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Branch and bound algorithm for discrete multi- level linear fractional programming problem

Arora R., Gupta K.

Operations Research and Decisions

2018

Vol. 28, No. 2

5--21

An algorithm is proposed to find an integer solution for bilevel linear fractional programming problem with discrete variables. The method develops a cut that removes the integer solutions which are not bilevel feasible. The proposed method is extended from bilevel to multilevel linear fractional programming problems with discrete variables. The solution procedure for both the algorithms is elucidated in the paper.

Bilevel limit analysis of self-hardening rod systemsunder moving load

Alawdin P., Urbańska K.

Computer Assisted Methods in Engineering and Science

2017

Vol. 24, no. 4

225--238

This paper considers results of an analysis of self-hardening systems (SHS), i.e. load-carrying systemswith improved strength and rigidity. The indicated structural features can be only found if geometricalnonlinearity is taken into consideration. Material deforming diagrams can be non-monotonic and non-smooth, and constraints can be unilateral, with gaps. Furthermore, optimisation of a mathematical modelof a rod structure as a discrete mechanical system withstanding dead (constant) and/or moving loadsis proposed. This model is formulated using bilevel mathematical programming. The limit parametersof standard loads and actions are found in the low-level optimisation. An extreme energy principle isproposed to obtain the limit parameters of these actions. Onthe upper level, the parameters of movingload are maximized. A positive influence of equilibrium or quasi-equilibrium constant load with the possiblepreloading of SHS is shown. A set of criteria for the stability of plastic yielding of structures, including non-smooth and non-convex problems of optimisation is given. The paper presents an exemplary application of the proposed method which takes into account the self-hardening effect.