Optimizing constrained non-convex NLP problems in chemical engineering field by a novel modified goal programming genetic algorithm

A novel modified goal programming genetic algorithm (MGPGA) is presented in this paper to solve constrained non-convex nonlinear programming (NLP) problems. This new method eliminates the complex equality constraints from original model and transforms them as parts of goal functions with higher priority weighting factors. At the same time, the original objective function has the lowest priority weighting factor. After all the absolute deviations of these equality constraints objectives are minimized, the final optimized solutions can be gained. Some applications in chemical engineering field are tested by this MGPGA. The proposed MGPGA demonstrates its advantages in better performances and abilities of solving non-convex NLP problems especially for those with equality constraints.

[1]  Domingos Barbosa,et al.  Optimization of reactive distillation processes with simulated annealing , 2000 .

[2]  C. Floudas,et al.  Global optimum search for nonconvex NLP and MINLP problems , 1989 .

[3]  N. Sahinidis,et al.  Global optimization of nonconvex NLPs and MINLPs with applications in process design , 1995 .

[4]  Jorge Nocedal,et al.  Numerical Experience with a Reduced Hessian Method for Large Scale Constrained Optimization , 1995, SIAM J. Optim..

[5]  I. Grossmann,et al.  Relaxation strategy for the structural optimization of process flow sheets , 1987 .

[6]  H. Ku,et al.  An evaluation of simulated annealing for batch process scheduling , 1991 .

[7]  Xingsheng Gu,et al.  Chance constrained programming models for refinery short-term crude oil scheduling problem , 2009 .

[8]  A. Charnes,et al.  Management Models and Industrial Applications of Linear Programming , 1961 .

[9]  Iiro Harjunkoski,et al.  An extended cutting plane method for a class of non-convex MINLP problems , 1998 .

[10]  Eric S. Fraga,et al.  Mass exchange network synthesis using genetic algorithms , 1998 .

[11]  Patrick D. Surry,et al.  The COMOGA Method: Constrained Optimisation by Multi-Objective Genetic Algorithms , 1997 .

[12]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[13]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[14]  Vasilios Manousiouthakis,et al.  A GLOBAL OPTIMIZATION APPROACH TO RATIONALLY CONSTRAINED RATIONAL PROGRAMMING , 1992 .

[15]  V. K. Jayaraman,et al.  Dynamic Optimization of Fed‐Batch Bioreactors Using the Ant Algorithm , 2001, Biotechnology progress.

[16]  Klaus Schittkowski,et al.  More test examples for nonlinear programming codes , 1981 .

[17]  Willi Hock,et al.  Lecture Notes in Economics and Mathematical Systems , 1981 .

[18]  Gary G. Yen,et al.  A generic framework for constrained optimization using genetic algorithms , 2005, IEEE Transactions on Evolutionary Computation.

[19]  Carlos A. Coello Coello,et al.  A simple multimembered evolution strategy to solve constrained optimization problems , 2005, IEEE Transactions on Evolutionary Computation.

[20]  V. S. Summanwar,et al.  Solution of constrained optimization problems by multi-objective genetic algorithm , 2002 .

[21]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization , 1999, Evolutionary Computation.

[22]  Yuan Xi-Gang,et al.  An improved PSO algorithm for solving non-convex NLP/MINLP problems with equality constraints , 2007 .

[23]  Linus Schrage,et al.  Modeling and Optimization With Gino , 1986 .

[24]  Venkat Venkatasubramanian,et al.  A genetic algorithmic framework for process design and optimization , 1991 .

[25]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[26]  I. Grossmann,et al.  Global optimization of nonconvex mixed-integer nonlinear programming (MINLP) problems in process synthesis , 1988 .

[27]  Ignacio E. Grossmann,et al.  A modelling and decomposition strategy for the MINLP optimization of process flowsheets , 1989 .