Optimal Solution of MINLP Problems Using Modified Genetic Algorithm

Abstract

Many engineering and industrial constrained optimization problems can be modeled as mixed integer nonlinear programming (MINLP) problems e.g. heat and mass exchange networks, reactor-separator networks, batch plant design and scheduling, flow sheeting etc. The global optima in such problems are ill-conditioned due to the involvement of continuous and discrete variables, nonlinearities and non-convexities.This research work concerns the development of a modified GA and to apply it to find the solutions of several difficult MINLP problems. The modified GA utilizes tournament selection, SBX cross-over, polynomial mutation and variable elitism operators, along with distance based dynamic penalty with anti-distortion. The algorithm has been programmed in MATLAB. Six MINLP problems, which emerged from the optimal design of sequential multi-product batch plants, and considered as difficult ones in literature, were successfully solved. The solutions thus obtained are either comparable or better than those available in literature. The above combination of various schemes in modified GA helps in achieving faster convergence to global optimum with comparatively less violation of constraints; population size required is also less. The effect of various parameters on the convergence to global optimum has also been studied along with setting of various parameters. In future, efforts may be devoted to search proper merging strategy of quality operators for the design of a general purpose and robust GA so as to use it for a variety of engineering, specifically process engineering problems, more effectively.