Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization

Abstract

In this paper, a recently proposed global Lipschitz optimization algorithm PLOR (Pareto-Lipschitzian Optimization with Reduced-set) is further developed, investigated and applied to truss optimization problems. Partition patterns of the PLOR algorithm are similar to those of DIRECT (DIviding RECTangles), 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.

Optimising the Active Muon Shield for the SHiP Experiment at CERN

“…Expression 2.1 is computationally expensive since it requires estimation of f (x * ), thus in present work we replace this criterion with its common approximation called Expected Improvement [13]:…”

Truss Structure Optimization with Subset Simulation and Augmented Lagrangian Multiplier Method

“…Loading conditions acting on the 25-bar truss. This truss problem has been previously studied by using deterministic global methods [3] and many stochastic optimization methods [21,27,28,31,[34][35][36][37][38][39]41,45]. Table 5 compares the best designs found by ALSSO and the above-mentioned stochastic methods.…”

“…Table 5 compares the best designs found by ALSSO and the above-mentioned stochastic methods. Among the deterministic global methods, the Pareto-Lipschitzian Optimization with Reduced-set (PLOR) algorithm is better than the three DIRECT-type algorithms [3]. Therefore, only the optimized result obtained by PLOR is listed in Table 5.…”

“…Although these methods have been often employed to solve structural optimization problems, solutions may not be good if the optimization problem is complex, particularly when the abovementioned major difficulties are involved. An alternative could be the deterministic global optimization methods, e.g., the widely used DIRECT method [2,3], which is a branch of gradient-free methods. Recently, Kvasov and his colleagues provided a good guide on the deterministic global optimization methods [4] and carried out a comprehensive comparison study between the deterministic and stochastic global optimization methods for one-dimensional problems [5].…”

“…Recently, Kvasov and his colleagues provided a good guide on the deterministic global optimization methods [4] and carried out a comprehensive comparison study between the deterministic and stochastic global optimization methods for one-dimensional problems [5]. One of the main disadvantages of the deterministic global optimization methods is the high-dimensionality issue caused by the larger number of design variables [3] or constraints. In contrast, another branch of gradient-free methods (or stochastic optimization methods), such as Genetic Algorithms (GA) [6][7][8][9][10][11][12], Simulated Annealing (SA) [13][14][15],…”