Mixed-Discrete Nonlinear Optimization With Simulated Annealing

Modelling the Vapor-Liquid Equilibrium of Polymer Solutions Using a Cubic Equation of State

“…[30] Indeed, the SAA allows downhill and uphill (acceptance of worse solutions) movements throughout the domain. These uphill movements, which are strongly controlled, allow the algorithm to jump out from local optimal regions.…”

“…Dekkers and Aarts [29] and Zhang and Wang [30] reported that the ratio between the accepted and rejected points should be close to unity, which means that the algorithm is capable of jumping out from local minimum regions and futhermore, in regions near the equilibrium point (in the neighborhood of the global minimum) all the movements might be very small.…”

“…The objetive is to find out a solution in the solution set for which the objective function (Gibbs free energy) achieves its smallest value, the global minimum. A reasonable review of global optimization methods, and specially of the simulated annealing algorithm, which was chosen for this work, was described by Dekkers and Aarts, [29] Zhang and Wang, [30] McDonald and Floudas, [31] Kirkpatrick et al, [32] and Eglese. [33] The simulated annealing algorithm was selected due to its trustworthiness and also because it seems more sensitive than other numerical optimization methods in relation to the natural constraints and the boundary conditions.…”

Discrete Differential Evolution for Mixed Discrete Non-Linear Problems

“…The threshold  is set Fig. 6 shows a simplified configuration of a compound gear train that has been investigated by many researchers [23][24][25][26][27][28]. It is desired to produce a gear ratio, or velocity ratio, as close as possible to 1/6.931.…”

“…Table 3 Comparison of results for the pressure vessel problem. (23) Zhang (25) Wu (26) Lin (27) Guo (28) Proposed Method He (30) Kitayama (12) …”