Determination of the region sizes for LJ optimization procedure

To improve the rate of convergence of the direct search optimization proced ure using random numbers and search region contraction as introduced by LUU S AND JAAKOLA [1], called LJ optimization procedure, a multi-pass method is suggested, where the region size for each variable at the beginning of eac h pass after the first one is determined from the extent of the variation o f the variable during the pass. Computational experience with several typic al chemical engineering systems shows that such a procedure enables the opt imum to be determined more efficiently than arbitrarily choosing the legion sizes through some preliminary runs, or by some intuitive approach. For il lustration and evaluation of the approach, three examples are chosen. The f irst example involves an alkylation process consisting of ten variables and seven equality constraints. The second example involves model reduction, a nd the third example is a non-linear nonseparable optimization problem invo lving 300 variables. In each case, the method was found to be robust, and t he optimum could be obtained considerably faster with this newly proposed m ethod of region size: determination.