Information-guided genetic algorithm approach to the solution of MINLP problems

Stochastic methods are widely used for the solution of optimization problems, because of the simplicities involved in algebraic manipulation of each particular problem. In practice, the feasible region of an engineering mixed-integer-nonlinear-programming (MINLP) problem is basically nonconvex and even rugged. Genetic algorithms (GAs) usually suffer from prematurity problems and require many different runs from different starting points, to avoid the trap of local minima. On the other hand, GAs may provide some possible local minima that have physical meanings for the engineers in its solution results. In this work, a novel genetic algorithmcalled a information-guided genetic algorithm (IGA)is developed to solve the general MINLP problems. This novel approach proposes the implementation of information theory to the mutation stage of GAs to refresh the premature population. Moreover, the detection index of prematurity of the population is based on the distances among the individuals. A local search is performed to improve the efficiency of this approach in every defined period. In this work, no initial feasible point or any problem transformation is required; thus, no additional variables and constraints are needed. On the other hand, in addition to the possible global optimum, some more local optimal solutions that may be interesting to the engineer were also found. Five examples, i.e., three multiproduct batch plant problems with different sizes, an optimization problem of regulatory metabolic reaction network, and a three-level pump network optimization problem are solved using this novel approach. The simulation results show that that the rate of convergence and discovery rate of the global minimum are substantially improved from the traditional GA.