Topic
Piecewise linear function
About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.
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TL;DR: Prefcalc as mentioned in this paper is a methodology for multi-objective linear programming (MOLP) problems that relies on three steps: (1) Generation of a subset of feasible efficient solutions (from 10 to 50) as representative as possible of the efficient set.
65 citations
TL;DR: This paper faces the problem of finding the optimal trade‐off between the number of arrivals and departures in order to reduce a delay function of all the flights, using a more realistic representation of the airport capacity, i.e. the capacity envelope.
Abstract: In most of the optimization models developed to manage airports operations, arrivals and departures capacities are treated as independent variables: that is the number of flights allowed to take off does not affect the number of landings in any unit of time, and vice versa. This assumption is seldom verified in most of the congested airports, where many interactions between arrivals and departures take place. In this paper, we face the problem of finding the optimal trade‐off between the number of arrivals and departures in order to reduce a delay function of all the flights, using a more realistic representation of the airport capacity, i.e. the capacity envelope. Under the assumption of piecewise linear convex capacity envelopes and of the exact interpolation of all the Pareto‐optimal operational points, we show that the problem can be formulated as a linear programming model. For general airport capacity envelopes, we propose a dynamic programming formulation with a corresponding backward solution algorithm, which is robust, easy to implement and has a linear computational complexity. The algorithm performances are evaluated on different realistic scenarios, and the optimal solutions are compared with those computed by a greedy algorithm, which can be seen as an approximation of the current decision procedures. The percentage deviation of the cost of these two solutions ranges from 3.98 to 35.64%
65 citations
TL;DR: In this article, a new method is presented for locating periodic steady-state response of piecewise linear dynamical systems with time periodic coefficients, which combines elements from approaches applied to piece-wise linear systems with constant coefficients as well as from classical perturbation techniques applied to systems with varying coefficients.
Abstract: A new method is presented for locating periodic steady-state response of piecewise linear dynamical systems with time periodic coefficients. As an example mechanical model, a gear-pair system with backlash is examined, under the action of a constant torque. Originally, some useful insight is gained on the dynamics by investigating the response of a weakly non-linear Mathieu–Duffing oscillator, subjected to a constant external load. The information obtained is then used in seeking approximate periodic solutions of the piecewise linear system. These solutions are determined by developing a new analytical method, which combines elements from approaches applied to piecewise linear systems with constant coefficients as well as from classical perturbation techniques applied to systems with time varying coefficients. The existence analysis is complemented by appropriate stability analyses, for all the possible types of the located periodic motions. In the second part of the work, this analysis is employed and numerical results are obtained. Namely, a series of typical response diagrams is first presented, illustrating the effect of the variable stiffness, the damping and the constant load parameters on the gear-pair response. Moreover, results obtained by direct integration of the equation of motion are finally presented, showing that the system examined can also exhibit more complicated or irregular dynamics.
65 citations
Abstract: We consider the identification of Hammerstein/non-linear feedback models by approximating internal non-linearities using piecewise linear static maps. The resulting method utilizes a point-slope parameterization that leads to a computationally tractable optimization problem. The computational appeal of this technique is derived from the fact that the method only requires a matrix inverse and singular value decomposition. Furthermore, the identification method simultaneously identifies the linear dynamic and static non-linear blocks without requiring prior assumptions on the form of the static non-linearity.
65 citations
Proceedings Article•
13 Jul 2008TL;DR: An exact dynamic programming update for constrained partially observable Markov decision processes (CPOMDPs) relies on implicit enumeration of the vectors in the piecewise linear value function, and pruning operations to obtain a minimal representation of the updated value function.
Abstract: We describe an exact dynamic programming update for constrained partially observable Markov decision processes (CPOMDPs). State-of-the-art exact solution of unconstrained POMDPs relies on implicit enumeration of the vectors in the piecewise linear value function, and pruning operations to obtain a minimal representation of the updated value function. In dynamic programming for CPOMDPs, each vector takes two valuations, one with respect to the objective function and another with respect to the constraint function. The dynamic programming update consists of finding, for each belief state, the vector that has the best objective function valuation while still satisfying the constraint function. Whereas the pruning operation in an unconstrained POMDP requires solution of a linear program, the pruning operation for CPOMDPs requires solution of a mixed integer linear program.
65 citations