873 research outputs found

    Learning to Pivot as a Smart Expert

    Full text link
    Linear programming has been practically solved mainly by simplex and interior point methods. Compared with the weakly polynomial complexity obtained by the interior point methods, the existence of strongly polynomial bounds for the length of the pivot path generated by the simplex methods remains a mystery. In this paper, we propose two novel pivot experts that leverage both global and local information of the linear programming instances for the primal simplex method and show their excellent performance numerically. The experts can be regarded as a benchmark to evaluate the performance of classical pivot rules, although they are hard to directly implement. To tackle this challenge, we employ a graph convolutional neural network model, trained via imitation learning, to mimic the behavior of the pivot expert. Our pivot rule, learned empirically, displays a significant advantage over conventional methods in various linear programming problems, as demonstrated through a series of rigorous experiments

    Experimental Geometry Optimization Techniques for Multi-Element Airfoils

    Get PDF
    A study is reported on geometry optimization techniques for high-lift airfoils. A modern three-element airfoil model with a remotely actuated flap was designed, tested, and used in wind tunnel experiments to investigate optimum flap positioning based on lift. All the results presented were obtained in the Old Dominion University low-speed wind tunnel. Detailed results for lift coefficient versus flap vertical and horizontal position are presented for two airfoil angles-of-attack: 8 and 14 degrees. Three automated optimization simulations, the method of steepest ascent and two variants of the sequential simplex method, were demonstrated using experimental data. An on-line optimizer was demonstrated with the wind tunnel model which automatically seeks the optimum lift as a function of flap position. Hysteresis in lift as a function of flap position was discovered when tests were conducted with continuous flow conditions. It was shown that optimum lift coefficients determined using continuous flow conditions exist over an extended range of flap positions when compared to those determined using traditional intermittent conditions

    A unified worst case for classical simplex and policy iteration pivot rules

    Full text link
    We construct a family of Markov decision processes for which the policy iteration algorithm needs an exponential number of improving switches with Dantzig's rule, with Bland's rule, and with the Largest Increase pivot rule. This immediately translates to a family of linear programs for which the simplex algorithm needs an exponential number of pivot steps with the same three pivot rules. Our results yield a unified construction that simultaneously reproduces well-known lower bounds for these classical pivot rules, and we are able to infer that any (deterministic or randomized) combination of them cannot avoid an exponential worst-case behavior. Regarding the policy iteration algorithm, pivot rules typically switch multiple edges simultaneously and our lower bound for Dantzig's rule and the Largest Increase rule, which perform only single switches, seem novel. Regarding the simplex algorithm, the individual lower bounds were previously obtained separately via deformed hypercube constructions. In contrast to previous bounds for the simplex algorithm via Markov decision processes, our rigorous analysis is reasonably concise
    • …
    corecore