Robust Multi-Objective Genetic Algorithm (RMOGA) with Online Approximation under Interval Uncertainty

The optimization of chemical processes is usually multi-objective, constrained and has uncertainty in the process inputs, variables and/or parameters. This uncertainty can produce undesirable variations in the process outputs, i.e., in the objective and/or constraint functions. The traditional multi-objective genetic algorithm (MOGA) assumes that all inputs are deterministic. However, optimal solutions obtained from MOGA can be sensitive to input uncertainty and, consequently, the solutions may be degraded. The goal in robust MOGA (RMOGA) is to obtain optimal solutions that are also relatively insensitive to uncertainty. In this chapter, two approaches to RMOGA, nested and sequential, are presented. In both approaches, a measure of robustness is considered using the worst-case analysis, which assumes that the uncertainty in inputs is expressed by an interval with known lower and upper bounds. The main difference between the nested and sequential RMOGA is that, in the nested approach, an upper level problem identifies and improves candidate points, while a lower-level subproblem evaluates robustness of the candidate points; on the other hand, in the sequential approach, a multi-objective optimization problem is first solved to obtain optimal solutions, and then the robustness of each optimal solution is evaluated. Both nested and sequential RMOGA approaches can be computationally costly. To reduce the computational cost, an online approximation assisted method is used in both approaches. The purpose of the approximation is to replace a computationally intensive simulation for objective and/or constraint functions with a computationally inexpensive surrogate model; the accuracy of the approximation is adaptively improved as the solutions are reached. Two examples, one numerical and the other based on petroleum refinery, are used to demonstrate and compare the applicability of the two RMOGA approaches.