasibility of mathematical model to solve the problem of earthwork quantity allocation through engineering examples. Finally, the plan of the earthwork allocation plan is drawn, which is convenient for the construction enterprise manager to make earthwork construction decision and formulate the earthwork construction plan in line with the actual project. The analysis shows that: Civil 3 D software is used to assist the calculation of earthwork volume with high efficiency and accurate results. It is feasible to solve the problem of earthwork allocation by using linear programming mathematical model.
It is well-understood that most eukaryotic genes contain one or more protein domains and that the domain content of a gene can change over time. This change in domain content, through domain duplications, transfers, o...
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ISBN:
(纸本)9781450357944
It is well-understood that most eukaryotic genes contain one or more protein domains and that the domain content of a gene can change over time. This change in domain content, through domain duplications, transfers, or losses, has important evolutionary and functional consequences. Recently, a powerful new reconciliation framework, called Domain-Gene-Species (DGS) reconciliation, was introduced to simultaneously model the evolution of a domain family inside one or more gene families and the evolution of those gene families inside a species tree. The underlying computational problem in DGS reconciliation is NP-hard and a heuristic algorithm is currently used to estimate optimal DGS reconciliations. However, this heuristic has several undesirable limitations. First, it offers no guarantee of optimality or near-optimality. Second, it can result in biologically unrealistic evolutionary scenarios. And third, it only computes a single DGS reconciliation even though there can be multiple optimal DGS reconciliations. In this work, we introduce the first exact algorithm for computing optimal DGS reconciliations that addresses all three limitations. Our algorithm is based on an integer linear programming formulation of the problem, which we solve iteratively by solving a series of linear programming relaxations. Our experimental results on over 3, 400 domain trees and over 7, 000 gene trees from 12 fly species shows that our new algorithmis highly scalable and that it leads to significant improvement in DGS reconciliation inference. An implementation of our exact algorithm is available freely from http://***/software/seadog/.
Following the breakthrough work of Tardos (Oper. Res.’86) in the bit-complexity model, Vavasis and Ye (Math. Prog.’96) gave the first exact algorithm for linear programming in the real model of computation with runn...
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Following the breakthrough work of Tardos (Oper. Res.’86) in the bit-complexity model, Vavasis and Ye (Math. Prog.’96) gave the first exact algorithm for linear programming in the real model of computation with running time depending only on the constraint matrix. For solving a linear program (LP) max cx, Ax = b, x ≥ 0, A ∈ Rm×n, Vavasis and Ye developed a primal-dual interior point method using a ‘layered least squares’ (LLS) step, and showed that O(n3.5 log(¯ χA + n)) iterations suffice to solve (LP) exactly, where χ¯A is a condition measure controlling the size of solutions to linear systems related to A. Monteiro and Tsuchiya (SIAM J. Optim.’03), noting that the central path is invariant under rescalings of the columns of A and c, asked whether there exists an LP algorithm depending instead on the measure χ¯∗A, defined as the minimum χ¯AD value achievable by a column rescaling AD of A, and gave strong evidence that this should be the case. We resolve this open question affirmatively. Our first main contribution is an O(m2n2 +n3) time algorithm which works on the linear matroid of A to compute a nearly optimal diagonal rescaling D satisfying χ¯AD ≤ n(¯ χ∗A)3. This algorithm also allows us to approximate the value of χ¯A up to a factor n(¯ χ∗A)2. This result is in surprising contrast to that of Tunçel (Math. Prog.’99), who showed NP-hardness for approximating χ¯A to within 2poly(rank(A)). The key insight for our algorithm is to work with ratios gi/gj of circuits of A—i.e., minimal linear dependencies Ag = 0—which allow us to approximate the value of χ¯∗A by a maximum geometric mean cycle computation in what we call the ‘circuit ratio digraph’ of A. While this resolves Monteiro and Tsuchiya’s question by appropriate preprocessing, it falls short of providing either a truly scaling invariant algorithm or an improvement upon the base LLS analysis. In this vein, as our second main contribution we develop a scaling invariant LLS algorithm, which uses and dynamically ma
Dantzig and Eaves claimed that fundamental duality theorems of linear programming were a trivial consequence of Fourier elimination. Another property of Fourier elimination is considered here, regarding the existence ...
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This paper works on a descent algorithm for continuous piecewise linear (CPWL) minimization problems. CPWL minimization is a widely applied nonlinear programming, which can be equivalently transformed into a differenc...
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ISBN:
(纸本)9781538673454
This paper works on a descent algorithm for continuous piecewise linear (CPWL) minimization problems. CPWL minimization is a widely applied nonlinear programming, which can be equivalently transformed into a difference of convex functions (DC) programming, and then, a concave optimization over a polyhedron. By utilizing the concavity of the objective function, the sequential global linear programming (SGLP) algorithm is proposed. The SGLP algorithm makes use of global information of the polyhedral feasible domain to gain superior optimizing capacity, while applies the mature linear programming technique to insure a rapid algorithm speed. In the numerical experiments, SGLP is compared with two other algorithms of DCA and DALPT, and shows its superior optimization efficiency.
In this work, we develop a model of fully fuzzy linear programming (FFLP) for the continuous and dynamic Berth Allocation and Quay Crane Assignment (BAP+QCAP). We assume that the arrival time of vessels is imprecise, ...
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ISBN:
(纸本)9783030039288;9783030039271
In this work, we develop a model of fully fuzzy linear programming (FFLP) for the continuous and dynamic Berth Allocation and Quay Crane Assignment (BAP+QCAP). We assume that the arrival time of vessels is imprecise, meaning that vessels can be late or early up to a threshold allowed. Triangular fuzzy numbers represent the imprecision of the arrivals. The model proposed has been implemented in MIP solver and evaluated to a study case composed of 10 vessels. The model allows us to obtain a fuzzy berthing plan assigning likewise an adequate number of cranes to each vessel. The plan is adaptable to incidences that may occur in the vessel arrivals.
In this letter, we develop an efficient linear programming (LP) decoding algorithm for low-density paritycheck (LDPC) codes. We first relax the maximum likelihood (ML) decoding problem to a LP problem by using check-n...
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There is a pressing need to verify robustness of classification deep neural networks (CDNNs) as they are embedded in many safety-critical applications. Existing robustness verification approaches rely on computing the...
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ISBN:
(纸本)9781728132945
There is a pressing need to verify robustness of classification deep neural networks (CDNNs) as they are embedded in many safety-critical applications. Existing robustness verification approaches rely on computing the over-approximation of the output set, and can hardly scale up to practical CDNNs, as the result of error accumulation accompanied with approximation. In this paper, we develop a novel method for robustness verification of CDNNs with sigmoid activation functions. It converts the robustness verification problem into an equivalent problem of inspecting the most suspected point in the input region which constitutes a nonlinear optimization problem. To make it amenable, by relaxing the nonlinear constraints into the linear inclusions, it is further refined as a linear programming problem. We conduct comparison experiments on a few CDNNs trained for classifying images in some state-of-the-art benchmark-s, showing our advantages of precision and scalability that enable effective verification of practical CDNNs.
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