Pareto Optimal Solutions in Process Design Decisions using Evolutionary Multi objective Optimization

Abstract

An optimization problem involving more than one objective to be optimized simultaneously newlineis referred as multi-objective optimization (MOO) problem. Unlike single objective newlineoptimization problems, multi-objective optimization problems deal with two kinds of search spaces. These are the decision variable search space and the objective search space. Thus,while searching for the optimum in MOO problems, (1) the perturbation of variables takes place in the decision variable space, (2) the cost corresponding to the objective space is newlineevaluated, and (3) the selection from the objective space is based on the value of objective function. The objective space for complex problems is often nonlinear and they have multidimensional decision variable space. The objective functions also conflict with each other. Thus, combining these basic aspects, the multi-objective optimization problems are more complex to solve than the single objective optimization problems. In case of multi-objective optimization problems, due to the conflicting nature of objectives, the decision maker is often newlineinterested in obtaining a set of on-dominated solutions (Pareto front) instead of a single solution. Therefore evolutionary multi-objective optimization algorithms (as they result in set of solutions in a single run) are preferred for solving multi-objective optimization problems newlineover the deterministic search methods which yield a single solution in a run. Due to the newlinenonlinear nature of objective functions and multi-dimensional decision variable space with nonlinear constraints, there is a need for developing new and efficient algorithms. newlineIn the present study, an existing volutionary multi-objective optimization algorithm,i.e., multi-objective differential evolution (MODE) is improved for better performance in terms of convergence to the Pareto front and the diversity of solutions on the obtained Pareto front. Strategies of MODE, namely, MODE II and MODE III are developed.