A Hybrid Global Optimization Approach for Solving MINLP Models in Product Design

Abstract This paper presents a hybrid global optimization approach for solving product design (specifically solvent design) problems modeled by mixed integer nonlinear programming (MINLP). The strategy incorporates a variant of the Outer Approximation mathematical programming algorithm and a soft computing global optimization approach (namely simulated annealing). The suggested approach is not provably globally optimal. However, computational experience with benchmark examples and solvent design MINLP models indicate strongly that the approach gives near globally optimal solutions.

[1]  Manish Sinha,et al.  Environmentally benign solvent design by global optimization , 1999 .

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

[3]  Sandro Macchietto,et al.  Computer aided molecular design: a novel method for optimal solvent selection , 1993 .

[4]  Efstratios N. Pistikopoulos,et al.  Optimal solvent design for environmental impact minimization , 1998 .

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

[6]  T. Westerlund,et al.  Convexification of different classes of non-convex MINLP problems , 1999 .

[7]  Rafiqul Gani,et al.  Design of environmentally benign processes: integration of solvent design and separation process synthesis , 1999 .

[8]  I. Grossmann,et al.  A combined penalty function and outer-approximation method for MINLP optimization : applications to distillation column design , 1989 .

[9]  Yushan Zhu,et al.  A reliable prediction of the global phase stability for liquid-liquid equilibrium through the simulated annealing algorithm: Application to NRTL and UNIQUAC equations , 1999 .

[10]  M. F. Cardoso,et al.  A simulated annealing approach to the solution of minlp problems , 1997 .

[11]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[12]  Ignacio E. Grossmann,et al.  An outer-approximation algorithm for a class of mixed-integer nonlinear programs , 1986, Math. Program..

[13]  Efstratios N. Pistikopoulos,et al.  Optimal design of solvent blends for environmental impact minimization , 1999 .

[14]  A. M. Geoffrion Generalized Benders decomposition , 1972 .

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

[16]  Emile H. L. Aarts,et al.  Global optimization and simulated annealing , 1991, Math. Program..

[17]  Esteban A. Brignole,et al.  Computer‐aided molecular design of solvents for separation processes , 1994 .

[18]  Luke E. K. Achenie,et al.  Designing environmentally safe refrigerants using mathematical programming , 1996 .

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

[20]  Luke E. K. Achenie,et al.  Novel Mathematical Programming Model for Computer Aided Molecular Design , 1996 .

[21]  Lino A. Costa,et al.  Evolutionary algorithms approach to the solution of mixed integer non-linear programming problems , 2001 .