We formulate a truss topology optimization problem as a bilevel programming problem and solve it by means of a line search type inexact restoration algorithm. We discuss details of the implementation and show results of numerical experiments.

A lower bound for a finite-scenario chance-constrained problem is given by the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of larger subproblems. The quality of the bound depends on how the scenarios are grouped. We formulate a mixed-integer bilevel program that o...

Bilevel programming is characterized by two optimization problems located at different levels, in which the constraint region of the upper level problem is implicitly determined by the lower level problem. This paper is focused on a class of bilevel programmingwith a linear lower level problem and presents a new algorithm for solving this kind of problems by combining an evolutionary algorithm ...

This paper presents fuzzy goal programming approach for bilevel linear fractional programming problem with a single decision maker at the upper level and a single decision maker at the lower level. Here, each level has single objective function, which are fractional in nature and the system constraints are linear functions. In the proposed approach, we first construct fractional membership func...

Bilevel programming can be used to formulate many problems in the field of power systems, such as strategic bidding. However, common reformulations bilevel mixed-integer linear programs make solving hard, which impedes their implementation real-life. In this paper, we significantly improve solution speed and tractability by introducing decision trees learn active constraints lower-level problem...

In this paper, we study bilevel mixed integer programming (MIP) problem and present a novel computing scheme based on reformulations and decomposition strategy. By converting bilevel MIP into a constrained mathematical program, we present its single-level reformulations that are friendly to perform analysis and build insights. Then, we develop a decomposition algorithm based on column-and-const...

This paper is devoted to the so-called pessimistic version of bilevel programming programs. Minimization problems of this type are challenging to handle partly because the corresponding value functions are often merely upper (while not lower) semicontinuous. Employing advanced tools of variational analysis and generalized differentiation, we provide rather general frameworks ensuring the Lipsch...

In this paper, we study bilevel mixed integer programming (MIP) problem and present a novel computing scheme based on reformulations and decomposition strategy. By converting bilevel MIP into a constrained mathematical program, we present its single-level reformulations that are friendly to perform analysis and build insights. Then, we develop a decomposition algorithm based on column-and-const...