Inventory is the basis of the normal operation of enterprises. Managing the inventory of multi-variety small batch material production well is an important basis to maintain the normal operation of manufacturing indus...
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ISBN:
(纸本)9781665464680
Inventory is the basis of the normal operation of enterprises. Managing the inventory of multi-variety small batch material production well is an important basis to maintain the normal operation of manufacturing industry, which relates to the efficiency and profit of the enterprise. This paper takes the historical data of an enterprise as an example and establishes a mathematical model to help the enterprise reasonably arrange its material production. This study also provides management suggestions for manufacturing enterprises in this field.
In this paper, an optimal control problem is considered where a target vehicle aims to reach a desired location in minimum time while avoiding a dynamic engagement zone. Using simple motion, four potential approaches ...
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ISBN:
(纸本)9781624106316
In this paper, an optimal control problem is considered where a target vehicle aims to reach a desired location in minimum time while avoiding a dynamic engagement zone. Using simple motion, four potential approaches are considered. First, the min-time strategy which ignores the engagement zone is posed and solved. Second, the min-time strategy which avoids the engagement zone entirely is considered. Third, the min-time strategy which allows for some time in the engagement zone;but, still strives to stay away from the center of the engagement zone is posed. Lastly, a fixed final-time strategy is considered, wherein the target tries to avoid the engagement zone;but, is required to arrive at the desired location at a specific time. Using a nonlinear program solver, the optimal strategies are numerically solved. From the results of the numeric solutions, the optimal strategies are discussed and comparisons are drawn.
This paper investigates an optimal bank angle generation method for two types of Mars entry guidance problems based on a predetermined bank angle structure. The Mars robotic mission, which is the first type of problem...
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ISBN:
(纸本)9781624106316
This paper investigates an optimal bank angle generation method for two types of Mars entry guidance problems based on a predetermined bank angle structure. The Mars robotic mission, which is the first type of problem, aims for the maximum terminal altitude at the end of the entry phase to secure enough time to deaccelerate an entry vehicle. The other type of problem, the human Mars mission, requires the minimum terminal velocity or energy to reduce the total amount of fuel consumed during the following powered descent phase. Several papers regarding the Mars optimal entry guidance have demonstrated that the optimal bank angle profile can be captured as a bang-bang structure, which is also the expected solution for the minimum terminal velocity problem based on the optimal control theory. By utilizing a few parameters, the bang-bang structure can easily be shaped;consequently, a parameter optimization approach turns the optimal control problem of the Mars entry guidance into a parameter searching problem, which is relatively simple to solve. Therefore, in this paper, a technique for formulating the two entry guidance problems into parameter optimization problems are proposed. To demonstrate the performance of the proposed guidance method, numerical simulations of two representative Mars entry examples are conducted. Simulation results verify that the parameter optimization approach generates the optimal entry trajectory, either maximizing or minimizing the target cost while satisfying terminal conditions and path constraints. Furthermore, the parameter optimization approach is shown to be superior in computational efficiency over a commercial nonlinear programming solver.
Any abnormal situation of the hub port may bring adverse effects such as time waste and cost increase to the shipping company. This paper solves the hub-and-spoke shipping network transportation optimization problem i...
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ISBN:
(纸本)9781665476614
Any abnormal situation of the hub port may bring adverse effects such as time waste and cost increase to the shipping company. This paper solves the hub-and-spoke shipping network transportation optimization problem in the case of partial failure and complete failure of hub ports. Partial failure means that the transshipment demand of the hub port exceeds its capacity, resulting in congestion at the hub port. Complete failure means that the hub port cannot continue to provide services for some reason. The purpose of this paper is to optimize the hub-and-spoke shipping network system to minimize the cost loss of shipping companies in the event of hub port failure. This is a mixed-integer nonlinear programming problem. The simulation example proves that the model in this paper can effectively reduce the loss of cargo flow due to the failure of the hub port and significantly improve the reliability of the shipping network.
This paper presents an automatic procedure to enhance the accuracy of the numerical solution of an optimal control problem (OCP) discretized via direct collocation at Gauss-Legendre points. First, a numerical solution...
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ISBN:
(纸本)9780791886304
This paper presents an automatic procedure to enhance the accuracy of the numerical solution of an optimal control problem (OCP) discretized via direct collocation at Gauss-Legendre points. First, a numerical solution is obtained by solving a non-linear program (NLP). Then, the method evaluates its accuracy and adaptively changes both the degree of the approximating polynomial within each mesh interval and the number of mesh intervals until a prescribed accuracy is met. The number of mesh intervals is increased for all state vector components alike, in a classical fashion. Instead, improving on state-of-the-art procedures, the degrees of the polynomials approximating the different components of the state vector are allowed to assume, in each finite element, distinct values. This explains the p(n)h definition, where n is the state dimension. Instead, in the literature, the degree is always raised to the highest order for all the state components, with a clear waste of resources. Numerical tests on three OCP problems highlight that, under the same maximum allowable error, by independently selecting the degree of the polynomial for each state, our method effectively picks lower degrees for some of the states, thus reducing the overall number of variables in the NLP. Accordingly, various advantages are brought about, the most remarkable being: (i) an increased computational efficiency for the final enhanced mesh with solution accuracy still within the specified tolerance, (ii) a reduced risk of being trapped by local minima due to the reduced NLP size.
We investigate an extension of Mixed-Integer Optimal Control Problems by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, cons...
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We investigate an extension of Mixed-Integer Optimal Control Problems by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the rounding turns out to be difficult in the presence of switching costs or switching constraints as the underlying problem is an Integer Program. We therefore reformulate the rounding problem into a shortest path problem on a parameterized family of directed acyclic graphs (DAGs). Solving the shortest path problem then allows to minimize switching costs and still maintain approximability with respect to the tunable DAG parameter theta. We provide a proof of a runtime bound on equidistant rounding grids, where the bound is linear in time discretization granularity and polynomial in theta. The efficacy of our approach is demonstrated by a comparison with an integer programming approach on a benchmark problem.
A general parametric nonlinear mathematical programming problem with an operator equality constraint and a finite number of functional inequality constraints is considered in a Hilbert space. Elements of a minimizing ...
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A general parametric nonlinear mathematical programming problem with an operator equality constraint and a finite number of functional inequality constraints is considered in a Hilbert space. Elements of a minimizing sequence for this problem are formally constructed from elements of minimizing sequences for its augmented Lagrangian with values of dual variables chosen by applying the Tikhonov stabilization method in the course of solving the corresponding modified dual problem. A sequential Kuhn-Tucker theorem in nondifferential form is proved in terms of minimizing sequences and augmented Lagrangians. The theorem is stable with respect to errors in the initial data and provides a necessary and sufficient condition on the elements of a minimizing sequence. It is shown that the structure of the augmented Lagrangian is a direct consequence of the generalized differentiability properties of the value function in the problem. The proof is based on a "nonlinear" version of the dual regularization method, which is substantiated in this paper. An example is given illustrating that the formal construction of a minimizing sequence is unstable without regularizing the solution of the modified dual problem.
Techniques of robust sensitivity design optimization involving nonlinear interior point algorithms and/or second derivatives are utilized in concert with recently developed generalized robust systems-based theoretical...
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Techniques of robust sensitivity design optimization involving nonlinear interior point algorithms and/or second derivatives are utilized in concert with recently developed generalized robust systems-based theoretical kinematic inverse/regular wedge cam procedures for producing self-centering motion applicable to three-point clamping device design about cylindrical workpieces that vary within a prescribed size range. With the use of the FindMinimum function in Wolfram Mathematica for exploring the specific optimization application to associated product designs in conjunction with computer-aided engineering validation efforts, significantly novel results are revealed related to improving force convergence and stabilization between grippers across the full diametral surface range (on the order of 15 to 10 times respectively) which is highly beneficial for clamping force and contact stress as well as dynamic characteristics including vibration among others. Essentially, the utilized systems-based quantitative model for inverse/regular wedge cam design coupled with robust sensitivity design optimization automatically develops and locates the perfect cam in connection to the overall mechanism system design layout within context of the desired self-centering function.
In this paper we study the worst-case complexity of an inexact augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded we prove a complexity bound of O(vertical...
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In this paper we study the worst-case complexity of an inexact augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded we prove a complexity bound of O(vertical bar log(epsilon)vertical bar) outer iterations for the referred algorithm to generate an epsilon-approximate KKT point for epsilon is an element of (0, 1). When the penalty parameters are unbounded we prove an outer iteration complexity bound of O(epsilon(-2/(alpha-1))), where alpha > 1 controls the rate of increase of the penalty parameters. For linearly constrained problems these bounds yield to evaluation complexity bounds of O(vertical bar log(epsilon)vertical bar(2)epsilon(-)(2)) and O(epsilon(-(2(2+)(alpha)/)(alpha-1+2))), respectively, when appropriate first-order methods (p = 1) are used to approximately solve the unconstrained subproblems at each iteration. In the case of problems having only linear equality constraints the latter bounds are improved to O(vertical bar log(epsilon)vertical bar(2)epsilon(-)((p+1)/p)) and O(epsilon(-(4/)(alpha-1+p+1/p))), respectively, when appropriate p-order methods (p >= 2) are used as inner solvers.
In this study, a mathematical programming model for using dynamically-positioned-rework stations for performing parallel tasks in assembly line balancing is proposed. We first introduce a nonlinear programming model, ...
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In this study, a mathematical programming model for using dynamically-positioned-rework stations for performing parallel tasks in assembly line balancing is proposed. We first introduce a nonlinear programming model, which is quadratic in constraints resulting from the modeling of the parallel task assignment and dynamic positioning of the rework station. We also establish some novel logical conditions in the model building process while deriving the proposed formulation. In the next step, we present appropriate variable transformations for linearization to take advantage of the algorithms for solving linear programs by noting that the quadratic expressions of the model are present as either the multiplications of binaries or binaries multiplied by continuous variables. After implementing the corresponding variable transformations, the model is transformed to a linear-mixed-integer program. A numerical example is then presented using the resulted linear model for illustration. We also perform some computational experiments using sample problems from the related literature to analyze the performance of the model.
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