Reliability based robust design optimization based on sensitivity and elasticity factors analysis

In this paper, a Reliability Based Robust Design Optimization (RBRDO) based on sensitivity and elasticity factors analysis is presented. In the first step, a reliability assessment is performed using the First-and Second Order Reliability Method (FORM)/ (SORM), and Monte Carlo Simulation. Furthermore, FORM method is used for reliability elasticity factors assessment, which can be carried out to determine the most influential parameters, these factors can be help to reduce the size of design variables vector in RBRDO process. The main objective of the RBRDO is to improve both reliability and design of a cylindrical gear pair under uncertainties. This approach is achieved by integration of two objectives which minimize the variance and mean values of performance function. To solve this problem a decoupled approach of Sequential Optimization and Reliability Assessment (SORA) method is implemented. The results obtained shown that a desired reliability with a robust design is progressively achieved

Evaluating the Hardness of SAT Instances Using Evolutionary Optimization Algorithms

Propositional satisfiability (SAT) solvers are deemed to be among the most efficient reasoners, which have been successfully used in a wide range of practical applications. As this contrasts the well-known NP-completeness of SAT, a number of attempts have been made in the recent past to assess the hardness of propositional formulas in conjunctive normal form (CNF). The present paper proposes a CNF formula hardness measure which is close in conceptual meaning to the one based on Backdoor set notion: in both cases some subset B of variables in a CNF formula is used to define the hardness of the formula w.r.t. this set. In contrast to the backdoor measure, the new measure does not demand the polynomial decidability of CNF formulas obtained when substituting assignments of variables from B to the original formula. To estimate this measure the paper suggests an adaptive (?,?)-approximation probabilistic algorithm. The problem of looking for the subset of variables which provides the minimal hardness value is reduced to optimization of a pseudo-Boolean black-box function. We apply evolutionary algorithms to this problem and demonstrate applicability of proposed notions and techniques to tests from several families of unsatisfiable CNF formulas

Portfolio selection problems in practice: a comparison between linear and quadratic optimization models

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices