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High-performance simulation-based algorithms for an alpine ski racer's trajectory optimization in heterogeneous computer systems

Roman Dębski (2014)

International Journal of Applied Mathematics and Computer Science

Effective, simulation-based trajectory optimization algorithms adapted to heterogeneous computers are studied with reference to the problem taken from alpine ski racing (the presented solution is probably the most general one published so far). The key idea behind these algorithms is to use a grid-based discretization scheme to transform the continuous optimization problem into a search problem over a specially constructed finite graph, and then to apply dynamic programming to find an approximation...

How much do approximate derivatives hurt filter methods?

Caroline Sainvitu (2009)

RAIRO - Operations Research

In this paper, we examine the influence of approximate first and/or second derivatives on the filter-trust-region algorithm designed for solving unconstrained nonlinear optimization problems and proposed by Gould, Sainvitu and Toint in [12]. Numerical experiments carried out on small-scaled unconstrained problems from the CUTEr collection describe the effect of the use of approximate derivatives on the robustness and the efficiency of the filter-trust-region method.

Hybrid algorithms for fixed charge transportation problem

Nermin Kartli (2025)

Kybernetika

In this paper, we consider the fixed-cost transportation problem. This problem is known to be NP-hard. Therefore, various heuristic and metaheuristic approaches have been proposed to find an approximate optimal solution. In this paper, we propose three hybrid algorithms that combine the ideas of metaheuristic and heuristic approaches in different ways. Two of the proposed algorithms consist of the sequential implementation of metaheuristic and heuristic algorithms, while the third one is a full...

Hybrid flow-shop with adjustment

Jan Pelikán (2011)

Kybernetika

The subject of this paper is a flow-shop based on a case study aimed at the optimisation of ordering production jobs in mechanical engineering, in order to minimize the overall processing time, the makespan. The production jobs are processed by machines, and each job is assigned to a certain machine for technological reasons. Before processing a job, the machine has to be adjusted; there is only one adjuster who adjusts all of the machines. This problem is treated as a hybrid two-stage flow-shop:...

Hyperbolische Transformation konvexer Polyeder

Ralf Gollmer (1981)

Aplikace matematiky

Der Artikel beschäftigt sich mit einigen Eigenschaften von hyperbolischen, d. h. gebrochen-affinen, Transformationen, welche für die Bilder konvexer Polyeder bei solchen Transformationen von Bedeutung sind. Es wird eine explizite Darstellung des Bildes eines konvexen Polyeders durch Ecken und Kanten des Urbildpolyeders gewonnen, die Konvexität des Bildes und das Bild des relativen Inneren einer konvexen Menge untersucht.

Identification of optimal policies in Markov decision processes

Karel Sladký (2010)

Kybernetika

In this note we focus attention on identifying optimal policies and on elimination suboptimal policies minimizing optimality criteria in discrete-time Markov decision processes with finite state space and compact action set. We present unified approach to value iteration algorithms that enables to generate lower and upper bounds on optimal values, as well as on the current policy. Using the modified value iterations it is possible to eliminate suboptimal actions and to identify an optimal policy...

Implementación de un algoritmo primal-dual de orden superior mediante el uso de un método predictor-corrector para programación lineal.

Jordi Castro (1998)

Qüestiió

Se presenta una implementación de un algoritmo primal-dual de punto interior para la solución de problemas lineales. El algoritmo difiere de otros ya existentes (como el implementado en el sistema LoQo) en el hecho de que soluciona las denominadas "ecuaciones normales en forma primal" (LoQo soluciona el denominado "sistema aumentado") y en que realiza una clara distinción entre variables acotadas superior e inferiormente, y aquéllas sólo acotadas inferiormente. La eficiencia de la implementación...

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