Application of reduced-set pareto-lipschitzian optimization to truss optimization

In this paper, a recently proposed global Lipschitz optimization algorithm Pareto-Lipschitzian Optimization with Reduced-set (PLOR) is further developed, investigated and applied to truss optimization problems. Partition patterns of the PLOR algorithm are similar to those of DIviding RECTangles (DIRECT), which was widely applied to different real-life problems. However here a set of all Lipschitz constants is reduced to just two: the maximal and the minimal ones. In such a way the PLOR approach is independent of any user-defined parameters and balances equally local and global search during the optimization process. An expanded list of other well-known DIRECT-type algorithms is used in investigation and experimental comparison using the standard test problems and truss optimization problems. The experimental investigation shows that the PLOR algorithm gives very competitive results to other DIRECT-type algorithms using standard test problems and performs pretty well on real truss optimization problems

BASBLib - A Library of Bilevel Test Problems

While the literature on the application of bilevel programming problems is extensive and diverse (see e.g., [1, 6, 7, 11] and references therein), there have been limited efforts to establish a systematic test library for the evaluation of the bilevel algorithms and their implementations. While there exist generators of bilevel test problems [2, 3, 4], they are limited to linear and quadratic problems. There already exist several collections of bilevel test problems, however, again, limited to special subclasses: Chapter 9 in [9] contains linear and quadratic problems (19 problems in total) The GAMS EMP Library [8] contains mainly linear and quadratic problems (33 problems in total) The test set included with BIPA [5] contains convex inner problems (22 problems in total) A test set for bilevel problems [10] containing either nonconvex inner problems or problems with a structure that causes convergence issues for algorithms (36 problems in total) MIPLIB [12] containing bilevel problems with only binary variables (57 problems in total) Bilevel optimization problem library, version 0.1 [13] containing binary bilevel problems (315 problems in total) Thus, with the introduction of BASBLib, we present an actively growing online collection of general bilevel test problems, gathered from the various sources and devoted to bilevel programming.While the literature on the application of bilevel programming problems is extensive and diverse (see e.g., [1, 6, 7, 11] and references therein), there have been limited efforts to establish a systematic test library for the evaluation of the bilevel algorithms and their implementations. While there exist generators of bilevel test problems [2, 3, 4], they are limited to linear and quadratic problems. There already exist several collections of bilevel test problems, however, again, limited to special subclasses: Chapter 9 in [9] contains linear and quadratic problems (19 problems in total) The GAMS EMP Library [8] contains mainly linear and quadratic problems (33 problems in total) The test set included with BIPA [5] contains convex inner problems (22 problems in total) A test set for bilevel problems [10] containing either nonconvex inner problems or problems with a structure that causes convergence issues for algorithms (36 problems in total) MIPLIB [12] containing bilevel problems with only binary variables (57 problems in total) Bilevel optimization problem library, version 0.1 [13] containing binary bilevel problems (315 problems in total) Thus, with the introduction of BASBLib, we present an actively growing online collection of general bilevel test problems, gathered from the various sources and devoted to bilevel programming.2.