A new approach based on support vector machine for solving stochastic optimization

Making decision usually occurs in the state of being uncertain. These kinds of problems often expresses in a formula as optimization problems. It is desire for decision makers to find a solution for optimization problems. Typically, solving optimization problems in uncertain environment is difficult. This paper proposes a new hybrid intelligent algorithm to solve a kind of stochastic optimization i.e. dependent chance programming (DCP) model. In order to speed up the solution process, we used support vector machine regression (SVM regression) to approximate chance functions which is the probability of a sequence of uncertain event occurs based on the training data generated by the stochastic simulation. The proposed algorithm consists of three steps: (1) generate data to estimate the objective function, (2) utilize SVM regression to reveal a trend hidden in the data (3) apply genetic algorithm (GA) based on SVM regression to obtain an estimation for the chance function. Numerical example is presented to show the ability of algorithm in terms of time-consuming and precision.

Stochastic optimization models for energy management in carbonization process of carbon fiber production

Industrial producers face the task of optimizing production process in an attempt to achieve the desired quality such as mechanical properties with the lowest energy consumption. In industrial carbon fiber production, the fibers are processed in bundles containing (batches) several thousand filaments and consequently the energy optimization will be a stochastic process as it involves uncertainty, imprecision or randomness. This paper presents a stochastic optimization model to reduce energy consumption a given range of desired mechanical properties. Several processing condition sets are developed and for each set of conditions, 50 samples of fiber are analyzed for their tensile strength and modulus. The energy consumption during production of the samples is carefully monitored on the processing equipment. Then, five standard distribution functions are examined to determine those which can best describe the distribution of mechanical properties of filaments. To verify the distribution goodness of fit and correlation statistics, the Kolmogorov-Smirnov test is used. In order to estimate the selected distribution (Weibull) parameters, the maximum likelihood, least square and genetic algorithm methods are compared. An array of factors including the sample size, the confidence level, and relative error of estimated parameters are used for evaluating the tensile strength and modulus properties. The energy consumption and N2 gas cost are modeled by Convex Hull method. Finally, in order to optimize the carbon fiber production quality and its energy consumption and total cost, mixed integer linear programming is utilized. The results show that using the stochastic optimization models, we are able to predict the production quality in a given range and minimize the energy consumption of its industrial process.