Optimization technique based on learning automata

Optimization techniques are finding increasingly numerous applications in process design, in parallel to the increase of computer sophistication. The process synthesis problem can be stated as a largescale constrained optimization problem involving numerous local optima and presenting a nonlinear and nonconvex character. To solve this kind of problem, the classical optimization methods can lead to analytical and numerical difficulties. This paper describes the feasibility of an optimization technique based on learning systems which can take into consideration all the prior information concerning the process to be optimized and improve their behavior with time. This information generally occurs in a very complex analytical, empirical, or know-how form. Computer simulations related to chemical engineering problems (benzene chlorination, distillation sequence) and numerical examples are presented. The results illustrate both the performance and the implementation simplicity of this method.Nomenclature c _i penalty probability - cp precision parameter on constraints - D variation domain of the variablex - f(·) objective function - g(·) constraints - i,j indexes - k iteration number - N number of actions - P probability distribution vector - p _i ith component of the vectorP as iterationk - r number of reactors in the flowsheet - u(k) discrete value or action chosen by the algorithm at iterationk - u _i discrete value of the optimization variable in [u _min,u _max] - u _min lowest value of the optimization variable - u _max largest value of the optimization variable - Z random number - x variable for the criterion function - xp precision parameter on criterion function - W(k) performance index unit output at iterationk - ₀, ₁ reinforcement scheme parameters - _p sum of the probability distribution vector components     

Well-posed constrained optimization problems in metric spaces

Relations between different notions of well-posedness of constrained optimization problems are studied. A characterization of the class of metric spaces in which Hadamard, strong, and Levitin-Polyak well-posedness of continuous minimization problems coincide is given. It is shown that the equivalence between the original Tikhonov well-posedness and the ones above provides a new characterization of the so-called Atsuji spaces. Generalized notions of well-posedness, not requiring uniqueness of the solution, are introduced and investigated in the above spirit.     

Validation of an optimization procedure to improve low frequency characteristics of rooms

A set of experiments was carried out to validate an optimization procedure based on finite element method (FEM). The idea of the procedure, fully presented in previous edition of this journal [Zhu X, Zhu Z, Cheng J. Using optimized surface modifications to improve low frequency response in a room. Appl Acoust 2004;65:841-60], is to produce an optimal geometry modification on the wall for improving low frequency sound uniformity in small rooms. Four experimental models were set up with a scale of 1:5. One was modified according to the optimized result and the others were treated with no optimization consideration. Measured frequency responses of four rooms were compared with numerical results calculated by FEM models. The transient responses in these rooms were also measured and analyzed. The agreements between calculation and measurement are satisfactory though the discrepancies due to the uncertainty of acoustic behavior of the room boundaries remain. The optimization procedure has been supported by the results that the optimized room produces the flattest frequency response and also the most smooth energy decay within the frequency range studied. The reductions of response fluctuation have reached 4.3 dB for prediction and 2.6 dB for measurement, respectively.     

Sulfur-Containing Vinyl Monomers. XV. Kinetic Study of Radical Polymerization of Vinyl Mercaptobenzothiazole and Its Copolymerization

A kinetic study of radical polymerization of vinyl mercaptobenzothiazole (VMBT) with α,α′-azobisisobutyonitrile (AIBN) at 60°C was carried out. The rate of polymerization (R_p) was found to be expressed by the rate equation: R_p = k[AIBN]^0.5 [VMBT]^1.0, indicating that the polymerization of this monomer proceeds via an ordinary radical mechanism. The apparent activation energy for overall polymerization was calculated to be 20.9 kcal/mole. Moreover, this monomer was copolymerized with methyl methacrylate, acrylonitrile, vinyl acetate, phenyl vinyl sulfide, maleic anhydride, and fumaronitrile at 60°C. From the results obtained, the copolymerization parameters were determined and discussed.     

Elimination of bounds in optimization problems by transforming variables

The problem of minimizing a nonlinear objective function ofn variables, with continuous first and second partial derivatives, subject to nonnegativity constraints or upper and lower bounds on the variables is studied. The advisability of solving such a constrained optimization problem by making a suitable transformation of its variables in order to change the problem into one of unconstrained minimization is considered. A set of conditions which guarantees that every local minimum of the new unconstrained problem also satisfies the first-order necessary (Kuhn—Tucker) conditions for a local minimum of the original constrained problem is developed. It is shown that there are certain conditions under which the transformed objective function will maintain the convexity of the original objective function in a neighborhood of the solution. A modification of the method of transformations which moves away from extraneous stationary points is introduced and conditions under which the method generates a sequence of points which converges to the solution at a superlinear rate are given.     

Using a virtual skeleton to increase printability of topology optimized design for industry-class applications

This article broadens the scheme previously developed to associate topology optimization with additive manufacturing through the use of a virtual skeleton, consisting in solving the same physical problem with a discrete approach and then with a continuum one. This procedure for 3D designs is applied to various domain geometries, to demonstrate its pertinence on high-resolution industrial cases. An algorithm searching for the best printing direction, exploring the solid angle, is also described and validated; the surface-shaped presentation of the result allows immediate understanding of the influence of the discrete problem parameters, while its running time is much lower than a unique continuum optimization simulation, which proves the attractiveness of the method. In the three examples studied, the procedure outputs exhibit greater printability than the ones produced by traditional methods in each of the printing direction tested, albeit responsibility is left to the final user to choose his best trade-off. Furthermore, the unprintable zones are readily displayed to be either reworked or supported. Explanations about increase of convergence likelihood on discrete structures despite the geometry complexity of an industrial application are also provided and demonstrated.     

On the effects of non-linear elements in the reliability-based optimal design of stochastic dynamical systems

The aim of the present paper is to study the effects of non-linear devices on the reliability-based optimal design of structural systems subject to stochastic excitation. One-dimensional hysteretic devices are used for modelling the non-linear system behavior while non-stationary filtered white noise processes are utilized to represent the stochastic excitation. The reliability-based optimization problem is formulated as the minimization of the expected cost of the structure for a specified failure probability. Failure is assumed to occur when any one of the output states of interest exceeds in magnitude some specified threshold level within a given time duration. Failure probabilities are approximated locally in terms of the design variables during the optimization process in a parallel computing environment. The approximations are based on a local interpolation scheme and on an efficient simulation technique. Specifically, a subset simulation scheme is adopted and integrated into the proposed optimization process. The local approximations are then used to define a series of explicit approximate optimization problems. A sensitivity analysis is performed at the final design in order to evaluate its robustness with respect to design and system parameters. Numerical examples are presented in order to illustrate the effects of hysteretic devices on the design of two structural systems subject to earthquake excitation. The obtained results indicate that the non-linear devices have a significant effect on the reliability and global performance of the structural systems.     

Temperature independent length optimization of L-band EDFAs providing flat gain

In this study, single stage (SS), double-stage (DS), and gain flattened (GF) DS L-band erbium-doped fiber amplifier (EDFA) configurations are designed in order to obtain a flat gain amplifier. Temperature dependence of the mentioned configurations is also analyzed. Maximum spectral dependence of EDFA gain with respect to temperature is obtained for SS EDFA design while smaller spectral dependence of gains is obtained for both DS and GF DS L-EDFA configurations. It is observed that the maximum temperature dependence is in the range of 1570-1580 nm band for all configurations. It has also been found that for all configurations, reducing the temperature has greater effect than raising the temperature on EDFA gain. The overall results show that a temperature independent L-band configuration has not been possible. However, for some signal wavelengths, the erbium-doped fiber (EDF) lengths at which the gain is temperature independent are observed.     

CO_2/NH_3复叠系统热力分析与冷凝蒸发器冷凝温度的优化

对CO2/NH3复叠制冷系统进行合理的假设,并将与压比有关的压缩机等熵效率拟合公式引用到计算中,其结果与实验数据吻合的比较好。通过热力分析,可知系统各主要部件由不可逆而多消耗的附加功在不同的Tcas_c下对系统的影响程度是不同的。对数据进行分析并应用多元线性回归法拟合出以Te、Tc和ΔT为自变量的最优Tcas_c及相应COPmax数学表达式。